Are space and time quantized quantities?

rpt

Does assuming time and space are quantized quantities make predictions of quantum physics more accurate?
I have heard about the "Planks time" but do not know whether its is really a concept in quantum theories.

andrebourbaki

No.

To begin with, QM does not proceed by starting with quantities and then quantising them.
So one should avoid using the phrase you use, except when it can do no harm.

When an observable has a discrete spectrum, then the result of measuring it can only take on those discrete values, and so it looks like something has been 'quantised'. But this is not the explanation for why charge is quantised, since charge is not an observable, it is not something that is measured in the sense of measurement in QM axioms. Spatial position is, but the eigenvalues are continuous, so it does not look like something that has been quantised even though it is a quantum observable.

I do not believe in trying to artificially quantise time or space, it would be a revolution in Physics to do so. The consequences would be unpredictable, and so far I have not heard of any good consequences at all.

rpt

I raised this issue not because I believed space and time are quantized but I thought that the subsequent discussion would clarify the real nature of space and time.

Strangely I have the feeling that time and space are not real but exists only in the mind of a conscious observer.

fleem

IMO neither space nor time have ever been observed directly. They are axioms upon which we based the classical behavior of matter. They are so ingrained in our classical minds that we insist they must also be axioms for a deeper understanding of particle interactions. They have to do with the "average" (large scale) interaction density (number of states) among a group of particles relative to that of the universe. Could it be that two nearby co-moving macroscopic clocks tick at the same rate on the average because they are both experiencing the same average interaction density with the rest of the universe, and there is no time "field" that exists regardless of the presence of the clocks? If you isolate a group of particles then their time and space can vary notably from the ambient. Perhaps that's why, for example, a decay rate is random (because tiny objects interact less with the rest of the universe, adding granularity) and why decay rate has less meaning when you consider what's going on within that tiny system without regard to the rest of the universe--it is the interactions with the rest of the universe that regulates the "rate" that an otherwise isolated system cycles through its various states. Without those interactions with the rest of the universe, it is welcome to cycle many states between one interaction with the universe and the next--as long as doing so obeys certain laws. I admit there are still questions, like why does a photon apparently follow a geodesic when it doesn't interact with its environment while it is in transit (i.e. maybe what we've been calling photons are really simply local interactions in a reference frame moving at c), but I suspect those answers will come.

A. Neumaier

In QED (the most accurate theory we have), space and time are continuous parameters ranging in R^4, coordinatizing the fields that contain the physical information. These coordinates are not quantized in any sense, and have no absolute meaning since changing them by means of a Poincare transformation (a combination of translation + rotation + Lorentz boost) does not alter the physics.

But the resulting affine pseudo-metric space, called Minkowski space, is absolute and meaningful (as long as we don't consider quantum gravity, which would change this picture). This means that the Minkowski distance between space-time points that can be defined in terms of the fields can (in principle) be determined objectively. Such space-time points include all positions of stars, which are local maxima of field intensities in the backward light cone of an observer at a particular time, singled out objectively by appropriate observables. (Example: The observer might be the Mount Palomar observatory, one year after it was built. This may be encoded in terms of QED using known physics.)

tom.stoer

There are two ways to introduce "quantized" space and time.

1) Discretization, assumptions, ... as calculational tricks, mathematical re-formulation, ..., w/o any physical justification
2) Discrete spectrum of observables: refer e.g. to rotational symmetry where a continuous symmetry (rotational invariance) 'produces' a discrete spectrum for angular momentum both mathematically and hysically (you can measure it ;-)

In quantum gravity (we do not have a final theory) we are not really there: there are indications for discreteness e.g. in Loop Quantum Gravity - the area operator has a discrete spectrum - but unfortunately this area operator is no (Dirac) observable, so you can't measure it (neither in principal nor in practice).

That means that it may very well be that we can use continuous/discrete mathematical entities to construct a theory mathematically, but that this does not mean that physical obervables are continuous/discrete automatically.

To bring it to the point: yes, it's a concept ...

sterss

it is welcome to cycle many states between one interaction with the universe and the next--as long as doing so obeys certain laws.

rpt

Whether it is Minkowski space or otherwise, the space to have a precise quantifiable meaning, we should be able to accurately define the meaning of distance. In doing so we have to use the abstract mathematical idea called "point" which does not really exist.
Point is only an abstract mathematical idea in the mind. Without reconciling this issue we accept that the space really exist. This is the main problem I have in understanding space.

A. Neumaier

Physics is not about exact points, distances or anything else, but about approximations valid at the level of measurement accuracies.

It is enough to have an approximate notion of point and distance, and to verify that these approximately satisfy the properties demanded from the ideal points and distances the theory speaks about. And this is amply satisfied.

A far away star is an excellent example of an approximate point - it appears pointlike in all our experiments.

According to established physics, a real observer is a macroscopic
object with the capacity to record information. The recording process
is described by means of irreversible thermodynamics. In particular,
observers can be described to good accuracy classically, in terms of
their associated macroscopic observables. These are expectation values
of corresponding aggregated microscopic variables, behaving essentially
classically according to Ehrenfest's theorem. Large objects such as
stars can similarly be described by their associated macroscopic
observables. The position of an observer and the objects it observes changes
in time, defining their trajectories = world lines (apart from a global Poincare
transformation). This change is (on the macroscopic description level
appropriate for observers) continuous. (The world lines get fuzzy as one
focusses on smaller and smaller details, and become undetermined in
principle when the scale is reached where quantum effects dominate.
Indeed, the Heisenberg uncertainty principle forbids well-defined
trajectories of arbitrary accuracy.)

Suppose that the observer is the Mount Palomar observatory at a given time t. The observer's past light cone cuts out from 4-space a 3-dimensional manifold, which intersects the world lines of the objects observed at definite points (within the accuracy of the whole construction) - the positions x(t) of the visible stars at time t. This is indeed consistent with how astronomical positions are determined.

All this has a precise quantifiable meaning, to the accuracy needed to compare with experiments.

rpt

Thanks Neumaier,

What I understand from your reply is that the ideal of 'point' in the space really exists, and a distance can be measured with a given accuracy subjected to limitations imposed by uncertainty principle. It is a matter of measurement accuracy.
Furthermore, if world lines become undetermined at the scales where quantum effects dominate, is it because space is not fundamental in nature or it again a limitation on measurement process.
Please correct me if I misinterpreted what you said.

A. Neumaier

The ideal points exist in the sense that they must be presupposed to be able to organize available data
in a sensible way; without an underlying space no meaningful concept of distance or coordinates.
Space is fundamental.

World lines cease to exist not because the nature of space changes but because the concept of a world line is not fundamental: The pointlikeness of the objects is the property that fails dramatically at small scales; and fuzzy points only have fuzzy trajectories.

Already in classical relativity, there is no good concept of interacting point particles with world lines, and one needs a field theory to specify the properties of tiny lumps of matter. Quantum theory just adds more color to this.

rpt

Thanks Neumaier,

You said that "Space is fundamental"
Is this an axiom?

You said,
"The pointlikeness of the objects is the property that fails dramatically at small scales; and fuzzy points only have fuzzy trajectories".

Does this mean that space becomes fuzzy at smaller scales or there is a measurement limitation at these scales and therefore points become fuzzy.?

Mazulu

One second is defined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom" (http://en.wikipedia.org/wiki/Second).

Can the number of cycles counted, from caesium 133 atoms, be considered a standard of both time and distance (between points in space-time) that is reliable even in general relativity?

Disregard.

tom.stoer

I would rather call it a belief.

From Wikipedia:

"In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. In other words, an axiom is a logical statement that is assumed to be true. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths."

There are research directions in quantum gravity and related topics which do not take the truth of the statement "Space is fundamental" for granted.

rpt

Thanks tom.stoer,

It would be really interesting to know how the concept of space is addressed in the research directions where space is not considered fundamental. Hope it does not involve lot of maths.

rpt

If we accept that point in space is something that really exists, space is nothing but infinite number of singularities (point in the space is a singularity).

If space becomes fuzzy at scales where quantum effects dominates due to some other reason than measurement limitations, space is not fundamental.

andrebourbaki

A point by itself is not a singularity. It is always some function on the surrounding space that has a singularity at that point...(or, of course, doesn't). We talk quickly and sloppily of a point as being a singularity and this may have misled you but if you look at the context, there is always some function there. For example, the pointy part of a cone is a singularity but only because the transition functions of the coordinate charts of the cone have an infinity or lack a derivative or are undefined at that point. Or in GR, some physical quantity like gravity becomes infinte at that point. Or the Coulomb potential at the centre of the electron, or something like that.

Also, the kind of approximation or idealisation referred to by several here (correctly) is the same as in classical physics....it is not the new kind of uncertainty that arises in Quantum Mechanics. Space and time are not quantum observables just because they can never be measured with certainty and absolute accuracy: if it is merely classical style uncertainty, they remain classical style coordinates and "point" remains the kind of object it always was for, say, Newton. (The exact natrue of such an object or concept is philosophy, not physics.) But if someone discovered a quantum-style uncertainty about this measurement of location and duration (*in themselves*, rather than what we really do, which is "location of a particle's collision with the detector"), that would be very different and would then suggest they needed to be quantised because they were observables.