Where does our arrow of time come from?

Adam Walanus
AGH University of Science and Technology





Absolute space: Aristotle, Copernicus, Isaac Newton:
Absolute, true and mathematical time, in and of itself, and of its own nature, without reference to anything external, flows uniformly.

(letter to the widow): He is now a little ahead of me in bidding this strange world farewell. That means nothing. For us devout physicists, the distinction between past, present and future likewise has no significance beyond that of an illusion, albeit a tenacious one.
(When Michele Besso - Einstein's lifelong friend - died)

... time, is something - perhaps the only thing - we can count on, in this world of vagaries and whims (modern author)






Thus each of us should remember that all his actions, even small, can have a dramatic impact on the future.

We call it the butterfly effect. (The artist: Vladimir Kush)






The many-worlds interpretation of quantum mechanics (Hugh Everett in 1957)

Schrödinger's cat




( Deterministic chaos ) OR ( noise AND energy dissipation )
have a look




Daily temperature in Warsaw, 8 years




Noise: random walk, Brownian motion, diffusion have a look


N = 400


Probability ( All in the middle half ) = 1/2400 = 0.4*10-120 (= 0.4e-120)

100 steps/s -> wait 0.01/0.4e-120 s = 2.6e118 s = 2e78 * 13.8 billion years

0000000000000000000 x
lifetime of our Universe

N = NA = 6e23 [mol-1]





NA; N = 3*1022 [1/L]


NA; N = 3*1016 [mm-3]     ( atoms are very very very small )




ΔQ / T1 < ΔQ / T2

- ΔQ / T1 + ΔQ / T2 > 0

Clausius (in 1865) concludes: The entropy of the universe tends to a maximum.

Heat can never pass from a colder to a warmer body

without some other change, connected therewith, occurring at the same time.


Eddington (1927): There have been nearly as many formulations of the second law as there have been discussions of it.

Difference Between First and Second Law of Thermodynamics

A cooling tower is a heat rejection device that rejects waste heat to the atmosphere

Roger Penrose, The Road to Reality     (Tuesday, 6pm, Auditorium Maximum)


Maxwell's demon










Polish proverb: Misfortunes are coming in pairs.

--------- time axis ---------->


Atoms desintegration







The Arrow of Time,

or Time's Arrow, is a concept developed in 1927 by the British astronomer Arthur Eddington involving the "one-way direction" or "asymmetry" of time.

Physical processes at the microscopic level are believed to be either entirely or mostly time-symmetric: if the direction of time were to reverse, the theoretical statements that describe them would remain true. Yet at the macroscopic level it often appears that
this is not the case: there is an obvious direction (or flow) of time.




The radiative arrow of time.

Waves, from radio waves to sound waves to those on a pond from throwing a stone, expand outward from their source, even though the wave equations allow for solutions of convergent waves as well as radiative ones.


Giuliano Carmignola

Wave on string

     a = y0[x-1] + y0[x+1] - 2*y0[x]
v[x] = v0[x] + a*dt             
y[x] = y0[x] + v0[x]*dt          

Wave on water surface




The particle physics (weak) arrow of time

Certain subatomic interactions involving the weak nuclear force violate the conservation of both parity and charge conjugation, but only very rarely.
According to the CPT Theorem, this means they should also be time irreversible, and so
establish an arrow of time.
Such processes should be responsible for matter creation in the early universe.




The quantum arrow of time

Quantum evolution is governed by the Schrödinger equation, which is time-symmetric,
and by wave function collapse, which is time irreversible.

As the mechanism of wave function collapse is philosophically obscure,
it is not completely clear how this arrow links to the others.


Cups of coffee cool, buildings crumble and stars fizzle out,
physicists say,
because of a strange quantum effect called “entanglement.”

Entanglement builds up between the state of the coffee cup and the state of the room

nature is inherently uncertain

John Bell says there is no “true” state of the particle; the probabilities are the only reality

Quantum uncertainty then gives rise to entanglement, the putative source of the arrow of time.

Albert Einstein: “spooky action at a distance”

Entanglement is in some sense the essence of quantum mechanics, quantum computing, quantum cryptography and quantum teleportation

the correlations contained all the information, and the individual particles contained none

The arrow of time is an arrow of increasing correlations.

When you read a message on a piece of paper, your brain becomes correlated with it through the photons that reach your eyes.

The present can be defined by the process of becoming correlated with our surroundings.

Natalie Wolchover, Quanta Magazine, April 16, 2014 -



Sean Carroll (cosmologist; on the arrow of time: From Eternity to Here)
The Big Picture: On the Origins of Life, Meaning, and the Universe Itself

The difference between the everyday and deeper descriptions arises from the arrow of time,
the distinction between past and future that can ultimately be traced to the special state in which our universe began near Big Bang.

Aristoteles – causes. The First Cause ... Thomas Aquinus

In equillibrum time has no arrow.





Wroc³aw, Museum of Contemporary Art



What are the reason for Time's Arrow?

We do understand the arrow of time from a thermodynamic perspective ...
But if you want to know why yesterday is in the immutable past, tomorrow will arrive in a day and the present is what you’re living right now, thermodynamics won’t give you the answer. Nobody, in fact, understands what will.
Ethan Siegel, Forbes, Oct 12, 2016