A Thought on the Apparent Asymmetry of Time (the "Arrow of Time")

[kmb]

I had an interesting thought regarding the "arrow of time" and, with the hope of getting the opinion of someone possessing more relevant knowledge than do I, I'm posting it here.

Essentially, I thought that it may be productive to contemplate the notion of a unidirectional flow of time. I do not see a causal connection running from future to past. From this, I would think that it does not make logical sense to say that time can be run in reverse (reworded: it only runs in one direction). It would not, by its very nature, support symmetry, rendering the problem of the arrow of time null.

That many physical processes seem to be able to be run in reverse is a result of our descriptions of these processes, not a property of time itself.

I realize that I may be unaware of an error in my reasoning, and if such an error exists, please make no attempt to spare my feelings, and please do enlighten me as to its existence and nature.

-kmb

 

[CWatters]

I'm no expert but how do we know that there is no "causal connection running from future to past"? Your argument appears to be... We don't experience it or can't see such a connection therefore it doesn't happen. That's a rather unwise approach. Perhaps it doesn't happen in our universe but works fine in another?

Particles in two states at once? Cats that are both dead and alive? All/most of the best theories predict the outcome or experiments that haven't or can't be done yet.

 

[Dale]

That many physical processes seem to be able to be run in reverse is a result of our descriptions of these processes, not a property of time itself.

How could you experimentally test this?

 

[kmb]

I'm no expert but how do we know that there is no "causal connection running from future to past"? Your argument appears to be... We don't experience it or can't see such a connection therefore it doesn't happen. That's a rather unwise approach. Perhaps it doesn't happen in our universe but works fine in another?

Particles in two states at once? Cats that are both dead and alive? All/most of the best theories predict the outcome or experiments that haven't or can't be done yet.

It's not that we don't see it. In my (admittedly limited) experience, I haven't come across any theories that directly necessitate that these processes be reversible (essentially, I haven't seen a theory, the functionality of which is dependent upon time being able to be run backwards in that it requires events in the future be able to influence events in the past).

Superposition and uncertainty, if I remember correctly, are both required by our best theories, and are both experimentally verifiable.

Article describing an experiment that produced a quantum "cat state" (superposition):
http://physics.nist.gov/News/Releases/n96-18.html

For the uncertainty principle, Richard Feynman explained in one of his Character of Physical Law lectures how the double-slit experiment demonstrates it (unfortunately, a link to this is not convenient to me, however, I'm sure it's available on Youtube).

 

[kmb]

How could you experimentally test this?

I lack the expertise to really say, but I posted this thought here with the hope of ameliorating this problem.

It seems that we have a reason to begin to question the reversibility of time (as far as my knowledge extends, the conflict between the second law of thermodynamics and the notion of a reversible (multidirectional) time).

 

[Dale]

I don't think it is a problem which can be ameliorated. I think that what you are asking is untestable, and therefore not scientifically addressable. Since we cannot distinguish experimentally between "our description of these processes" and "time itself" the distinction is philosophical, not scientific.

Certainly you are correct that the second law of thermo is not T-symmetric. But all of the fundamental laws of physics are T-symmetric (actually CPT-symmetric), and thermo is not a fundamental law, but a statistical law.

For fundamental questions I would tend to look at fundamental laws.

 

[kmb]

I agree that it is, as it sits now, nothing more than a philosophical proposition. I imagine the difficulty in experimentally verifying this lies in demonstrating the impossibility of something. It seems that any experiment would involve verifying that information must travel with time (change cannot occur instantaneously (an object cannot move from one position to another, one state to another, etc..., without a change in time)), then (possibly) establishing minima and maxima for the rate of this travel (the latter I believe has already been established).

Upon further thought, I realize I should have written "current descriptions" instead of just "descriptions."

 

[vanhees71]

I think on a fundamental level the orientedness of the time axis is a postulate. I'd call it the "causality principle", according to which physical laws are causal, i.e., there time is directed from the past to the future and this direction is determined by cause and effect.

Another thing is what's meant by "time reflection symmetry". The mathematical formal definition is a bit misleading. You just make $t \rightarrow -t$ and transform the quantities in your theory appropriately such that the equations take the same form. If such a choice is possible, you call the theorem time-reflection invariant. E.g., take Newtonian mechanics of a closed system of point particles with conservative actions-at-a-distance force. The Hamiltonian reads
$$H=\sum_{j} \frac{1}{2 m_j} \vec{p}_j^2 + \frac{1}{2} \sum_{i \neq j} V_{ij}(|\vec{x}_j-\vec{x}_i|).$$
This obeys all the continuous symmetries of the inhomogeneous Galilei group and is also time-reflection invariant. The transformation laws read
$$t \rightarrow -t, \quad \vec{x}_j \rightarrow \vec{x}_j, \quad \vec{p}_j \rightarrow -\vec{p}_j.$$
This obviously leaves the Hamiltonian unchanged and thus also the Hamilton canonical equations, the equations of motion of the system, stay unchanged.

Physically that does not mean that you can flip the orientation of time, of course. Thus, the symmetry should be relabeled somehow and not call it time-reversal invariance but reversal-of-motion invariance. It means that when you evolve a system from a time $t_1$ to a time $t_2$ with given initial conditions $\vec{x}_j(t_1)$ and $\vec{p}_j(t_1)$ and then perform an experiment, where you choose the time-reflected state of the outcome of the first situation at time $t_2$ as initial conditions, i.e., $\vec{x}_j'(t_1')=\vec{x}_j(t_2)$ and $\vec{p}_j'(t_1')=-\vec{p}_j'(t_2')$ then at the time $t_2'$ with $t_2-t_1=t_2'-t_1'$ you end up with the time-reversed initial conditions of the first experiment, if the laws are "time-reversal invariant".

Nature, BTW, is for sure not time-reversal invariant. The T symmetry is violated by the weak interaction (it also violates parity (reflection symmetry) P, charge conjugation C, and the combined CP symmetry). This has been shown only recently by the BABAR Collagoration in an experiment involving the decays of neutral B-mesons:

http://arxiv.org/abs/1207.5832

The violation of P symmetry was discovered by Wu and others in 1956

http://en.wikipedia.org/wiki/Parity_(physics )

and CP violation by Cronin and Fitch 1964

http://en.wikipedia.org/wiki/CP_violation

There's the already mentioned famous theorem by Pauli and Lüders: In any relativistic, local, microcausal QFT with a stable ground state the "grand reflection" CPT is always a symmetry. So far no CPT violation has been seen, and the Standard Model which is such a relativistic QFT, works to an amazing precision.

The obvious violation of T symmetry in our everyday experience is due to Boltzmann's H theorem, according to which the total entropy of a system never decreases with time. It's proof, however, of course assumes the above stated postulat of the directedness of time, i.e., in the derivation a clear distinction between future and past is already involved. So the proof doesn't prove a directedness of time by this "thermodynamical arrow of time" but just that this "thermodynamical arrow of time" gives the same direction of time as is assumed in the sense of the fundamental "causality arrow of time". In this sense the directedness of time is not derivable from the other fundamental natural laws and must be taken as a basic postulate.

 

[Philip Wood]

Thus, the symmetry should be relabeled somehow and not call it time-reversal invariance but reversal-of-motion invariance.

I like this. I've always worried about talk of 'reversing the direction of time', because I don't know against what are we judging it to be reversed. It's not the same as saying that the direction of flight of an arrow is reversed. Here the meaning is perfectly clear.

I throw in a quote from Ernst Mach in translation. "There is no cause nor effect in nature. Nature simply is."
How many physical laws need cause or effect in their statement?