(alpha) The Arrow of Time

BenTheMan

Dr. of Physics, Prof. of Love
Valued Senior Member
I thought I'd start an alpha thread on this topic because there are two (presumably) different opinions on it in the blogosphere. I haven't read the blog entries yet, but I assume they're different because I know the people who are posting these things and I know they have opposing opinions.

The first entry is from Sean Carroll at Cosmicvariance.com.

The second is from Lubos Motl at his blog.

I shouldn't have to mention this, but this is an alpha thread. We will discuss this concept ``the arrow of time'' vis a vis the two opinions of Lubos and Sean. This is not a place for posting your own pet theories. As such, all off-topic posts will be deleted.
 
Hum,
it seems that they both put forward arguments that equate changing entropy to the `arrow of time`. Which is similar to saying that my wrist watch gives time its direction.

http://www.sciforums.com/showthread.php?t=51901&highlight=arrow+time

But both increasing entropy and moving hands on clock faces are the consequence of time being a dimension that can convey quantum information waves forwards or backwards through time. The direction of time is just a consequence of the boundary conditions of the universe. ie There is a temporal direction because the universe has a `big bang` moment, and it is `open`. Collective interactions by these temporal waves with particles will naturally produce a defined direction.
There is no need for exotic physics or magic; a meaningful explanation for the arrow of time is by regarding time as a ` special` spatial dimension which allows normal quantum wave functions to move through it and interact, as well as interact with the boundary conditions of the universe.
 
Ben, Thanks for those links, I enjoyed reading them. Obviously I can't take sides, but let me ask a couple of questions.

The issue, it seems to me is this: we perceive time to be asymmetric, so is there a physical law that says this must be so. Quite naturally, both Carroll and Motl use the second law as an example of one that might be - hence Eddington's "entropy is the arrow of time". You and I have discussed this before, albeit briefly, but I think this is flawed logic. This is not the point however.

So, is there an analogue of the second law in the quantum world?

Both bloggers point out that almost all quantum processes are invariant under time reversal, the exception being kaon decay. But then this is also true of the macroscopic world, the exception being the second law.

In spite of his somewhat sneering and abrasive, and at times personalized, style, I found Motl's blog persuasive. But I was puzzled by his assertion that initial states are averaged whereas final states are summed (presumably in both cases over all microstates?). This is an important point for him, and I don't quite get it. Can you explain?

Anyway, whatever he might mean by this, he then seems to argue that this introduces a logical asymmetry into the notion of initial versus final states, therefore the asymmetry of time must be natural.

But isn't this to deny the (probable) fact that logic itself is a construct of the human mind? If so, he is merely stating the obvious: the human mind perceives an asymmetry to time - time's arrow ?

Oh and this. Carroll makes the startling assertion that, as entropy "almost always increases, then if a system in state A evolves into a system with state B, we can assume that entropy has increased". I find that a slightly troubling assertion. Any thoughts?
 
The arrows are usefule to:

1. Map out entropy on scales we cannot but speculate >

2. That the entropy had to extrapolate from a cosmological arrow

3. The arrows are useful for understanding consciousness, through the pshychological arrow of time

and

4. then we need to ask what this intimate relationship between what we see as forward, to that which cannot be termed as forward: such as an antiparticle, retrocausality or even time-like-curves.
 
Hum,
it seems that they both put forward arguments that equate changing entropy to the `arrow of time`. Which is similar to saying that my wrist watch gives time its direction.

Well, I don't think so. At least I don't see the connection...maybe you can make it for me. The idea is that the arrow of time is a macroscopic manifesation of the second law of thermodynamics. This is the opinion held by most of the people I've talked to, but I don't think that a fully rigorous argument has ever been given.
 
The issue, it seems to me is this: we perceive time to be asymmetric, so is there a physical law that says this must be so. Quite naturally, both Carroll and Motl use the second law as an example of one that might be - hence Eddington's "entropy is the arrow of time". You and I have discussed this before, albeit briefly, but I think this is flawed logic. This is not the point however.

So, is there an analogue of the second law in the quantum world?

Well, yes. You can define entropy in quantum processes. But more generally, you can see entropy at work in particle physics---there the arguments are phase space arguments. Phase space (or momentum space) is the set of allowed momentum for physical processes. When particles decay, for example, the decay with the largest phase space is always preferred.

For example, when particles decay, the end products are always the lightest allowed particles. When things are massless, they have a larger momentum space because there is no rest mass---for example, a photon can have a very small energy if its wavelevgth is sufficiently long. An electron, though, will always have at least 511 keV of energy.

This is why most things decay into photons. When something can decay into photons it will, because the phase space of the decay to photons is much bigger than the decay into electrons.

You can see the second law at work here---the final state with more, lighter particles, is in general preferred. This is exactly the second law :)

Note, however, that the uncertainty principle says that violations of the second law are much more common at very short time scales. For example, two photons can form an electron-positon pair on sufficiently short time scales.

In spite of his somewhat sneering and abrasive, and at times personalized, style, I found Motl's blog persuasive. But I was puzzled by his assertion that initial states are averaged whereas final states are summed (presumably in both cases over all microstates?). This is an important point for him, and I don't quite get it. Can you explain?

I will have to recall this point. It has something to do with how one prepares experiments verses what one measures. I know where to look it up, it's in chapter 3 of Peskin's textbook on QFT.

Anyway, whatever he might mean by this, he then seems to argue that this introduces a logical asymmetry into the notion of initial versus final states, therefore the asymmetry of time must be natural.

But isn't this to deny the (probable) fact that logic itself is a construct of the human mind? If so, he is merely stating the obvious: the human mind perceives an asymmetry to time - time's arrow ?

I think it's more than that, though. The averaging over initial states and summing over final states happens whether we are doing experiments in the LHC, or we are observing processes in the early universe. Let me think about this a bit more and make some more (hopefully helpful) comments.

Oh and this. Carroll makes the startling assertion that, as entropy "almost always increases, then if a system in state A evolves into a system with state B, we can assume that entropy has increased". I find that a slightly troubling assertion. Any thoughts?

Well, I think the statement is an if and only if, so it can work both ways.
 
Mod note:

BenTheMan said:
I shouldn't have to mention this, but this is an alpha thread. We will discuss this concept ``the arrow of time'' vis a vis the two opinions of Lubos and Sean. This is not a place for posting your own pet theories. As such, all off-topic posts will be deleted.
 
Well, I don't think so. At least I don't see the connection...maybe you can make it for me.

Let me summarize: there exists some knowledge about the arrow of time and the second law of thermodynamics” - Lubos Motl.

These irreversibilities are summarized by the Second Law of Thermodynamics” - Sean Carroll.

What they highlight in their blogs are essentially correct, but for very different reasons.
i find it is better to discard the Eddington's "entropy is the arrow of time" way of thinking.

The idea is that the arrow of time is a macroscopic manifestation of the second law of thermodynamics.

The subtly is that the 2nd law and entropy are a product of the `arrow of time`.
The `arrow of time` is a product of the geometry and physics of the universe. ie, its `hardwired` into spacetime.
 
The `arrow of time` is a product of the geometry and physics of the universe. ie, its `hardwired` into spacetime.

Well...perhaps. Your argument is that the character of the ``time'' in space-time somehow implies that it has a direction.

What makes you say this?
 
I think he/she says this, because the arrow can be applied to both microscopic systems and macroscopic systems. ??
 
Without trying to sound too obtuse, I was not wanting to put forward any specific theory but was merely putting forward a statement what current theories are proposing.
ie that the `arrow of time` naturally comes out of the equations if the boundary condition of the universe is that it has no boundary.
 
I must be being dim today, but this makes no sense to me. Are you simply saying that the universe is unbounded? It might well be, for all I know. What equations are you referring to? And how does the unbounded property of the universe impose a preferred direction for time?

Ah. Maybe you're saying that, as the universe is expanding, and is expected to do so indefinitely (say), then entropy will continue to increase, therefore time walks hand-in-hand with expansion, with entropy? This isn't obvious to me, and anyway, isn't this the whole point of the debate, though? It looks highly circular to me, but maybe I misunderstood you.
 
Yeah I didn't get that out of the blog postings. For example, suppose the universe begins to contract again. Will the second law cease to be valid? I don't know.
 
Lubos Motl says such things as this:

The people who believe the myth think that all these factors are equal to one. Logicians have a part of their brain occupied by the Bayes' formula; ordinary people store their common sense in the same piece of their brain. The believers in this myth have a hole in that region instead...

Shockingly enough, the answer is political correctness. Sean Carroll, one of the staunchest champions of this totalitarian ideology, writes very seriously: "We human beings are terrible temporal chauvinists." So it is really politically incorrect to point out that his opinions about the origin of the arrow of time are silly - because you would become a chauvinist!

I find it difficult to respond in an Alpha fashion to a topic of discussion that does not in itself adhere to good manners. Whilst I lean towards Lubos Motl's view, I have a clear understanding why both he and Sean Carroll are mistaken in their own separate ways. However political correctness such as "your own pet theories" and "all off-topic posts will be deleted" will censor any genuine discussion of the subject.
 
Yeah I didn't get that out of the blog postings. For example, suppose the universe begins to contract again. Will the second law cease to be valid? I don't know.
Well precisely. I think it must, or rather it at least implies a transition from a high entropy state to a lower one. Does this therefore mean that the "arrow of time" is reversed? I see no reason to think so!
 
Whilst I lean towards Lubos Motl's view, I have a clear understanding why both he and Sean Carroll are mistaken in their own separate ways.
OK, would you care to explain, in some detail, why you think this? Bald assertions simply don't cut it with me.
 
Forum trolling and censorship

We will discuss this concept ``the arrow of time'' vis a vis the two opinions of Lubos and Sean.

Any of opinions of Lubos or Sean cannot explain the question of arrow of time. In fact, they doesn't care about it at all. This fundamental question is:

"If the time is just one of dimensions of space-time, why the time dimension differs by its arow from space dimensions? Why the time coordinate has a direction, while the space coordinate not?"

We should point out, the correct answer should be symmetric for time and space dimensions. The babling about thermodynamical arrow of time doesn't count, until we explain, how the thermodynamic is related to the space dimensions by the same way, like the time dimensions. It means, you'll need a coherent definition of space-time itself to be able to explain both time, both space dimensions at the scope of the same definition consistently. It means, your explanation of time should be able to explain both the symmetry of space-time, both the time arrow at the scope of single (and simple, if possible...) space-time concept definition. It means, you'll need to define/explain at first, what the space-time concept is and every other explanations of time and space should be done at the scope of the space-time definition subsequently.

Due the semantical hiearchy, you should be able to explain, what the space-time is, then what's the difference between space and time, and just after then you can start to sermonize, what the time arrow is. Without it your explanation cannot be consistent with definition of space-time. Frankly, I'm not very interested about definitions of time, which aren't consistent with definition of space-time concept as well. The contemporary physics distinguishes many definitions of time, the radiative, imaginary, cosmologic or psychological arrows of time, the thermodynamical one is just one of many time definitions possible. Due the consistency requirements, I'd preffer the definition of time, which remains consistent both with thermodynamics, both with relativity concept of space-time. Therefore the introductory question is far not so trivial and it cannot be based on thermodynamics at all!

At the moment, when nobody else can explain this difference by clear and transparent way, why the only post, which can answer it is deleted from here? Are you people really interested about explanations, or are you just dumb trolls who want to spent their time by neverending incoherent babbling on the web? Why the discussion are artifically restricted just to the opinions, which brings nothing new into understanding (of arrow of time)? Is this sane decision? Why we should spend our precious time by some blunders?

You're not required to love me or my "pet" theory. But I'm not looking for just another theory, but consistent explanation of all scientific concepts. You can call it theory, if you want, I don't care. But at the moment, you've no such concept, the only thing, which is expected from You is to discuss it and help to reveal it's limits and weakness by relevant causual arguments. Only relevant opinions counts here, not personal feelings.

Or simply shut up, if you have nothing to say about topic. This topic is named "Arrow of time", not "Arrow of time by Lumo and/or Sean". We aren't disputing the personal opinions, but intersubjective opinions. And the mutually contradicting opinions are incoherent at the first sight, so they should be handled with caution from theirs very beginning.
 
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