# Why is there an arrow of time?

1. Jan 12, 2010

### DrChinese

I have a question, hope maybe someone has seen some papers on the subject and can point me in a direction. I searched arxiv/astro-ph with the search paprameter "arrow of time" but could not find anything in the following specific area:

Hypotheses:

a) Time is symmetric.
b) When the big bang occurred, half the mass went forward in time, half went backwards in time.

Anti-matter universe <------- Big Bang --------> Our universe

Would provide a simple explanation of why we see effects dominating in one time direction and not the other... it is a result of initial conditions. I am pretty certain someone must have speculated on this before, there are probably plenty of citations but I can't find the right phrase. Any suggestions? There have been new interpretations of QM which involve time symmetry (I searched on that too) which I suspect would have some cosmological implications. So that is what is driving the question.

2. Jan 12, 2010

### Dmitry67

DrChinese, are you talking about the macroscopic arrow of time or QM arrow of time?

Macroscopic arrow of time I guess had been explained a long time ago as a consequence of the Big Bang (low entropy initial conditions -> Loschmidt's paradox)

QM arrow of time (CP violation = T-symettry violation) is a mystery.

3. Jan 12, 2010

### Carid

Ilya Prigogine wrote a book on this called "The End of Certainty"

http://www.absoluteastronomy.com/topics/Ilya_Prigogine" [Broken]

Last edited by a moderator: May 4, 2017
4. Jan 12, 2010

### BillSaltLake

There's a "coincidence" that suggests something like the idea of antimatter going backward in time and matter going forward, but this would have occurred much later than the Bang, at around a microsecond. At the time of stable baryon pair production, there were around 1018 total baryons + photons per Planck mass-equivalent of mass+energy. Because of charge conservation, the number of protons produced must have been exactly equal to the number of antiprotons, but baryon number conservation did not necessarily apply to neutrons and antineutrons.

If (for some unknown reason) there is a conservation principle in which any sample with mass+energy equal to the Planck mass must have its mass+energy conserved despite gaussian statistical fluctuations, then there could be an interesting consequence. This "conservation principle" is the same as saying that there's a node in the gaussian count fluctuations for ensembles equaling the Planck mass.

One reason that mass+energy fluctuations occurred during pair production because the mass per massive particle pair was not changing while the energy per photon pair was decreasing. Converting back and forth several times between photon pairs and massive pairs introduces some variation. Some samples would be expected to end up with less mass+energy than average and some with more. For a sample of 1018, the standard deviation would be about 109 particles.

Suppose that each Planck-massed sample was brought up to or down to average by spontaneous creation/destruction of neutrons or antineutrons. If the neutrons (in the Feynman-diagram sense) go "forward" in time while the antineutrons go "backward", then a sample that lost excessive mass+energy during the baryon pair production era would supplement that lost mass+energy by creation of neutrons, while a sample that ended up with an excess of mass+energy would spontaneously annihilate some of the antineutrons. The result would be an excess of neutrons with about 1 neutron per 109 photons, which is about the observed baryon:photon ratio.

5. Aug 24, 2010

### dleiter

THE ANSWER TO THE QUESTION: WHY IS THERE AN “ARROW OF TIME”?

In the following two papers has been shown that description of the quantum measurement process can be “completed” by incorporating an operator symmetry of microscopic observer-participation called “Measurement Color” into the formalism of quantum electrodynamics (Leiter, D. 2009), http://journalofcosmology.com/LeiterArrowofTime.pdf
Leiter, D. 2010), http://journalofcosmology.com/LeiterQUANTUMREALITY.pdf)

It has been shown that the Measurement Color operator symmetry within MC-QED generates a spontaneous CPT symmetry breaking effect which causes the photon to carry the quantum electrodynamic arrow of time by virtue of the fact that it has a negative parity under Wigner time reversal. This resolves the age old puzzle about the origin of the arrow of time in the universe.

However even though this result is interesting it is natural to ask if there exists any experimental evidence which supports the idea that “the photon carries the arrow of time”?

The answer is that in new paper to be published in the near future (D. Leiter 2010 in press) it has been shown that recently performed Michelson interferometer experiments, using combinations of ordinary mirrors and phase conjugate mirrors, contain experimental results which offer strong evidence that the photon has a negative parity under Wigner time reversal in support of the MC-QED prediction that “the photon carries the arrow of time”.

6. Aug 26, 2010

### Dmitry67

Whats so special about the photons?
Photon is just one of 16 SM particles.

7. Aug 26, 2010

### Orion1

The law of entropy and the second law of thermodynamics...

The largest contributor to the entropy budget of the Universe is super massive black holes.

$$R_s = \frac{2GM}{c^2}$$

Schwarzchild black hole sphere surface area:
$$A_s = 4 \pi R_s^2 = 4 \pi \left( \frac{2GM}{c^2} \right)^2 = \frac{16 \pi G^2 M^2}{c^4}$$

$$r_P = \sqrt{\frac{\hbar G}{c^3}}}$$

Schwarzchild black hole entropy integration by substitution:
$$S_{BH} = \frac{dE}{dT} = k_B \ln \Omega_s = k_B \left( \frac{A_s}{4 r_P^2} \right) = \frac{k_B}{4} \left( \frac{16 \pi G^2 M^2}{c^4} \right) \left( \frac{c^3}{\hbar G} \right) = \frac{4 \pi k_B G}{\hbar c} M^2$$

Schwarzchild black hole entropy:
$$\boxed{S_{BH} = \frac{4 \pi k_B G}{\hbar c} M^2}$$

Entropy of the Universe:
$$S_u = \sum_{i = 1}^{n} S_i = k_B \ln \Omega_u$$

$$S_u = 3.1 \cdot 10^{104} \; \frac{\text{j}}{\text{K}}$$

$$\boxed{\ln \Omega_u = \frac{S_u}{k_B} = 2.245 \cdot 10^{127}}$$
$$\Omega_u$$ - number of equally probable states in the Universe

The law of entropy and the second law of thermodynamics are more fundamental laws in the Universe than those involved with symmetry breaking events such as the phase transition of Planck epoch energy to baryonic matter, grand unification theory, matter over antimatter asymmetry and the Standard Model, etc., because those two laws were in effect prior to these epochs in the Universe during the Planck epoch, when the dimensions of space-time and energy and possible equally probable states were generated.

Reference:
Second law_of_thermodynamics - Wikipedia
http://en.wikipedia.org/wiki/Boltzmann%27s_constant" [Broken]
http://en.wikipedia.org/wiki/Entropy_%28arrow_of_time%29" [Broken]
http://en.wikipedia.org/wiki/Arrow_of_time" [Broken]
http://en.wikipedia.org/wiki/Grand_unification_epoch" [Broken]
http://en.wikipedia.org/wiki/Baryogenesis#Baryon_asymmetry_parameter"
http://en.wikipedia.org/wiki/Black_hole_thermodynamics#Black_hole_entropy"
http://theastronomist.fieldofscience.com/2009/09/entropy-of-universe.html" [Broken]
http://en.wikipedia.org/wiki/Planck_length#Value"

Last edited by a moderator: May 4, 2017
8. Aug 26, 2010

### dleiter

Hi Dmitry67,

This is a very good question and here is the answer.

Measurement Color Electrodynamics (MC-QED) is a gauge invariant quantum field theory of electrons, positrons, and photons in which a quantum electrodynamic arrow of time emerges due to spontaneous CPT symmetry breaking.

However since it is a gauge field theory Measurement Color generalizations of the quantum electrodynamic formalism to the case of SU(3)xSU(2)xU(1) quantum gauge particle field theories with appropriately chosen Higgs sectors can be formulated. In this higher internal symmetry context the effects of spontaneous CPT symmetry breaking would then imply that the massless photon as well as all of the masssive gauge bosons carry the quantum field theoretic arrow of time.

Darryl Leiter

9. Aug 26, 2010

### Dmitry67

I was blocked at the sentence

As I see, measurement is analyzed from CI perspective, while Copenhagen does not make any sense in new millenium. Whats about the decoherence?

10. Aug 27, 2010

### Orion1

The particle physics weak arrow of time...

Reference:
http://en.wikipedia.org/wiki/Arrow_of_time#The_particle_physics_.28weak.29_arrow_of_time"
http://en.wikipedia.org/wiki/Irreversible_process_%28thermodynamics%29" [Broken]

Last edited by a moderator: May 4, 2017
11. Aug 27, 2010

### Dmitry67

For me it is a biggest mystery
I dont know why it is not discussed on these forums.
That 'weak' T-symmetry violation is THE ONLY real T-symmetry violation, because all other 'arrows' (quantum, thermodynamical) are explaned based on the low entropy state at BB

12. Aug 27, 2010

### dleiter

ON SPONTANEOUS CPT BREAKING AND DECOHERENCE IN MC-QED

First of all if you look more carefully at the two papers on MC-QED and the arrow of time

http://journalofcosmology.com/LeiterArrowofTime.pdf

http://journalofcosmology.com/LeiterQUANTUMREALITY.pdf

you will see that MC-QED does not use the CI since it contains its own dynamically determined interpretation.

Second, by virtue of the Measurement Color symmetry within MC-QED, operators associated with localized fermionic “system + apparatus” can be defined in terms of a finite range of fermion Measurement Colors. In this context a reduced density matrix operator, associated with the localized fermionic (system + apparatus) in the presence of an external environment, can be defined by tracing over the states of the “environment”.

Then because of the spontaneous CPT symmetry breaking in the MC-QED formalism, the expectation value of the reduced Von Neumann entropy operator for the (system + apparatus) in the presence of an external environment has a time dependence which is both non-unitary and time-reversal violating.

Hence MC-QED contains a combination of (decoherence + dissipation) which occurs in the context of the expectation value of the reduced “Von Neumann Entropy operator, that describes a finite (system + apparatus) in the presence of an external environment by tracing over the states of the “environment”.

13. Aug 28, 2010

### Orion1

In my opinion, the quantum arrow of time and the thermodynamic arrow of time are linked by entropy. Time irreversibility asymmetry and symmetry breaking events and the Schrödinger equation, which is time-symmetric, and wave function collapse, which is time irreversible, all obey the law of entropy and the second law of thermodynamics.

Planck energy:
$$E_P = \sqrt{\frac{\hbar c^5}{G}}$$

Planck temperature:
$$T_P = \frac{m_P c^2}{k_B} = \sqrt{\frac{\hbar c^5}{G k_B^2}}$$

Planck entropy integration by substituion:
$$S_P = \frac{dE}{dT} = \frac{E_P}{T_P} = \left( \sqrt{\frac{\hbar c^5}{G}} \right) \left( \sqrt{\frac{G k_B^2}{\hbar c^5}} \right) = k_B$$

$$\boxed{\ln \Omega_P = 1}$$

Planck entropy:
$$\boxed{S_P = k_B \; \; \; \Omega_P = e}$$

Number of equally probable Planck states:
$$\boxed{\Omega_P = e = 2.71828}$$

Reference:
http://en.wikipedia.org/wiki/Arrow_of_time#The_weak_arrow_of_time"
http://en.wikipedia.org/wiki/Boltzmann%27s_constant" [Broken]
http://en.wikipedia.org/wiki/Planck_energy" [Broken]
http://en.wikipedia.org/wiki/Planck_temperature" [Broken]
http://en.wikipedia.org/wiki/Planck_entropy" [Broken]
http://en.wikipedia.org/wiki/E_%28mathematical_constant%29" [Broken]

Last edited by a moderator: May 4, 2017
14. Aug 28, 2010

### dleiter

Reply to Orion1 as to "Why is there an arrow of time"

Orion1 commented that:

In my opinion, the quantum arrow of time and the thermodynamic arrow of time are linked by entropy. Time irreversibility asymmetry and symmetry breaking events and the Schrödinger equation, which is time-symmetric, and wave function collapse, which is time irreversible, all obey the law of entropy and the second law of thermodynamics.

In reply dleiter wishes to point out that in the context of the papers on Measurement Color Quantum Electrodynamics (MC-QED)
http://journalofcosmology.com/LeiterArrowofTime.pdf
http://journalofcosmology.com/LeiterQUANTUMREALITY.pdf
the reverse of the logic in Orion1's comment occurs.

This is because by virtue of the Measurement Color symmetry within MC-QED, operators associated with localized fermionic “system + apparatus” can be defined in terms of a finite range of fermion Measurement Colors. Then a reduced form of the “Von Neumann Entropy operator”, which is associated with the localized fermionic (system + apparatus) in the presence of an external environment, can be defined by tracing over the states of the “environment”.

Because of the spontaneous CPT symmetry breaking in the MC-QED formalism, the expectation value of the reduced Von Neumann entropy operator for the (system + apparatus) in the presence of an external environment in has a time dependence which is both non-unitary and time-reversal violating.

Hence in the context of the expectation value of the reduced “Von Neumann Entropy operator which describes a finite (system + apparatus) in the presence of an external environment by tracing over the states of the “environment”, a quantum electrodynamic description of the Second Law of Thermodynamics can be obtained by generalizing on the work done in section 4.1 of the book by Zeh 2007 and section 2.4.3 of the book by Schlosshauer 2007).

In MC-QED this is due to the effects of Measurement Color which creates the spontaneous CPT symmetry breaking in the formalism and causes the photon operator to carry the arrow of time, also underlies the origin of the Second Law of Thermodynamics in the quantum electrodynamic context.

Since result is not limited to quantum electrodynamics alone it can be shown that Measurement Color generalizations of SU(3)xSU(2)xU(1) quantum gauge particle field theories (associated with the Standard Model and Grand Unified Models) can be constructed in the context of which the effects of spontaneous CPT symmetry breaking cause the photon as well as the massive gauge bosons carry the quantum field theoretic arrow of time.

Hence in this manner the idea that the origin of the Second Law of Thermodynamics can be connected to spontaneous CPT symmetry breaking effects in the universe can be extended to include all elementary particle interactions.

15. Aug 29, 2010

### Orion1

Riemann zeta function...

CBR photon equilibrium temperature:
$$T_{\gamma} = 2.725 \; \text{K}$$

CBR photon density at equilibrium temperature $$T_{\gamma}$$:
$$n_{\gamma} = \frac{1}{\pi^2} {\left(\frac{k_B T_{\gamma}}{\hbar c}\right)}^3 \int_0^\infty \frac{x^2}{e^x - 1} dx$$

This is my solution for the integration equation on post #7.

Integration:
$$\int_0^\infty \frac{x^2}{e^x - 1} dx = 2 \sum_{n=1}^\infty n^{-3} = 2 \zeta(3)$$

Complex variable:
$$\boxed{s = 3}$$

$$\boxed{\int_0^\infty \frac{x^2}{e^x - 1} dx = 2 \zeta(3)}$$

Where $$\zeta(s)$$ is the Riemann zeta function.

Riemann zeta function:
$$\zeta(s) = \sum_{n=1}^\infty n^{-s}$$

The CBR photon density at equilibrium temperature $$T_{\gamma}$$:
$$\boxed{n_{\gamma} = \frac{2 \zeta(3)}{\pi^2} {\left(\frac{k_B T_{\gamma}}{\hbar c}\right)}^3}$$

$$\boxed{n_{\gamma} = 4.105 \cdot 10^{8} \; \frac{\text{photons}}{\text{m}^3}}$$

Are these equations correct?

Reference:
http://en.wikipedia.org/wiki/Riemann_zeta_function" [Broken]
http://en.wikipedia.org/wiki/Baryogenesis#Baryon_asymmetry_parameter"