Space-time and the thermodynamic arrow of time.

[Sorcerer]

I'm sure all of us have a pretty good idea of what time is, it seems so obvious, however whenever someone says "time" with relation to a question in this forum, what do they actually mean?

 

As far as I can tell there are actually 2 forms of time:

 

1. space-time, which is symetrical, and its proceedings make sense equally well in forward and reverse.

 

2. the thermodynamic arrow of time, which relates to the overall trend for an increase of entropy and the expansion of the universe, this is asymetric.

 

What theories are used to try and unite these 2 forms of time, are there any and how plausible are they?

 

When space-time is influence by relativistic effects, for example when an object approaches a singularity, does the same apply to the thermodynamic arrow of time?

 

Space-time is relative to the observer, is this also true for the thermodynamic arrow of time?

[swansont]

The thermodynamic arrow of time isn't a measure of time. It's just the observation that there are irreversible processes once you get to macroscopic collections of particles. Spacetime isn't time - it's a 4-dimensional vector that's used to describe things, as relativity insists that the universe is four dimensional, and how you move through space affects how you move through time.

[Severian]

The thermodynamic arrow of time is just an observation that phase-space opens up when particles interact.

 

In other words: if I have one particle in the universe, the only quantities which are important are its internal quantum numbers, since there is no extrenal reference to compare the momentum (or even mass) of the particle with.

 

If the particle decays into 2 particles, they will be back-to-back in the CM frame and have a pre-determined magnitude of momentum and energy, but the direction they fly off in is random. So the system needs at least one more variable to describe it. The 'phase-space' for the new state is bigger than the old one - the number of possible configuration of the universe increase with each interaction. While it is possible (statistically speaking) for the universe to return to the initial state, it does not happen because there are so many other possible states opening up, that the probability of returning to the initial state becomes (effectively) zero.

[Sorcerer]

So the thermodynamic arrow with respect to the relatavistic arrow requires one more variable? Hang on, don't you need a 3rd party observer to tell wether 2 objects are moving, or 1 stationary 1 moving. Theres a similarity there..... that sort of answers #3, wanna attempt my other questions?

[Sorcerer]

The thermodynamic arrow of time isn't a measure of time. It's just the observation that there are irreversible processes once you get to macroscopic collections of particles. Spacetime isn't time - it's a 4-dimensional vector that's used to describe things, as relativity insists that the universe is four dimensional, and how you move through space affects how you move through time.

 

So on the quantum level can things happen then "un-happen" without any net increase of entropy? Is there no arrow of time at this level, if so how can no time at a quantum level turn into time at a macroscopic level if the former produces the latter.

[Severian]

So on the quantum level can things happen then "un-happen" without any net increase of entropy? Is there no arrow of time at this level, if so how can no time at a quantum level turn into time at a macroscopic level if the former produces the latter.

 

Entropy is a macroscopic statistical quantity. You can't talk about statistics for one particle, so one particle doesn't have a defined entropy. Entropy only makes sense when talking about ensembles of particles.

 

When you discuss macroscapic quantities you are talking about averages of the individual particle properties. So even though these properties are quantum mechanically uncertain, the mean-value-theorem tells you that this uncertainty will become very small when you take the average of a large number of states. A lot of uncertain quantum properties give you your macroscopic classical measurement.

 

Statistically multiparticle states become more disordered (because phase space opens up) and Entropy increases. But you are right, in principle, all the particles in a large ensemble could suddenly line up and dance the tango (so to speak) - the probability will be very low but not necessarily zero. (The probability of all the oxygen molecules in the air around you tunnelling into the next room and sufocating you is also non-zero.) Things only become more disordered on average, but since the universe contains a heck of a lot of particles, the increase of entropy with time is a very very good macroscopic premise.

 

So the entropy 'arrow of time' is inescapably linked to the space-time definition of time as the forward (or backward) light cone.

 

Incidentally, you have missed the obvious quantum level 'arrow of time': CP violation. We know that CPT is conserved (i.e. that a charge conjugation © (swapping matter for antimatter) followed by a parity switch (P) (looking in a mirror) followed by reversing the direction of time (T) leaves the physics laws unchanged), so CP violation (which has been observed in nature) implies that T is not conserved. The laws of nature are not the same in the reverse time direction.

[Sorcerer]

Incidentally' date=' you have missed the obvious quantum level 'arrow of time': CP violation. We know that CPT is conserved (i.e. that a charge conjugation © (swapping matter for antimatter) followed by a parity switch (P) (looking in a mirror) followed by reversing the direction of time (T) leaves the physics laws unchanged), so CP violation (which has been observed in nature) implies that T is not conserved. The laws of nature are not the same in the reverse time direction.[/quote']

 

"Implies" that T is not conserved..... I'd be sceptical that just because we haven't seen it, (yet we've seen the other 2), that it happens. Is the CP violation you are referring the discrepancy which aparently allowed matter to be dominant over antimatter..... the K^0 meson is the exception (and there may be more) if I'm not mistaken. What was the P violation? How can u mirror a particle, I mean I can understand stereoisomers etc, but particles/waves which are feilds of probability, how can these be mirrored?

 

Anyway I think the question I really want the answer to is will relativity be merged with another theory giving it an arrow of time? Is this one of the goals of GUT's?

[swansont]

What was the P violation?

 

Neutrinos maximally violate parity. All neutrinos are left-handed; the spin vector and linear momentum vector always have the same relationship.

[Severian]

"Implies" that T is not conserved..... I'd be sceptical that just because we haven't seen it' date=' (yet we've seen the other 2), that it happens.

[/quote']

 

Well, since CPT is conseved, T must be violated (since CP is). If CPT was not conserved, the world would be a very strange place.

 

Is the CP violation you are referring the discrepancy which aparently allowed matter to be dominant over antimatter..... the K^0 meson is the exception (and there may be more) if I'm not mistaken.

 

Yes - possibly. The Baryon asymmetry (the dominance of matter over anti-matter) is not properly understood. Our models don't have enough CP violation to account for it (this is one of the BIG questions in physics right now, since it appears contradictory to the Big Bang). And K⁰ decays are indeed one place where CP violation is seen.

 

What was the P violation? How can u mirror a particle, I mean I can understand stereoisomers etc, but particles/waves which are feilds of probability, how can these be mirrored?

 

The world would be P symmetric if you could take the laws of physics and subtitute x->-x, y->-y, z->-z (where x, y and z are the usual Cartesian coordinates) and get exactly the same laws back. So F=ma for example is parity conserving. As swansont said, neutrinos violate parity because they are all left handed - there is no right handed neutrinos. A parity transformation would map a left handed neutrino onto a right handed one, so clearly the universe is not P conserving.

 

Anyway I think the question I really want the answer to is will relativity be merged with another theory giving it an arrow of time? Is this one of the goals of GUT's?

 

I am not sure what you mean by that. A GUT does not include gravity though - a GUT is a union of the three lower energy forces (weak nuclear, strong nuclear and electromagnetism). A theory of everything (TOE) would include gravity.

[detrituse]

"When space-time is influence by relativistic effects, for example when an object approaches a singularity, does the same apply to the thermodynamic arrow of time?"

 

If we are to go with relativity theory, at the point of a singularity, there are no inertial frames by virtue of the fact that time is "infinitely warped" at the point of singularity.

 

Therefore, necessarily, there are no arrows of time (thermodynamic or otherwise) nor even is there a causal arrow (generally considered to be the most basic) at a singularity. In many senses, a singularity may be considered time independent.

 

Also, the thermodynamic arrow can be misleading and in many extreme cases, can lead to erroneous thought processes since: (a) the thermodynamic arrow does not always point in the same direction; (b) the mechanism of time passage (whatever that may be) is qualitatively different from the mechanism of increasing entropy in that it appears to always point in the same direction and move at a constant, smooth rate - unlike the thermodynamic arrow.

 

Due to these latter points, it is in general best to dispense of the "thermodynamic arrow of time" altogether as somewhat of a misconception (leave it for the engineers to use in their ridiculously over-simplified version of reality) and try to think "outside the box" (I do apologise for the cliché) when thinking about matters related to time, the passage of time and extreme natural phenomena (such as black holes, singularities, the big bang etc.).

 

Time for a bit of speculation: indeed it wouldn't at all surprise me if the reason that scientists' explanation of the big bang/start of the Universe are so weak in their explanatory force is largely (if not entirely) stemmed from a misconception about the nature of time. Especially the notion that it is forward-moving and immutable.

[July281995]

We still have no complete definition of time.