CPT Theorem and Entropy: Exploring the Concept of Time Reversal and T-Violation

[kurious]

Entropy does not allow things to happen in reverse in time.
In CPT theorem would this mean that entropy represents a T violation
of some sort?

 

[Antonio Lao]

In CPT theorem would this mean that entropy represents a T violation
of some sort?

You are correct. But no one has a good explanation why.

 

[Antonio Lao]

Increase of entropy is just one of the four time's arrows.

1. Thermodynamics (entropy) - Heat flows from hot to cool.
2. Electromagnetic - Radiation emanate outward from source.
3. Cosmology - The universal expansion of space.
4. Psychology - We remember the past not the future.

 

[Alkatran]

I thought life took unordered stuff and turned it into order? Isn't that going against entropy? (The energy coming from the sun is not ordered, right?)

 

[Antonio Lao]

Relatively speaking, at the local region of any open system, order is seemed to be realized but there is always some amount of energy loss in the form of heat to the environment.

If we shuffle a brand new ordered deck of cards, we need to spend energy. The more we shuffle the more random is the deck of cards but the more energy is spended. The increase in randomness of the deck of cards is entropy. How much we have to shuffle to regain the original order of the deck of cards?

 

[kurious]

Energy flows from hot to cold.This is a net flow that has one space direction
and one time direction.CP and T are violated so CPT symmetry is restored.
The fact that no process has been found which breals CPT symmetry might just be because no process can break the second law of thermodynamics.

Space might be expanding i.e dark energy increasing, because
dark energy has entropy that increases with time - that is to say:
dark energy has energy microstates.If it does have microstates then it
could absorb energy from other particles in the universe e.g microwave background photons.

 

[Antonio Lao]

dark energy has energy microstates

Are you referring to the ultra-high frequency polarized radiation? Short wavelengths comparable to Planck length?

 

[kurious]

I'm just suggesting that dark energy if it has microstates could be absorbing nergy from photons and other particles in the universe.It is my belief that dark energy + vacuum particle energy + energy of antimatter = constant if dark energy is made from vacuum energy and/or antimatter enrgy.

 

[Antonio Lao]

dark energy if it has microstates

Is microstate the same as a wave function, $\psi$? If it is, this implies that dark energy can be derived from Dirac's relativistic equation as the negative square root of $E^2 = c^2 \vec{p}^2 + m^2 c^4$.

 

[kurious]

Microstates justs means different energy levels much as a group of atoms is composed of individual atoms at different levels of excitation.

 

[Antonio Lao]

different energy levels

These energy levels must be the complex conjugate of the energy operator in the relativistic wave equations.

 

[Antonio Lao]

atoms at different levels of excitation

Excitations are not stable. Excited atoms seek stability by quickly radiate photons.

 

[kurious]

What information does this complex conjugate of the energy operator carry in relativistic quantum mechanics - any information about dark energy is useful information to me.I expect dark energy to be non-uniform because if it can come from other energy sources in the universe, then since no other enrgy source in the universe can be uniformly distributed throughout it,dark energy shouldn't be either.

 

[sol2]

What information does this complex conjugate of the energy operator carry in relativistic quantum mechanics - any information about dark energy is useful information to me.I expect dark energy to be non-uniform because if it can come from other energy sources in the universe, then since no other enrgy source in the universe can be uniformly distributed throughout it,dark energy shouldn't be either.

You haven't accepted which geometry you are going to use then?

 

[Antonio Lao]

complex conjugate of the energy operator carry in relativistic quantum mechanics

This was already used by Dirac to explain the existence of antimatter.

 

[sol2]

This was already used by Dirac to explain the existence of antimatter.

If you limit yourself to SR approaches, you limit yourself to further explanations on the nature of the geometries. If you join electromagnetism and Gravity, there is a result theoretically, and a geometry, that helps you move forward.

You use Dirac yes, but its gone much further then this.

 

[Antonio Lao]

sol2,

Dirac could not give any geometric interpretation. The best he did was the sea of negative energy.

My interpretation for $E^2$ is the existence of two distinct topologies of fully twisted Moebius strip. And with your suggestion, and I already mentioned in other posts, the spin is related to the genus of the topologies.

 

[Antonio Lao]

My interpretation of $E^2$ is that it can also be given by

$$E^2 = \psi_i \times \phi_i \cdot \psi_j \times \phi_j$$

When for time independency, $\psi$ is the wave function of QM and $\phi$ is the conjugate variable of momentum.

 

[Antonio Lao]

any information about dark energy is useful information to me

I think, at first many physicists, no doubt, thought that dark energy should come from antimatter. But the problem is antimatter cannot be found globally. Locally, it happens at quantum fluctuations of the vacuum and high energy domains in particle accelerators. But the vacuum is highly uniform because of the isotropy and homogeneity of the cosmos regardless of the existence of stars and galaxies and other interstellar or intergalactic gases and nebulae.

 

[kurious]

Antimatter cannot be found globally if nearly all of it has already become dark energy.
This suggests the universe will stop accelerating soon and the dark energy density
will decrease as antimatter reforms from dark energy.

 

[sol2]

sol2,

Dirac could not give any geometric interpretation. The best he did was the sea of negative energy.

My interpretation for $E^2$ is the existence of two distinct topologies of fully twisted Moebius strip. And with your suggestion, and I already mentioned in other posts, the spin is related to the genus of the topologies.

I do not think we should forget what has been happening in Gaussian fields, yet we would have extended this vision to include the same dynamics. So, you have to encapsulate all of it. It still allows you to think in higher dimensions and understand the topologies that are dynamcially taking place.

I gave a discription pictorially that might help you understand the energy values in relation to where the graviton can go, but still, you have to follow the graviton.

Does this leave you with a holographical vision of those hidden dimensions(branes), as intersections points?

Look at what is being described in relation to the graviton?

 

[Antonio Lao]

I gave a discription pictorially that might help you understand the energy values in relation to where the graviton can go, but still, you have to follow the graviton.

I keep seeing the the decrease in volume as the energy scale approaches the Planck domain. I came up with quantized mass values as positive and negative roots that is equaled to the double time integrals of a convolution of density function and a volume function.

 

[Antonio Lao]

antimatter reforms from dark energy

But antimatter is fermionic and dark energy is bosonic. So you need a theory of supersymmetry to show us how the reformations are carried out. Many theoretical physicists are presently working on supersymmetry. You might like to join the bandwagon just to find out how they are doing. Personally, i don't think there is any more fundamental symmetry than the ones we already have.

 

[sol2]

I keep seeing the the decrease in volume as the energy scale approaches the Planck domain. I came up with quantized mass values as positive and negative roots that is equaled to the double time integrals of a convolution of density function and a volume function.

What result would you get, if you adjusted to this?

it turns out that within string theory ... there is actually an identification, we believe, between the very tiny and the very huge. So it turns out that if you, for instance, take a dimension - imagine its in a circle, imagine its really huge - and then you make it smaller and smaller and smaller, the equations tell us that if you make it smaller than a certain length (its about 10-33 centimeters, the so called 'Planck Length') ... its exactly identical, from the point of view of physical properties, as making the circle larger. So you're trying to squeeze it smaller, but actually in reality your efforts are being turned around by the theory and you're actually making the dimension larger. So in some sense, if you try to squeeze it all the way down to zero size, it would be the same as making it infinitely big. ... (CSPAN Archives Videotape #125054)

 

[Antonio Lao]

The area of a triangle is computed by multiplying the magnitude of one side with the distance from its opposite vertex. But two of the sides can be changed in such a way that the area remains the same. And when the area is calculated from the longest side and its distance from the opposite vertex, the side can approach infinity and the distance can approach zero but the product is the same area. So when we talk about duality, we are really comparing by an analogy to the constant area of a distorted and stretched triangle which minimum configuration is that of an isosceles triangle (side and distance are equals) more so than an equilateral triangle.

 

[sol2]

The area of a triangle is computed by multiplying the magnitude of one side with the distance from its opposite vertex. But two of the sides can be changed in such a way that the area remains the same. And when the area is calculated from the longest side and its distance from the opposite vertex, the side can approach infinity and the distance can approach zero but the product is the same area. So when we talk about duality, we are really comparing by an analogy to the constant area of a distorted and stretched triangle which minimum configuration is that of an isosceles triangle (side and distance are equals) more so than an equilateral triangle.

It is easy to understanding the dynamcial relationship of the saddle, versus the sphere, and the nature of that triangulation. Those are non-euclidean realzations developed from the fifth postulate?

Being lead through GR why did Einstein rely on Reimann? http://cerval.murdoch.edu.au/kissane/e162lect06/sld001.htm

The non-eucldean world seemed very attractive for obvious reasons, and lead the thinking to move to higher dimensional considerations?

There had to be something consistant through it all?

I think if ones considers the "point" on the brane, and supersymmetry, what value would you give a "point". Consider the graviton as time. Discrete structures would not apply here, but "topologies," that are very smooth.

I for one do not like uncertainty, but if higher energies are any indications we have found a tesing ground for soemthing that calls for "emergent realities."

For enjoyment entertain the graviton in all these hidden dimensions of the brane.

http://www.sukidog.com/jpierre/strings/extradim.gif

This is actually a very old idea dating back to the 1920's and the work of Kaluza and Klein. This mechanism is often called Kaluza-Klein theory or compactification. In the original work of Kaluza it was shown that if we start with a theory of general relativity in 5-spacetime dimensions and then curl up one of the dimensions into a circle we end up with a 4-dimensional theory of general relativity plus electromagnetism! The reason why this works is that electromagnetism is a U(1) gauge theory, and U(1) is just the group of rotations around a circle. If we assume that the electron has a degree of freedom corresponding to point on a circle, and that this point is free to vary on the circle as we move around in spacetime, we find that the theory must contain the photon and that the electron obeys the equations of motion of electromagnetism (namely Maxwell's equations). The Kaluza-Klein mechanism simply gives a geometrical explanation for this circle: it comes from an actual fifth dimension that has been curled up. In this simple example we see that even though the compact dimensions maybe too small to detect directly, they still can have profound physical implications. [Incidentally the work of Kaluza and Klein leaked over into the popular culture launching all kinds of fantasies about the "Fifth dimension"!]

Maybe even entertain the notion Lubos Motl is challenging you? :rofl:

[Moderator's note: Good textbooks and lectures of string theory - e.g.
chapters 3 of Green+Schwarz+Witten and of Polchinski - derive that
the background metric must satisfy the correct Einstein equations if
the worldsheet theory is conformal i.e. consistent. They also explain
that the same effective action is seen by the scattering of the
perturbations - namely by the gravitons. This is such a basic feature
of string theory - and a key motivation to study that I would say
that someone who has not this calculation does not really know
what string theory is at the technical level. LM]



[Moderator's note: Certainly not as anything analogous to string theory as
we know it. String theory, in the conventional meaning of the word,
always automatically includes gravity, and it is unique - once the five
different perturbative versions are unified. The idea that one can make
a consistent string theory that gives "electroweak theory only" is
a misunderstanding of basics of string theory. What sort of "new" string
theory do you have in mind? I think that this is a very popular laymen's
misunderstanding - they often think that it is possible to modify string
theory in hundreds of ways and define hundreds of different sibblings of
string theory. No, string theory - or a theory of quantum gravity -
is unique. LM]

 

[Antonio Lao]

Whether Euclidean or non-Euclidean, we can start with two parallel lines. Starting with a base interval of a triangle on one line and construct a distance that is the same length as the base to the line and both magnitudes are of unit length. Now pick a point on the line not of the base and joining the ends of the base to this point to create a triangle whose area is 1/2. Moving the point left and right to infinity creating distorted and stretched out triangle but the area remains 1/2 unit. Now tracing the loci of all points of intersection of distances with the other two sides, creates a semicircle with radius 1/2. That means the circle is also a constant even though both the sides and its respective distance are made to approach either zero or infinity.