I've heard many examples of how Time-symmetry might work if it could be observed in our universe. The most famous example is of the egg falling off the table and breaking apart upon hitting the ground. If you played this scenario in reverse then you could (possibly) measure the energy 'jumping back into' the shattered pieces of egg in such a way that it would reform and bounce back onto the table from which it fell. I have no problem with this description. I've also read that: "Time asymmetries are generally distinguished as either those intrinsic to the dynamic laws of nature, and those due to the initial conditions of our universe." This is because: ", ... (our) observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics." Once again, I have no problem with this description either.
http://en.wikipedia.org/wiki/T-symmetry
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Now I'm probably missing something but, every time I hear this "Humpty Dumpty" example (and others like it) I automatically think of a flag flapping in the wind. If you were to time reverse this scenario then the wind would change direction but the flag itself will be pointing in the wrong direction. Is this an example of spacetime-symmetry or some kind of T-asymmetry? It seems to me that, for the flag example at least, space as well as time must be reversed in order for the laws of physics to properly apply. Like I said, "I'm probably missing something but, ..." Regardless of the flow of time, shouldn't the flag always be pointing in the same direction as the wind is blowing towards?

Yes - even this example given is an example itself of a symmetry in time. This symmetry is usually called the Big Crunch, or the Omega Point. If gravity successfuly ''collapses'' the universe, which it probably won't, then systems will act as if they are quite literally moving back in time.

If gravity successfully ''collapses'' the universe, which it probably won't, Why not? Are you sure?
then systems will act as if they are quite literally moving back in time."Quite literally"? I don't think so. Please explain what you mean

Why not? Are you sure? "Quite literally"? I don't think so. Please explain what you mean

Sorry if you thought I was incoherent.

Yes, I'm quite sure that there is no immediate gravitational collapse in a model of the universe which has to be accelerating. The acceleration dictates there is just enough matter not to cause a collapse, that there is an antigravitational force now repelling this gravitational action.

And by,'quite literally', I mean dynamical physical systems will begin to move back in time if the universe suffered a collapse. Hawking makes this amusing statement himself in his infamous book, A Brief History of Time.

Yes, I'm quite sure that there is no immediate gravitational collapse in a model of the universe which has to be accelerating. I take it you mean its expansion is accelerating? So what about acceleration, in this sense, "back" (whatever that means) to the primordial singularity? Is this acceleration or not?
The acceleration dictates there is just enough matter not to cause a collapseDoes it? Are you sure? I am not convinced. Maybe it's the other way round? That is, there is "just enough matter" to dictate accelerated expansion? Which is it? It seems to me to make difference


And by,'quite literally', I mean dynamical physical systems will begin to move back in time if the universe suffered a collapse. I find it hard to follow your thought process here. Let's try this: over time, any closed system will, with very high probability, evolve from a state of low entropy to one of high entropy.

Suppose we now allow our system to evolve from a state of high entropy to one of low entropy (as in "big crunch"). Why does this mean that time is reversed? Are you perhaps thinking of Eddington's pop-sci assertion that entropy increase is the "arrow of time"?

I suspect you are.

BTW I am not proud; I am quite happy to be corrected!

In all sake of being clear, as far as I understand it, there really isn't such a thing as a direction in time. No such thing as a true arrow. But a universe collapsing on itself would be like changing the temporal feature of the systems we are dealing with, and this includes changing their CPT-symmetries. As far as the universe would be considered, it's evolution would now be coming back to whence it began, a completely symmetry in time.

And I said it's accelerating, and I thought it was obvious why I said this. Before acceleration, we simply thought it was expanding, meaning the chances of gravity taking hold and slowing it down would have been quite high. But now since the observable universe is now seen to be accelerating many multitudes the value of c, we now realize that the universe can't be generally made of this attractive gravitational matter we are made of - there must be some other stuff out there making it acclerate and overcome the power of gravity.

And I don't understand why you made you statement on being proud.

there really isn't such a thing as a direction in time. Oh? Is this, or this not a true quote of yours?
then systems will act as if they are quite literally moving back in time. I cannot reconcile these two statements.

Also, maybe you might like to explain the following
changing their CPT-symmetries. because I don't quite understand what this means.

Do you?

PS I am well aware that others here do understand this, I am asking if you do......

Duration can't be reversed. If you try you will simply add more duration.


Does time reverse when you travel in your car in one direction, and throw it in reverse and travel the opposite direction? NO! You simply change direction of travel, but the distance traveled increases and the duration of time increases.

Oh? Is this, or this not a true quote of yours? I cannot reconcile these two statements.

Also, maybe you might like to explain the following because I don't quite understand what this means.

Do you?

PS I am well aware that others here do understand this, I am asking if you do......

Well, as far as I am aware, Einstein was the first to proclaim there was no true past or future in his relativity.

From the link http://en.wikipedia.org/wiki/Present

'' Einstein phrased this as: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion" ''

Now, if I would be right, arrows exist to us because of the psychological arrow of time ~ and it highlights why we have a past, present and future-distinction, but quite clearly Einsteins theory posits a problem on the nature of whether such a real arrow exists, wouldn't you say?

For the record, T-symmetry simply states that the laws of physics will always hold true no matter which direction the "arrow of time" is pointing. I meant to state, in the "Humpty Dumpty" example, that the same quantity of force and energy that is recorded as the egg falls off the table and shatters is exactly the same quantity required for the egg to reform and bounce back onto the table. I never intended for this to be a taken as an insightful proclamation of how I think the universe is hardwired. It's simply a question that's been bouncing around my head for several years now. If I had a gun put to my head I would assume that this flag example is a valid example of T-symmetry for the same reasons that energy would seem to spontaneously enter the broken egg and cause it to reform into a hole egg. In other words, the pushing force of the wind on the flag would be reversed and reveal itself as a "sucking" force but, this is an assumption none the less, a.k.a. an educated guess. For some reason I'm thinking that the reversal of pressure is a different type of symmetry altogether than T-symmetry.
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I'm not asking for an elaborate explanation. Is a flag required to point towards the same direction as the wind is blowing in order for it to be considered T-symmetric? If so then, what type of symmetry does this example follow? If not then, ... well, ... why? like I said, you don't have to give an elaborate explanation if you don't want to so long as you know the answer.

For the record, T-symmetry simply states that the laws of physics will always hold true no matter which direction the "arrow of time" is pointing. I meant to state, in the "Humpty Dumpty" example, that the same quantity of force and energy that is recorded as the egg falls off the table and shatters is exactly the same quantity required for the egg to reform and bounce back onto the table. I never intended for this to be a taken as an insightful proclamation of how I think the universe is hardwired. It's simply a question that's been bouncing around my head for several years now. If I had a gun put to my head I would assume that this flag example is a valid example of T-symmetry for the same reasons that energy would seem to spontaneously enter the broken egg and cause it to reform into a hole egg. In other words, the pushing force of the wind on the flag would be reversed and reveal itself as a "sucking" force but, this is an assumption none the less, a.k.a. an educated guess. For some reason I'm thinking that the reversal of pressure is a different type of symmetry altogether than T-symmetry.
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I'm not asking for an elaborate explanation. Is a flag required to point towards the same direction as the wind is blowing in order for it to be considered T-symmetric? If so then, what type of symmetry does this example follow? If not then, ... well, ... why? like I said, you don't have to give an elaborate explanation if you don't want to so long as you know the answer.

I do believe I said CPT-Symmetry because an electron moving back in time has been modelled with different symmetries - even in a picture of the universe moving back in time would exhibit an electron moving back in time, which for arguements sake, is how we model the positron.


''Properties of antiparticles
A particle's wave function can be changed to that of its antiparticle by applying the charge conjugation, parity, and time reversal(which, contrary to the name, involves complex conjugation in addition to replacing t with -t) operations.

The charge conjugation operator has no effect on the momentum. The parity operation negates the momentum, since -∂/∂x=∂/∂(-x). The time reversal operator also negates the momentum, because the momentum operator is changed from to . Thus the net effect of the CPT operation leaves the momentum unchanged.

The energy is unchanged by the parity and charge conjugation operators. The time reversal operator also leaves the energy unchanged as shown. Complex conjugation negates the energy(see above argument for momentum). Replacing t with -t also negates the energy(see above argument for momentum under parity transformations). Thus the net effect of time reversal leaves momentum unchanged, as was to be shown. Since energy is invariant under the C, P, and T operators, it is invariant under CPT transformations as well.''

http://www.fact-index.com/a/an/antiparticle.html

However, I do know it's not the general consensus to treat the positron as really an electron going back in time, but mathematically it is consistent.

Well, as far as I am aware, Einstein was the first to proclaim there was no true past or future in his relativity.

From the link http://en.wikipedia.org/wiki/Present

'' Einstein phrased this as: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion" ''

Now, if I would be right, arrows exist to us because of the psychological arrow of time ~ and it highlights why we have a past, present and future-distinction, but quite clearly Einsteins theory posits a problem on the nature of whether such a real arrow exists, wouldn't you say?Well now, indirect appeals to authority won't do! As in, you quote what Wiki says what Einstein says and expect us to take it as gospel.

Why should we? Can you not make the argument on your own behalf? Strange as it may seem, we all here have access to the internet and can look at Wikipedia any time we want

So, although I am well aware of the reasons for E.'s somewhat throwaway statement, perhaps you would like to carefully step us through the following conundrum:

Classically, cause precedes effect, temporally. If there is no objective distinction between past, present and future, does this mean that there are situations where the effect can precede the cause except "in our own minds"?

Why not? Or conversely how can this be? (In your own words please!)

Well now, indirect appeals to authority won't do! As in, you quote what Wiki says what Einstein says and expect us to take it as gospel.

Why should we? Can you not make the argument on your own behalf? Strange as it may seem, we all here have access to the internet and can look at Wikipedia any time we want

So, although I am well aware of the reasons for E.'s somewhat throwaway statement, perhaps you would like to carefully step us through the following conundrum:

Classically, cause precedes effect, temporally. If there is no objective distinction between past, present and future, does this mean that there are situations where the effect can precede the cause except "in our own minds"?

Why not? Or conversely how can this be? (In your own words please!)

I don't need to ramble on about this with you.

"Need"? No, but I would certainly enjoy it if you gave it a try. Your choice however

Originally Posted by Green Destiny
I do believe I said CPT-Symmetry because an electron moving back in time has been modeled with different symmetries - even in a picture of the universe moving back in time would exhibit an electron moving back in time, which for arguements sake, is how we model the positron.
CPT symmetry is not, as I understand it, the same thing as T-symmetry, C-symmetry, P-symmetry or even CP-symmetry. http://en.wikipedia.org/wiki/CPT-symmetry states:

Wikipedia


CPT theorem requires the preservation of CPT symmetry by all physical phenomena. It assumes the correctness of quantum laws and Lorentz invariance.


CPT symmetry is recognized to be a fundemental property of physical laws. In order to preserve this symmetry, every violation of the combined symmetry of two of its components (such as CP) must have a corresponding violation in the third component (such as T); in fact, mathematically, these are the same thing. Thus violations in T symmetry are often referred to as CP violations.


The commutation relations of the Hamiltonian, and the Lorentz generators, guarantees the Lorentz invatiance implies rotational invariance, so that any state can be rotated by 180 degrees. Since a sequence of two CPT reflections is equivalent to 360-degree rotation, fermions change by a sign under two CPT reflections, while bosons do not. This fact can be used to prove the spin-statistics theorem.

Before we can start talking about the localized micro-enviroments of electrons and positrons, you'll have to answer this macro question. Does a flag have to point in the same direction as the wind is blowing in order for it to be considered T-symmetric?

CPT symmetry is not, as I understand it, the same thing as T-symmetry, C-symmetry, P-symmetry or even CP-symmetry.

Forgive me, but that is not how I read the document.

It says that T-symmetry for microscopic systems (and we are allowed to invoke this) http://en.wikipedia.org/wiki/T-symmetry , and it furthers by stating that ''Thus violations in T symmetry are often referred to as CP violations'' - it would seem CPT violation is in fact mathematically-equivalent to saying a violation in CP is a violation in T, and vice versa.

Originally Posted by Green Destiny
Forgive me, but that is not how I read the document. It says that T-symmetry for microscopic systems (and we are allowed to invoke this) ..., it furthers by stating that "Thus violations in T symmetry are often refferred to as CP violations" - it would seem that CPT violation is in fact mathematically - equivalent to saying a violation in CP is a violation in T, and visa versa.
If I knew more about this topic I wouldn't have needed to start this thread. I can't debate an answer I do not know. It is my understanding that (through wiki):
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C symmetry means "the symmetry of physical laws under charge-conjugation transformation. Electromagnetism, gravity, and the strong interaction all obey C-symmetry."
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P symmetry (parity transformation) "is the flip in sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates."
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"CP symmetey states that the laws of physics should be the same if a particle were interchanged with its antiparticle (C symmetry), and left and right were swapped (P symmetry)." It's in the violations of CP-symmetry where particle relationships are found.
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"T symmetry is the symmetry of physical law under a time reversal transformation:" It goes on to say; "Physicists also discuss the time-reversal invariance of local and/or macroscopic description of physical systems, independent of the invariance of the underlying microscopic physical laws."
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"CPT symmetry is a fundamental symmetry of physical laws under transformations that invole the inversions of charge, parity, and time simultaneously."
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My question is a macroscopic description independent of the invariance of the microscopic physical laws. In other words. Is a flag flapping in the wind a violation of T-symmetry?

"CPT symmetry is a fundamental symmetry of physical laws under transformations that invole the inversions of charge, parity, and time simultaneously."

To this we probably should ask whether CP is in fact a T symmetry phenom. If it is, then even macroscopic objects are subject to CP violations if and only if there is a T-symmetry break down.

Originally Posted by Green Destiny
To this we probably should ask whether CP is in fact a T symmetry phenom. If it is, then even macroscopic objects are subject to CP violations if and only if there is a T-symmetry break down.
I understand what you are saying. Any reversal of T-symmetry should automatically produce a reversal in CP symmetry because this is considered to be (mathematically) the same thing as CPT symmetry breaking. The thing is, I don't know if this always has to hold true for macroscopic observations. If it does then there would be nothing to distinguish a flag flapping in the wind from a flag being anchored between two poles at both of its ends. Like I said before; "I can't debate an answer I do not know." Besides the direction of the wind, where is the P symmetry of the cloth in this T reversal scenario? Is it negated by an automatic reversal of C symmetry?

Originally Posted by QuarkHead
PS I am well aware that others here do understand this, ...
I am also well aware of this fact. So then, why the silence? Would they prefer me to walk around with a proverbial booger hanging out of my nose? I'm not there yet but I've found this to be quite frustrating in the past.
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The ironic thing is, I started this thread to break the monotony of two extraordinarily tedious extracurricular projects I've been working on. Now I can't get back into their flow. Seeing that Green Destiny is the only member willing to add any input (and I thank you for it), I'm left with no closure what so ever on either front. There is not a single thing I am responsible for that requires me to know anything about CPT symmetries other than my own curiosity. I want to know more but I can't do it on my own. Any input is welcomed (and this goes for you too Green Destiny).

Does it apply to macroscopic bodies? I am not sure.

Is a flag required to point towards the same direction as the wind is blowing in order for it to be considered T-symmetric?
It's a good question. Think about the wave as it moves along the flag...the energy imparted to the flag returns to the breeze via a "whipping motion", giving the energy back to the air in the form of molecular motion, sound, heat, etc. Now, when you run the camera in reverse we cannot normally see this energy returning to the loose end of the flag but you must imagine it: all of this energy in the heat, sound and motion of the air "colludes with itself" in order to create an energy wave that perfectly balances the flags orientation such that it does not turn itself around.

It's much easier to imagine a rigid, rooster-topped wind vane when trying to see this...

STORY A -- Picture a vane being blown towards the west from strong gusts of wind. Now imagine the vane tilted just a hair towards the north-west, but was quickly brought back into line from a strong west-blowing gust which itself it ricocheted off towards the north...

Now reverse the flow of time and the story:

STORY B -- A rooster-topped wind vane is pointed as if it were being blown towards the west, yet the wind is blowing to the east. Through an apparent miracle, the wind cannot spin the vane around correctly. For a moment the vane tilts toward the northwest, but then a "colluding" gust of air comes in from the north, ricochets off of the vane, and again somehow perfectly balances it to remain pointing in its original orientation.

There is no physical law that is broken here, the only difference between story A and B is that A is more likely than B. This exposes the connection between entropy and time. :bugeye:

I need to make it clear that the "corrective" gusts of wind are not the same in each description. On the contrary, the corrective gust in Story A is the corrupting gust in Story B and vice versa. Rereading my post after a good night's sleep made me think this could be potentially confusing.

Originally Posted by RJBeery
There is no physical law that is broken here, the only difference between story A and B is that A is more likely than B. This exposes the connection between entropy and time.
If there is one thing that I've learned through the years it's that nature is anything but intuitive. If I had money on it I would agee that:

... the energy imparted to the flag returns to the breeze via a "whipping motion", giving the energy back to the air in the form of molecular motion, sound, heat, etc. Now, when you run the camera in reverse we cannot normally see this energy returning to the loose end of the flag but you must imagine it: all of this energy in the heat, sound and motion of the air "colludes with iteself" in order to create an energy wave that perfectly balances the flags orientation such that it does not turn itself around.
That being said, I still find it to be odd that the sail of a boat will always point in the same direction no matter the direction time may be traveling. Everything else, such as the waves, the wind and the direction of the boat itself seem to follow P-symmetry, but not the sail. It always points in the same direction. I know that this is the same type of example as the flag example and I accept the fact that this observation does not violate any of the known physical laws. It's just, well, ... so queer. It this a violation of P-symmetry because of the reversal of C-symmetry? Or, was Green Destiny's initial assertion correct ... A reversal in T-symmetry automatically correlates to a reversal of both C&P symmetries no matter what(?).

There is no violation of any sort here. The "queerness" is completely related to the 2nd law of thermodynamics. If we existed in a thermodynamic equilibrium t-symmetry would be plainly obvious, as coordinated incoming waves would be just as likely to be experienced as coordinated outgoing ones (both of which would be exceedingly rare).

That being said, I still find it to be odd that the sail of a boat will always point in the same direction no matter the direction time may be traveling.
Well, I agree that it "seems odd" but it also isn't necessarily true. Recall that the wind pane was perfectly balanced while pointing the wrong direction because of what I labeled collusion of the wind. Have you never, ever seen the sail on a boat be turned in a circle even though the wind was generally blowing in a single direction? What you might be calling turbulence could just as easily be called collusion in that case. Of course the sail pointing in the wrong direction doesn't tend to last very long (because the odds of that happening quickly grow very small) but it does happen all the time.

Originally Posted by RJBeery
There is no violation of any sort here. The "queerness" is completely related to the 2nd law of thermodynamics. If we existed in a thermodynamic equilibrium t-symmetry would be plainly obvious, as coordinated incomming waves would just as likely to be experianced as coordinated outgoing ones (both of which would be exceedingly rare).
Well RJ (if I can call you that) I must say, thank you very much. You've coaxed my mental "weather vain" into its proper (and T-symmetric) direction. As far as I'm concerned, you helped solidify a long standing assumption of mine (assuming nobody else comes along to dispute your claims). Your contribution to this thread is graciously noted. Even though I assumed to correct answer, I know better than to derive a definitive conclusion from an assumption. Thanks again. :cheers:

Five things...

1) Any time you have a hanging booger I'll be glad to hand you a tissue (if I have one). ;)
2) For future reference, if you highlight text from a post and then click the "quote" button it will automatically do the work for you.
3) Calling me RJ is just fine.
4) I don't presume to have all the answers so if anyone else wants to further debate on this subject I would welcome it.
5) Thanks for the graciousness!

Originally Posted by RJBeery
Five things...
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1) Any time you have a hanging booger I'll be glad to hand you a tissue (if I have one). ;)
I hope it will be a clean one, but then again, ... I'm not picky :D .

2) For future reference, if you highlight text from a post and then click the "quote" button it will automaticlly do the work for you.
Yes. Unfortunate for me, my internet browser sucks. I haven't had an internet connection for my PC in over five years so, I have to type everything in by hand (actually, it's with my thumbs :thumbsup: ).

3) Calling me RJ is just fine.
I just wanted to make sure.

4) I don't presume to have all the answers so if anyone else wants to further debate on this subject I would welcome it.
As would I. At least you know that entropy and time go hand in hand.

5) Thanks for the graciousness!
I hope it didn't come across as gushing. I re-read my post today and couldn't stop laughing. You see, I went to my favorite brewpub after work yesterday and indulged myself in more than a few of their latest concoctions. With all due respect, my last post was more of a drunken "I love you man" than anything else (without the slurring and beer breath). That being said, this should not take away from my genuine gratitude that someone who actually knows the difference between an individuals frame of reference and the apparent frame dragging between observers, such as yourself (EDIT: After reading some of your threads, this exact point may have been a little premature. Even still, I see that this topic is of interest to you so, none the less...), contributed more than two sentence to one of my few hard science threads.
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For the record, I know more than I let on but, I can also reconize that I don't know as much as I know I should know. This lack of confidence is what brought me to Sciforums in the first place. I just wish there were more people like you willing to chime in.

someone who actually knows the difference between an individuals frame of reference and the apparent frame dragging between observers, such as yourself
How did frame-dragging enter the picture? Just curious as I don't recall discussing it. Maybe you're confusing me with someone else?

For the record, I know more than I let on but, I can also reconize that I don't know as much as I know I should know. This lack of confidence is what brought me to Sciforums in the first place. I just wish there were more people like you willing to chime in.
I used to think that the atmosphere here wasn't very conducive to sticking one's neck out because the critiques turn to criticisms which quickly degrade to ad hominems. I've changed my mind on this recently because I realized, as long as one can suffer the ad hominems, posters here do put a lot of effort into explaining their knowledge and tearing down other positions which is a useful process. It's an epic battle of fragile egos :)

Originally Posted by RJBeery
How did frame-dragging enter the picture? Just curious as I don't recall discussing it. Maybe you're confusing me with someone else?
You are correct on all points. When I typed that post, I was confusing you with somebody else. After reading a few of the threads you started I quickly realized my mistake. No biggie, you're still cool in my book :cool: . I could have erased my mistake but, I said it none the less.

I used to think that the atmosphere here wasn't conducive to sticking one's neck out because the critiques turn to criticisms which quickly degrade to ad hominems. I've changed my mind on this recently because, I realized' as long as one can suffer the ad hominems, posters here do put a lot of effort into explaning their knowledge and tearing down other positions which is a useful process.
This is very good advice. I can take constructive criticism as long as it's just that, constructive. My personality will not allow me to act authoritive in matters of true science.