Is Quantizing Spacetime Possible According to the 2nd Law of Thermodynamics?

[Antonio Lao]

If space is restricted to just one dimension, can this 1-dim space together with the 1-dim time be subjected to a process of quantization?

 

[AWolf]

Planck's constant.

 

[AKG]

Why would space be restricted to one dimension? And no, I don't think it can be quantized. The Planck Length refers to something like the smallest space you can contain a particle in, any smaller and it would explode or something. I suppose you should look this up, because I obviously don't know too much with regards to this. Planck Time is said to be the smallest unit of meaningful time, I don't know if this means that half a Planck Time cannot exist though.

 

[Mike2]

If space is restricted to just one dimension, can this 1-dim space together with the 1-dim time be subjected to a process of quantization?

How can any kind of information travel from one region of space to another through gaps in space that represent no medium at all. It cannot. Therefore, space is connected and continuous.

 

[Antonio Lao]

How can any kind of information travel from one region of space...

I supposed you meant that space is static. But if space is dynamic, then information can move from point to point.

 

[Antonio Lao]

Quantization of spacetime resulted the square of energy given by the following vector cross and dot products.

[tex] E^2 = \psi_i \times \phi_i \cdot \psi_j \times \phi_j[/tex]

 

[christian_dude_27]

...anything is possible. if you could find out the basics for quantizing spacetime, then yea, it can be.

 

[AWolf]

Why would space be restricted to one dimension? And no, I don't think it can be quantized. The Planck Length refers to something like the smallest space you can contain a particle in, any smaller and it would explode or something. I suppose you should look this up, because I obviously don't know too much with regards to this. Planck Time is said to be the smallest unit of meaningful time, I don't know if this means that half a Planck Time cannot exist though.

In 1900, Max Planck was working on the problem of how the radiation an object emits is related to its temperature. He came up with a formula that agreed very closely with experimental data, but the formula only made sense if he assumed that the energy of a vibrating molecule was quantized - in other words, it could only take on certain values. The energy would have to be proportional to the frequency of vibration, and it seemed to come in little "chunks" of the frequency multiplied by a certain constant - Planck's constant.

One of the many quantum theories - Loop Quantum Gravity - refers to Space as being granular, the size being based on Planck's Constant.

Planck's Time is referred to as the smallest unit of measurable time because any smaller and it becomes meaningless, mainly because all measurable events happen at multiples of Planck Time.

 

[Antonio Lao]

Planck time ([itex]10^{-43}[/itex] sec) is more formally defined as the time it takes light to travel the distance of a Planck length ([itex] 10^{-33}[/itex] cm).

 

[kurious]

As the gravitational force between galaxies weakens with expansion of the universe,
dark energy mass increases.If this mass increase comes from gravitons losing energy to dark energy,then perhaps gluons do also.Gluons emit gluons - quanta of energy,
and presumably these can become dark energy mass.Therefore dark energy can increase in mass in a quantum way.The amount of Dark energy is related to the increase of space with increasing time, so space-time is quantised.

 

[Antonio Lao]

As the gravitational force between galaxies weakens with expansion of the universe,...

The weakening of gravity between galaxies (ordinary matter) does not affect the amount of dark energy. What affect the dark energy is the change of dark matter. This kind of matter does not emit light, it cannot be seen, therefore dark and still it can exert gravity causing the discovered anomalous motions of stars in a galaxy.

Dark energy does contribute to the expansion of the universe because it's more than just energy. Dark energy possesses intrinsic pressure (force per unit area). This pressure can become negative, positive or zero. When it's positive, it give rise to attractive gravity. When it's negative, it give rise to repulsive gravity or antigravity. When it's zero, the gravity force is also zero and experimental mass is zero.

The gluons are quanta of the strong nuclear force. They are messenger particles of the binding force. This strong force is attractive because the color charges are attractive charges. Gluons do not affect the change of dark matter or dark energy. The quanta of dark matter or dark energy are similar to the Higgs bosons or inflatons (in contrast, the quanta of ordinary matter are the gravitons). These are still not settled by theorists. These are RIPs (research in progress).

 

[Mike2]

One of the many quantum theories - Loop Quantum Gravity - refers to Space as being granular, the size being based on Planck's Constant.

What is this silliness of quantizing space-time? Quantization is acheived through the eigenvalues of a differential equation of continuous variables. So there must be some background of continuous variables.

 

[sol2]

What is this silliness of quantizing space-time? Quantization is acheived through the eigenvalues of a differential equation of continuous variables. So there must be some background of continuous variables.

After reading Three Roads to Quantum Grvaity by Lee Smolin, this question ( discreteness and continuity), becomes really interesting in terms of the background.

Now you have two choices. Marcus helps to elucidate this question, as it is one of deep concern. I have been trying to concretize this in conceptualization.

Background

Again the logic here of Venn diagrams is troublesome, in that we have to answer this question. This also points us to the question of the universe and its formation.

Self Adjoint in Mkaku today, speaks to this in energy conservation, and for me, this lays the foundation of the Eykroptic universe, versus the Big Bang.

The dynamical nature of this one scenario, recognizes the dynamical nature that this universe is going through, and does not define some beginning.

Taken aside http://superstringtheory.com/forum/geomboard/messages2/117.html has been a issue along this line I tried to understand and the issue was rebuked here by logical explanation in the following linked responses. Is this part of our troubles in acceptance of the Eykroptic scenario?

 

[Antonio Lao]

Using the concept of set, the continuous background of the universe is the null set. In this set all distances are zero. The space dimension is zero. There is no time dimension in this background. This is the missing dimension (background dimension) discovered by M-theory.

 

[AWolf]

This is the missing dimension (background dimension) discovered by M-theory.

Theorized by M-theory, not discovered.

Using the concept of set, the continuous background of the universe is the null set.

The NULL set would define the universe prior to the Big Bang - albiet apart from the pythagorian point/ origin of the Big Bang, which would be the !NULL set.

As a consequence of the Big Bang, the NULL set would no longer be ( NULL + !NULL = !NULL ).

The only way any part of the post Big Bang Universe could be viewed as NULL, including the background, would be if you ignored everything else.

The background only becomes the background when there is a foreground, so it cannot be viewed in isolation, or as a NULL.

 

[Antonio Lao]

The background only becomes the background when there is a foreground, so it cannot be viewed in isolation, or as a NULL.

What you said make sense. This lead me to wonder if this foreground/background can explain why the the N-pole and S-pole of magnetism cannot be isolated into monopoles.

 

[AWolf]

Assuming magnetism is a flow by way of alignment with an structure, you have a flow from right to left or from down to up giving you the two poles.

To isolate them into monopoles, you would have to isolate the from right from the to left. Now if something is flowing to the left, surely it must have come from the right.

 

[Antonio Lao]

The left-right symmetry is just part of eight symmetric properties of a principle of directional invariance given by top-right-front, top-right-back, down-right-front, down-right-back, top-left-front, top-left-back, down-left-front, down-left-back. These eight properties have to exist before any object can be observed, physically speaking.

 

[member 11137]

Sorry this discussion certainly overpasses my poor knowledges but I should want to bring some new elements.
In observing the nature, one can recognize objects and structures separated from other objects; because of this, we can count and say I have 1, 2, 3, cars f. ex. (I have only one in fact) I can't have 1,3455 car. Each of this observable object is clearly identified because it has a limit, a boundary. That means (doing it very short) no boundary = no quantification.
On an other side the universe is what it is and does not need the human existence to exist itself. Human people just observe the universe with binoculars and tools. One of these tools are the mathematical frames that we need to answer to following questions: how long is this car? how many time do I need to go to Paris? I mean, there is in fact no real frame but only the frame that we mentally built to make a map of our world, a good representation of the universe.
Conclusion: would any mathematical systematic quantization of the space not only be an illusion of our mind, even if the future proves that it is a good tool to describe our reality (= what we see with our binoculars)? A real physical quantization of the space would mean that this space would be built with small separate balls that a good microscope could identify... Blackforest

 

[Antonio Lao]

A real physical quantization of the space would mean that this space would be built with small separate balls that a good microscope could identify...

When space is static then its points are separated by quantization. But when all the space points are moving then when a point move there another point move here so that there is always something here and there and space remains continuous. The quantization of spacetime is the quantization of this local movement of space points. It is quantized and yet it is also continuous.

 

[member 11137]

This would mean we absolutely need a mathematical theory considering collections of "separated points (s.p.)" and defining the motion of each s.p. relatively to the others [This theory certainly exists under the form of the geometrodynamics (?)]; but not only that, we need to make the choice of an arbitrary configuration to control if the new configurations (the evolutive geometry after the chek-point) effectively cover continuously all fictive positions between two real s.positions of the arbitrary initial configuration. Is the necessity of this choice not hurting a basic principe of the Relativity? Other question: we have to define the word "continuously" in mathematical terms and I presume it will not be so easy (is R -collection of all real number- continuous?) Blackforest

 

[Antonio Lao]

...the new configurations (the evolutive geometry after the chek-point)...

The topology is a doubly twisted Moebius strip (as close as possible to being one dimensional strip instead of being a surface) cut through the middle. The closest similarity is that of a Hopf ring. When the points are moving, two basic topologies are created.

Geometrodynamics uses tensor calculus. But I am using just ordinary vectors to describe the topologies summarized as follow:

The quantum is the square of energy, [itex]E[/itex].

[tex] E^2 = \psi_E \times \phi_E \cdot \psi_B \times \phi_B [/tex]

 

[AWolf]

Is the necessity of this choice not hurting a basic principe of the Relativity?

If you are implying that the quantization of space would effect Relativity - why should it ?

If you took a 1 metre rule from Earth and put it into orbit close to a BlackHole, it would still be a 1 metre rule, even though it would now be subjected to a larger graviational field. Close to the BlackHole, the rule will be compressed, but since everything in its proximatey would be compressed as well, it would still be 1 metre in length.
The amount of quantized space between the two ends of the metre rule would remain constant.

Even though the size of a single quantum of space would vary dependant on its location, it would always be constant when measured locally.

 

[member 11137]

If you are implying that the quantization of space would effect Relativity - why should it ?

If you took a 1 metre rule from Earth and put it into orbit close to a BlackHole, it would still be a 1 metre rule, even though it would now be subjected to a larger graviational field. Close to the BlackHole, the rule will be compressed, but since everything in its proximatey would be compressed as well, it would still be 1 metre in length.
The amount of quantized space between the two ends of the metre rule would remain constant.

Even though the size of a single quantum of space would vary dependant on its location, it would always be constant when measured locally.

I agree but try to consider my question without compression or dilatation, only at a given scala (your choice will be mine). We have an arbitrary quantified static frame (no continuum) at the beginning (we answer with yes to the question asked at the beginning of this thread). And now how define a continuous motion in this quantified space? If everything is really quantified in this virtual frame any motion should be a "Sprung" from a s.p. to the other... and where is the continuity? A quantified space should (at least in my eyes and in a mental experiment) be like a cristal. All positions are not occupied. Sorry my knowledges are not sufficient concerning the motions inside a cristal but I have some difficulty to believe that it can be continous; I am sure you could explain me a lot of interesting things. Thanks

 

[Antonio Lao]

...but I have some difficulty to believe that it can be continous...

The continuity of space comes from its topology. The quantization of space comes from its twisting (local motion). Twisting is analogous to 2 dimensional rotation. Where the path of motion (one point after the other and one behind the other and one in the middle) for an infinite number of points is the circle. The circle contains infinite number of points hence it is continuous. For three dimensions, this topology is the Hopf ring which is a one dimensional Moebius strip of double twists.

 

[AWolf]

And now how define a continuous motion in this quantified space?

2nd Law of Thermodynamics.

Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused or dispersed and spread out.

Any amount of energy concentrated in one place is essentially unstable and must adhere to the 2nd law of thermodynamics. The motion is the direct effect of the energy's instability.