Hard Light Productions Forums
Off-Topic Discussion => General Discussion => Topic started by: General Battuta on May 14, 2011, 08:36:54 pm
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One of the biggest mysteries left to man.
What is it?
Physics should be time symmetric. Relativity implies all of the universe should exist as one enormous block, past present and future already fixed and complete.
Why do we experience it as moving down a path with a 'now'? Why is there an arrow to causality?
For a while I pondered the possibility that there's simply a 'now', a stage, no past or future to reach - just one instant in which the universe exists, coupled to the past and future only inasmuch as the laws of physics dictate how the layout of the stage will change. But relativity requires time to be accessible in a cross-sliced fashion.
This question is critical because it ties into the mystery of consciousness. We do not yet understand why we experience experience the way we do, moment to moment. If we were able to resolve the arrow of time and understand why the now is the now, we might have a better idea. If the mind is a physical system, and the mind experiences time, there must be a physical reason for time.
Ideas?
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We don't exist, existence is an aberration.
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I liked the "universe born within the event horizon of a black hole in another universe" idea that was discussed a while back, though that simply places the burden of explanation further back by having to explain why that parent universe has such an arrow of time as well.
So uh, I really don't know why we only see time flowing in one direction. It's a very strange concept to think about.
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Western Culture is based on a linear timeline (Christianity, Islam, Judahism, Athiesm, Evolutionist, etc.). Essentially Creation (by God, Big Bang etc) and it follows a single line until the end (Rapture, universal doom or whatever). We make decisions which can change the course of this linear timeline, we can alter our own 'world' and such.
India for example, has followed a circular timeline, everything is the same and always will be. If we try to make changes, we are fighting how reality is and in the end we are forced to conform to the circle again.
(Been learning about this in regards to Post-Colonial Literature. Not easy for me to try and comment on.)
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Western Culture is based on a linear timeline (Christianity, Islam, Judahism, Athiesm, Evolutionist, etc.). Essentially Creation (by God, Big Bang etc) and it follows a single line until the end (Rapture, universal doom or whatever). We make decisions which can change the course of this linear timeline, we can alter our own 'world' and such.
India for example, has followed a circular timeline, everything is the same and always will be. If we try to make changes, we are fighting how reality is and in the end we are forced to conform to the circle again.
(Been learning about this in regards to Post-Colonial Literature. Not easy for me to try and comment on.)
This is an interesting point, but the question is more profound than 'mere' culture - there is a clear, intuitive, physical perception of linear local time shared by all humans, even those with perfect episodic memory.
I've updated the first post with a bit more meat.
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Just an aside, doesn't relativity also state that there also no real such thing as "now"? (Relativity of simultaneity) (http://en.wikipedia.org/wiki/Relativity_of_simultaneity)
Case in point, what time is it on Mars right now?
Answer: At time of writing, Mars is about 19 light-minutes from earth, so the current time on Mars actually has a +/- ~19 minute window relative to earth. In other words, there is a roughly 38 minute time interval during which an event on Mars could be seen to be simultaneous to an event on Earth, depending on the velocity of an observer passing through the vicinity.
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Yes, I made that point in the original (and current) version of the first post. It is the primary objection to the 'stage of the now' conception of time.
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I like time.
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I like time.
me too, we have so much in common wanna get married
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I like time.
me too, we have so much in common wanna get married
Until the END of TIME!?
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Well, I mean... you've got irreversible processes in physics. And you're always going to have that net entropy increase going on. So that might have something to do with it, or maybe I'm thinking about it backwards. Are you saying that those kinds of things are just symptoms of this ARROW OF TIME?
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Well thanks to the ARROW OF TIME it is now 4am and im not happy
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I like time.
me too, we have so much in common wanna get married
Until the END of TIME!?
"Till death do us part". :P
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Well, I mean... you've got irreversible processes in physics. And you're always going to have that net entropy increase going on. So that might have something to do with it, or maybe I'm thinking about it backwards. Are you saying that those kinds of things are just symptoms of this ARROW OF TIME?
The thing is that all processes in physics should be totally time-symmetric. You could turn the clock back and the universe would neatly run in reverse. So what establishes the direction of causality? Why do we go only one way?
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Western Culture is based on a linear timeline (Christianity, Islam, Judahism, Athiesm, Evolutionist, etc.). Essentially Creation (by God, Big Bang etc) and it follows a single line until the end (Rapture, universal doom or whatever). We make decisions which can change the course of this linear timeline, we can alter our own 'world' and such.
India for example, has followed a circular timeline, everything is the same and always will be. If we try to make changes, we are fighting how reality is and in the end we are forced to conform to the circle again.
(Been learning about this in regards to Post-Colonial Literature. Not easy for me to try and comment on.)
This is an interesting point, but the question is more profound than 'mere' culture - there is a clear, intuitive, physical perception of linear local time shared by all humans, even those with perfect episodic memory.
I've updated the first post with a bit more meat.
Perhaps the progression of time is fundamentally related to our perception of time. If there was nothing alive to comprehend the passage of time, then how would we know time passes? What is "time"? Perhaps it is a construct only of living consciousnesses - Iron or Helium has no concept of time, for instance. It seems as if the mortal progression of our lives unto an idea (an end, visa vi death), gives the universe it's forward pattern.
What is time measured in to a fly? Is a fly's "seconds" the same as ours? What fundamentally different concepts would that fly understand the world through, compared to ours, if it's seconds were different than ours?
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The thing is that all processes in physics should be totally time-symmetric. You could turn the clock back and the universe would neatly run in reverse. So what establishes the direction of causality? Why do we go only one way?
But WHY should they be time symmetric? Some stuff just only happens one way. You saying there just shouldn't be a "way" in the first place? Hmmm...
Well, one thing I liked from the black hole thread, was the notion that we have this infinite loop of universes containing black holes, that then contain more universes, etc. and so then the irreversibility of time and other stuff arises from the irreversibility of stuff falling into black holes.
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Yes, but that only pushes the question back further by requiring an arrow of time to exist in the parent universe.
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Well, I was kind of operating under the assumption that we had a loop of universes instead of an infinite chain. That is, the "bottom" universe might have a black hole in it that contains the "top" universe. So then information and entropy are endlessly funneled from universe to universe. Which I suppose gives rise to the question "why is there gravity?"
EDIT:
Wait, ****. That doesn't help at all does it? Because even in that case, stuff falls into black holes irreversibly because the gravity of the black hole causes stuff to accelerate towards it. That is, the velocity of nearby stuff increases towards the black hole over time. FUUUUUUUUUUUUU- WHY IS THERE TIME?
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Hmmm, can the anthropic principle be called upon here? Is it possible for life to exist in a universe where time flows backwards or has no preferential direction at all?
...is it even possible for such a universe to exist?!
¯\(°_o)/¯
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Yeah, I don't know. I think for the time being all we can really say is "that's the way it is." To me, it kind of seems like asking why we have EM radiation, or why it propagates at c. What if c were some other value? Would the universe still work? Does it matter?
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One of the biggest mysteries left to man.
What is it?
Physics should be time symmetric. Relativity implies all of the universe should exist as one enormous block, past present and future already fixed and complete.
Why do we experience it as moving down a path with a 'now'? Why is there an arrow to causality?
For a while I pondered the possibility that there's simply a 'now', a stage, no past or future to reach - just one instant in which the universe exists, coupled to the past and future only inasmuch as the laws of physics dictate how the layout of the stage will change. But relativity requires time to be accessible in a cross-sliced fashion.
This question is critical because it ties into the mystery of consciousness. We do not yet understand why we experience experience the way we do, moment to moment. If we were able to resolve the arrow of time and understand why the now is the now, we might have a better idea. If the mind is a physical system, and the mind experiences time, there must be a physical reason for time.
Ideas?
First off, why must physics be time-symmetric, as redsniper noted? I mean, for the most part it is, sure, but there is no objective reason why this should be the case. There are also at least two cases of physics not being time symmetric at all: thermodynamics and quantum mechanics. Entropy is an obvious one, but QM also is not time-symmetric. Rather, it follows CPT symmetry (if you simultaneously reverse time, charge, and parity, you end up where you were). A less obvious example of time assymmetry is GR. If you time-reverse a black hole, you get a white hole, not another black hole.
Second, I'm not sure what you mean here by "relativity requires time to be accessible in a cross-sliced fashion." It also, to my mind, does not imply that past present and future are fixed and complete; what in the equations leads you to believe this to be so?
Third, why must there be a physical reason for time itself? Why not simply the perception of time? Having the latter is an obvious benefit to the organism. I would argue that the mind is a physical system, and it gives us the experience of time because it was evolutionarily advantageous to do so. It chooses irreversible processes for what are again seemingly obvious reasons (this is where it gets a bit circular).
Just an aside, doesn't relativity also state that there also no real such thing as "now"? (Relativity of simultaneity) (http://en.wikipedia.org/wiki/Relativity_of_simultaneity)
No, it states that there is no concept of a universal now. If there was no now at all, you couldn't talk about the time coordinate having any value in any frame whatever. Rather, what is happening "now" is frame-dependent, but "now" is not an obsolete concept.
Hmmm, can the anthropic principle be called upon here? Is it possible for life to exist in a universe where time flows backwards or has no preferential direction at all?
...is it even possible for such a universe to exist?!
¯\(°_o)/¯
What would "time running backwards" be? If you flip time around, in QM at least you flip the antimatter and matter states, so there's nothing necessarily special there. You don't really run into problems in GR, either (black holes become white holes, etc.). The Friedman equations look weird, but if the universe is either inhomogenous or non-isotropic, they don't apply anyway. Time having no particular direction is also possible (I think), though it involves changing how entropy works (e.g., ALL processes are now reversible, perpetual motion machines are possible, etc.), and all the wonderfully weird stuff you get out of GR if you invent negative matter and such would probably be possible as well. Well, QM would also be radically different, but I still think such a universe is at least conceptually possible.
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If the future was set in stone, then a lot of the probabilistic properties of quantum physics would not work at all.
As a good basic example - if we take the double-slit diffraction experiment and run it in reverse time, we would see photons being emitted by the shader towards the double slit, go through it, and converge into the original laser emitter.
This would, of course, never be predicted by quantum physics. If you plug variables with appropriate uncertainties into Schrödinger equation, it outputs wave function which is always probabilistic in nature, it won't predict all the photons that go through the double slit to converge in one spot. Hell, it won't even be able to say where one photon came from (without knowing beforehand that it came from the laser emitter). That'd be completely uncharacteristic of quantum mechanics.
It is my view that the inherent randomness of quantum physics makes it unsymmetric on time axis. Every quantum tumbler can go either way (or more), and if you backtrack the process it should only be able to go one way - it's original state. Even if you look at CPT symmetry, quantum mechanics still isn't time symmetric because of the statistical qualities.
Thermodynamics and one-way trip to increasing enthropy is really more about losing information in the process and the fact that running the simulation from END STATE in reverse time and expect it to end up in START STATE is impossible because the original start state information has been lost.
If you have Zoidberg in a pool and he releases the ink in his pouch as the START STATE of an experiment, and END STATE is ink spread evenly into the water and Zoidberg hiding in the middle of the pool, then even if you run the simulation backward from END STATE, you can't really know where all the ink came from just based on the END STATE alone. Time symmetric thermodynamics would be able to recreate the START STATE information from the END STATE (all the ink in Zoidberg's pouch), but that's impossible as the ink is evenly spread to the pool; you can with good reason assume the ink came from the pouch, but you can't know for sure that the ink even became from Zoidberg's pouch, or what was Zoidberg's position at START STATE or his movements mixing the water during the experiment...
Conclusion: Future is fluid and not set in stone. Deterministic, discrete models such as classical mechanics and relativity are outside their application range in this context.
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So it goes.
/Vonnegut
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woopwoopwoop
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Perhaps it also has to do with the movements of the galaxy, and our planet around the sun, combined with a need to address the past with fitting words and dates? Weeks, months and years are things we thought of ourselves, but time itself, well, the only way we can really compare time is what we can perceive because of the four seasons and the birth and death of others, as well as the time they would have generally left to biologically live.
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One of the biggest mysteries left to man.
What is it?
Physics should be time symmetric. Relativity implies all of the universe should exist as one enormous block, past present and future already fixed and complete.
Physics implies none of this. The arrow of time is defined by the presence of a low entropy in the universe.
That's it. Simple as that.
Why do we experience it as moving down a path with a 'now'? Why is there an arrow to causality?
These are two different questions. One is about conscience, another is about the arrow itself.
Let's stick to physics, shall we.
It is very simple, stick with me. Imagine a wave splashin on a beach. All of that action seems quite directed towards one direction of time. Yet, as yourself noted, microscopically one could metaphorically say that it is like "Billiards", where the movements aren't assymetrical at all. So what causes this assymetry in our own scale of perception?
Entropy is the answer. Let's invoke a classical example. We have two boxes of gas. One is a red gas, another is a blue gas. They have "low entropy" in the sense that they are each one neatly arranged in each box. Now we open a gate that was between these boxes, and the gases mix. What happens? The resulting gas becomes a mix between blue and red. No matter how hard you wait, you will never* see the reverse happening. So, although microscopically, all the gas balls are floating and hitting the walls of the boxes as they always were, macroscopically we do recognize a difference in the arrow of time. This happens because there is a million more opportunities for these gas balls to intermix than to magically "divide themselves" into their own boxes again.
This difference is all that is needed to get an arrow of time.
Ideas?
There are more things to say than this, since other questions that are now really interesting begin to form. Why was Entropy so "low" in the beggining of the Big Bang? The answer seems to be that it was at its maximum possible! Entropy depends upon the size of the "pool" so to speak, and the crazy fast inflation of the universe since the big bang lowered Entropy to very small levels.
The future is defined by heat death. It's when even all the mesons degenerate, and all that remains is radiation.... fully homogeneized, with maximum entropy. In that moment, "Time" is no longer meaningful. When all is homogeneous noise, "Time" stops. There is no causality any more, there are no more events to report.
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One of the biggest mysteries left to man.
[...]
Why do we experience it as moving down a path with a 'now'? Why is there an arrow to causality?
[...]
Ideas?
maybe this is helping:
Kant, Critique of Prue Reason
Edition B, p. 13f [Causality as example of a "synthetisches Urteils apriori"; contains a short explaination what Casaulity is]
Edition B, p. 46f ["Trancendental Aethetiscs - Second Part - On the Time"]
=> Both the fact and the way we percieve time and causality are hardwired into our conciousness... It is a necessary fact to constitutes our (human) understanding of reality - reality itself by itself maybe entirely different (but we can't know - we are human)
The fact what we notice slip-ups as Science advances is not a flaw of Reality or Science but our limitation being reached...
"Critique of Pure Reason" contains the most convinient attempt on explainations on the way we percieve reality I've yet encountered and its's from 1787 ...
Though I've admit I've not read the whole book (you can see it that I have to pull the part for Causality form Introduction-chapter of Edition B, while it is actually fully explained in somewhere in "Trancendental Logics") ... but reading CoPR in its full and understanding it is a life-long task as I can confirm from experience: even understanding the indroduction chapters (of both Edition A and B) in full strains the mind (and that's not just because Kant is unable to formulate short sentences)...
ps. I still wonder how I managed to pass the exam on that lecture... maybe I'll find out once I get the exam back (the results have been released but actual sheets of paper are stuck somewhere in my university's administration - common german problem)
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Yes, I made that point in the original (and current) version of the first post. It is the primary objection to the 'stage of the now' conception of time.
The following is more about conciousness in general than about the passage of time specifically, but it seemed relevant as you touched on the former as well.
Recent scientifice research discusses that we make our choices before our consciousness knows what we choose... what always irked me is that this does not begin to answer the question what comes before the decision... which may as well be conciousness... again.
Wouldn't it be rather plausible if conscious review of decisions was just one stage in a circular decision loop.
Would it then even matter if we "only" review our choices after we made them when that constant review could as well influence the next decision cycle(s)?
I.e. Does it matter if conciousness comes after decision if it also comes before every decision?
We may as well make our decisions before we become aware of them, but is there any reason other than blind assumption that decisions are completely unrelated to any conscious thought that we had *before* we made them? (It's been a while since i digged into the field, so please enlighten me if I'm missing something.)
That line of thinking goes hand in hand with linguistic theory and the "monitor hypothesis" btw.
I.e.: If foreign language learners actively/conciously review their language according to the grammatic rules they learned while the speak/write, the language they produce is very different than when they simply write or speak "without thinking" about it: So conscious appliance of rules to actions while performing those actions does obviously influence the outcome.
Couldn't conciousness well have a similar effect on decisions?
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The thing is that all processes in physics should be totally time-symmetric. You could turn the clock back and the universe would neatly run in reverse. So what establishes the direction of causality? Why do we go only one way?
Quite a lot of macroscopic processes are actually not time symmetric. Also, don't mix up that Mathematics allow for a negative time solution which might or might not happen in a physical real world. There might be negative time, or there might not.
Nevertheless, you are now meditating on Physics issue that even Physicists themselves are not very familiar with. What is time is a fundamental question in Physics, and currently there's no answer.
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People assume that time is a strict progression of cause to effect, but *actually* from a non-linear, non-subjective viewpoint - it's more like a big ball of wibbly wobbly... time-y wimey... stuff.
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The thing is that all processes in physics should be totally time-symmetric. You could turn the clock back and the universe would neatly run in reverse. So what establishes the direction of causality? Why do we go only one way?
Quite a lot of macroscopic processes are actually not time symmetric. Also, don't mix up that Mathematics allow for a negative time solution which might or might not happen in a physical real world. There might be negative time, or there might not.
Nevertheless, you are now meditating on Physics issue that even Physicists themselves are not very familiar with. What is time is a fundamental question in Physics, and currently there's no answer.
Yeah, that's exactly why we have this thread, to talk about it.
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Consciousness is not an objectively observable phenomenon. Your question in the OP is an unfalsifiable intellectual neurosis with no meaningful answer. Good luck. :)
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The thing is that all processes in physics should be totally time-symmetric. You could turn the clock back and the universe would neatly run in reverse. So what establishes the direction of causality? Why do we go only one way?
Quite a lot of macroscopic processes are actually not time symmetric. Also, don't mix up that Mathematics allow for a negative time solution which might or might not happen in a physical real world. There might be negative time, or there might not.
Negative time? Lol. That's as meaningless as saying there might be a "negative down slope".
Nevertheless, you are now meditating on Physics issue that even Physicists themselves are not very familiar with. What is time is a fundamental question in Physics, and currently there's no answer.
Utter bollocks. Time is simple to understand, and if you had only avoided certain physicists who are seemingly mesmerized with the obvious (I'm looking at you, Sean Carroll), and instead went to listen to the real giants like Feynmann, you'd see that this is not even a puzzle in physics.
What is indeed puzzling is our own perception of time. But this is going to be solved by neuroscience, not physics.
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Negative time? Lol. That's as meaningless as saying there might be a "negative down slope".
Utter bollocks. Time is simple to understand, and if you had only avoided certain physicists who are seemingly mesmerized with the obvious (I'm looking at you, Sean Carroll), and instead went to listen to the real giants like Feynmann, you'd see that this is not even a puzzle in physics.
What is indeed puzzling is our own perception of time. But this is going to be solved by neuroscience, not physics.
Observation: You seem to have pretty bold statements of the topic considering your education. Which begs the question are you absolutely sure you understood the underlying theories?
For some reason, there seems to be a minimum time step that can possibly observed by the current knowledge. The current understanding is that there is no way to know whether time is even continuous or stepwise and same applies for the usual three dimensions. I can't even fathom what step like time progression would mean in the context of the world. Nor can I get my head around how do the proposed extra dimensions work in quantum world, and have their existence been confirmed.
There's quite a lot of research work to be done to take out those orders of magnitude to be able to observe processes that happen within Planck time, whether that is even possible or not I don't know.
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Negative time? Lol. That's as meaningless as saying there might be a "negative down slope".
Utter bollocks. Time is simple to understand, and if you had only avoided certain physicists who are seemingly mesmerized with the obvious (I'm looking at you, Sean Carroll), and instead went to listen to the real giants like Feynmann, you'd see that this is not even a puzzle in physics.
What is indeed puzzling is our own perception of time. But this is going to be solved by neuroscience, not physics.
Observation: You seem to have pretty bold statements of the topic considering your education. Which begs the question are you absolutely sure you understood the underlying theories?
What do you know about my education? I've been a finalist in physics olympiads in my country, to which I had to learn quantum physics. Thermodynamics is ****ing easy in comparison.
For some reason, there seems to be a minimum time step that can possibly observed by the current knowledge. The current understanding is that there is no way to know whether time is even continuous or stepwise and same applies for the usual three dimensions. I can't even fathom what step like time progression would mean in the context of the world. Nor can I get my head around how do the proposed extra dimensions work in quantum world, and have their existence been confirmed.
No, their existence has not been confirmed, they are astonishingly tiny. Imagine something tinier than an electron. Then imagine something more tinier than that. There yet? No, not even close. It's megatiny. And things that are so tiny as that require huge swaths of power to unravel. Solar System sized particle accelerators.
The fact that time is not continuous, but rather "bubbly" in planck's scale, is a direct consequence of quantum mechanics. There are no problems here, except if you have too many classical prejudices runnning in your brain. Even then, you'll be fine, if you think that "time" as measured by, say, the scale of atoms, is too far away from planck's scale for these bubbliness to matter in the equations.
In these scales, the arrow of time is meaningless. These are "billiard balls" doing their thing, symetrically in time.
There's quite a lot of research work to be done to take out those orders of magnitude to be able to observe processes that happen within Planck time, whether that is even possible or not I don't know.
Solar System Scale. Everything is possible, but everything has a cost. And this is irrelevant to the issue of the arrow of time (there are questions whose answer is not located at the deep end of everything, be them strings, branes, or whatever).
EDIT: Here, there are good videos on the net about these issues, specially when they are lectures by actual top physicists. And there were no greater physics lecturers than Feynman, so I'll give you this:
http://www.youtube.com/watch?v=_Kab9dkDZJY
"Richard Feynman - The distinction between past and future"
I hope it is relevant to the thread :p
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Negative time? Lol. That's as meaningless as saying there might be a "negative down slope".
Why? Time is dealt with in most areas physics by ascribing it a coordinate. This coordinate may have any possible value; the zero point is one of convenience. So negative time is certainly possible.
Utter bollocks. Time is simple to understand, and if you had only avoided certain physicists who are seemingly mesmerized with the obvious (I'm looking at you, Sean Carroll), and instead went to listen to the real giants like Feynmann, you'd see that this is not even a puzzle in physics.
What is indeed puzzling is our own perception of time. But this is going to be solved by neuroscience, not physics.
Oh? Then, pray tell, what is time? What does Feynman say about time? I'm not familiar with his writings/discussions on the subject; I want to see direct quotes. EDIT: Didn't see your edit.
These are "billiard balls" doing their thing, symetrically in time.
NO interpretation of QFT (and necessarily, string theory) of any sort is time-symmetric in ANY way, shape, or form.
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Negative time? Lol. That's as meaningless as saying there might be a "negative down slope".
Why? Time is dealt with in most areas physics by ascribing it a coordinate. This coordinate may have any possible value; the zero point is one of convenience. So negative time is certainly possible.
Yeah, it's called "The Past".
Utter bollocks. Time is simple to understand, and if you had only avoided certain physicists who are seemingly mesmerized with the obvious (I'm looking at you, Sean Carroll), and instead went to listen to the real giants like Feynmann, you'd see that this is not even a puzzle in physics.
What is indeed puzzling is our own perception of time. But this is going to be solved by neuroscience, not physics.
Oh? Then, pray tell, what is time? What does Feynman say about time? I'm not familiar with his writings/discussions on the subject; I want to see direct quotes. EDIT: Didn't see your edit.
Yeah well sorry. I didn't mean to say "TIME" is simple, I meant to say that understanding the arrow of time is simple enough, so the claims that this question is still puzzling physicists is just ludicrous.
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NO interpretation of QFT (and necessarily, string theory) of any sort is time-symmetric in ANY way, shape, or form.
Oh **** now you open a can of worms.... (let them rest quiet!)
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No no, let them speak, please. :nod:
Negative time? Lol. That's as meaningless as saying there might be a "negative down slope".
The negative of a negative slope is a positive slope...
And Astronomiya, could you describe why reversing time would involve flipping matter and antimatter states as you mentioned earlier?
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And Astronomiya, could you describe why reversing time would involve flipping matter and antimatter states as you mentioned earlier?
In QFT, if you imagine a normal particle running backwards in time, it turns out to be exactly mathematically equivalent to an antiparticle running forwards in time, and vice versa. So, if time suddenly reversed, matter could be said to become what is now antimatter, and vice versa. It is an interesting interpretation of the underlying physics, and I feel it could very well be reality. I should have been more clear it was only an interpretation, though. The first answer (http://physics.stackexchange.com/questions/391/is-anti-matter-matter-going-backwards-in-time) there says it better.
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Fascinating. I wonder if that might apply to tachyons as well (assuming they exist... which is pretty doubtful).
Also found out my university offers a course in QFT this fall. Think I might sign up for it. :pimp:
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And Astronomiya, could you describe why reversing time would involve flipping matter and antimatter states as you mentioned earlier?
In QFT, if you imagine a normal particle running backwards in time, it turns out to be exactly mathematically equivalent to an antiparticle running forwards in time, and vice versa. So, if time suddenly reversed, matter could be said to become what is now antimatter, and vice versa. It is an interesting interpretation of the underlying physics, and I feel it could very well be reality. I should have been more clear it was only an interpretation, though. The first answer (http://physics.stackexchange.com/questions/391/is-anti-matter-matter-going-backwards-in-time) there says it better.
The famous notion describes every proton and antiproton in the universe as a single particle moving backwards and forwards through time.
(i never bought it, but it's cool)
(that proton is a champ)
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What do you know about my education? I've been a finalist in physics olympiads in my country, to which I had to learn quantum physics. Thermodynamics is ****ing easy in comparison.
You said yourself you are an architect. Participating in Physics olympics is good, but now I'd like to see your publications about quantum mechanics and quantum dynamics also.
Any question related to Arrow of Time usually tends to lead to the nature of time itself, hence my answer.
I think the way to start thinking about this is to gather what is known, Planck time is the shortest observable time by the current understanding. Beyond that, we cannot know whether time is stepwise or continuous.
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Let's be a little careful about E-Dick waving or making definite statements about an unknown quantity please, we can have a discussion without it :)
On subject, I think the problem is that 'Time' is kind of two different sciences. As Luis says, for a human "Time flies when you're having fun", but that's a perception thing. The life of a Star is still the life of a star.
I, for example, cannot image certain reactions taking place in reverse, because that not only implies that time is going backwards, but some major laws are being broken. I think that the concept of it being like a video on rewind probably wouldn't work and that Time is more complex than that.
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I've always thought that the increase of entropy marked the direction of where time flowed.
I remember reading that this made the Big Crunch theory somewhat weird.
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What do you know about my education? I've been a finalist in physics olympiads in my country, to which I had to learn quantum physics. Thermodynamics is ****ing easy in comparison.
You said yourself you are an architect. Participating in Physics olympics is good, but now I'd like to see your publications about quantum mechanics and quantum dynamics also.
Do you also ask for mathematics papers from your interlocutors if they teach you what matrixes are?
Don't believe me if you want. I've linked you to a good video that is not boring, and should be enough for you. The person in question has done something about quantum mechanics (mother of all euphemisms).
Any question related to Arrow of Time usually tends to lead to the nature of time itself, hence my answer.
Yes, but that's due to the nature of the conversation more than the nature of the question. People like to talk about metaphysics, and so they will ask things like "what is Time itself?", instead of focusing on the answers that were provided to the precisely worded question, that was about why there is an arrow of time at all. Which has a simple answer. QM et al may not be time symmetrical, but as I said, it's a can of very difficult worms that are not that relevant to upper scales of existence, so to speak. Entropy really is the key to understand why we do remember about the past and not the future, why time really seems assymetrical to us.
I think the way to start thinking about this is to gather what is known, Planck time is the shortest observable time by the current understanding. Beyond that, we cannot know whether time is stepwise or continuous.
Or if those categories are even useful. Mostly, they seem not to be. There are no hidden variables inside the quantum soap, which means that these questions are irrelevant.... and specially irrelevant towards the theme in question. You're trying to answer a question about the forest using solely a microscope. You're missing the big picture, where the stuff is actually happening.
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I've always thought that the increase of entropy marked the direction of where time flowed.
You thought correctly.
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I've always thought that the increase of entropy marked the direction of where time flowed.
You thought correctly.
Not quite - or at least, not completely. The thermodynamic arrow of time is not an adequate explanation and does not even encompass all known arrows of time (though it gets most of them, including, in the modern synthesis, the quantum arrow of time).
There have also been a number of statements here that physics is not time-symmetric, but at the subatomic level this seems like far too strong an assertion for me - at least off the top of my head I believe most subatomic processes are time-symmetric. The obvious exceptions are (probably) some weak forces processes. I am particularly interested in the weak arrow of time as it seems to provide a possible (how well-substantiated?) explanation for the predominance of matter in the universe.
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Do you also ask for mathematics papers from your interlocutors if they teach you what matrixes are?
Don't believe me if you want. I've linked you to a good video that is not boring, and should be enough for you. The person in question has done something about quantum mechanics (mother of all euphemisms).
I should have done that even more when I was in the University back then. If a teacher is smart, he's glad his student is curious.
By all indications, what you are doing here is repeating what Feynmann said without deeper understanding why things are the way they are. Feynmann has a lot of merits in different fields of Physics, including popularization of the quantum world. There's a catch though, by only reading the popularized texts one is still unable to predict what will happen once the question is not mentioned or covered by that particular text. The other thing to consider is that the image you get from the popularized text might sound reasonable, but could still be very much wrong - a convenient lie that makes understanding easier if you have the necessary background, or to give you an approximate mental image of what's going on if you don't. But there is still a possibility that you got it all wrong too! Hence I ask your publications on the field. I don't consider myself an expert in the field (with a possible exception of photons) and reserve that I might actually have it wrong, but I also give Feynmann the possibility of being wrong. Bear in mind, the way he describes some of the quantum interactions are how he understood them and the justification of continuing to use them is that they seem to work and describe the reality adequately.
I also have a (faint) recollection that Feynmann had a rather short temper on students who just parroted the results and really pushed his students to get over that.
Battuta, I get the feeling that you are also aiming at something else by this question. What would be your hypothesis on the weak arrow of time?
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Battuta, I get the feeling that you are also aiming at something else by this question. What would be your hypothesis on the weak arrow of time?
Well I'm not really sure, I haven't kept up on it - but am I wrong in recalling that there are certain (apparent) time asymmetries in kaon decay that might have ramifications for cosmology?
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Well I'm not really sure, I haven't kept up on it - but am I wrong in recalling that there are certain (apparent) time asymmetries in kaon decay that might have ramifications for cosmology?
Nope. Read on below.
There have also been a number of statements here that physics is not time-symmetric, but at the subatomic level this seems like far too strong an assertion for me - at least off the top of my head I believe most subatomic processes are time-symmetric. The obvious exceptions are (probably) some weak forces processes. I am particularly interested in the weak arrow of time as it seems to provide a possible (how well-substantiated?) explanation for the predominance of matter in the universe.
The electromagnetic and strong interactions are time-symmetric so far as we know, as is our only field theory of gravity (Newton). However, GR is not, which leads me to believe that the eventual theory of quantum gravity we come up with won't be either (especially with Gravity Probe B just having confirmed both effects it was looking for to good precision). As you noted, the weak interaction isn't time-symmetric either, due to its CP-violation.
CP-violation in the very early universe is almost certainly part of the explanation of baryogenesis; however, it is not the only necessary condition. There are three of these, called the Sakharov Conditions (http://en.wikipedia.org/wiki/Baryogenesis):
1. Baryon number must not be conserved.
2. C- and CP-violation must occur. (Note that this is fully equivalent to saying T-violation must occur if CPT-symmetry holds)
3. The interaction must not take place in thermal equilibrium.
What is interesting is that the strong interaction doesn't seem to cause CP-violation, seeing as there are terms that could easily do it in the QCD Lagrangian. However, if these terms are not zero or extremely close to it, you would expect to see the neutron have an electric dipole moment about a billion times stronger than it is experimentally constrained to have. The upshot of this is that CP-violation in the Standard Model is not nearly strong enough to cause the distribution of matter seen today (according to Wiki, using weak interaction CP-violation, you get enough baryons to make all of one galaxy). So either strong CP-violation occurs at extremely large energies, or there's new physics there we don't understand yet. It's a really neat question to think about.
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The electromagnetic and strong interactions are time-symmetric so far as we know, as is our only field theory of gravity (Newton). However, GR is not, which leads me to believe that the eventual theory of quantum gravity we come up with won't be either (especially with Gravity Probe B just having confirmed both effects it was looking for to good precision). As you noted, the weak interaction isn't time-symmetric either, due to its CP-violation.
How is electromagnetic interaction time-symmetric when the behaviour of photons (which are the bosons of electromagnetic interaction) is clearly not time-symmetric?
In fact I don't see any part of any interaction described in quantum mechanics to be time-symmetric due to the statistical nature of wave functions which is what quantum mechanics provides as far as predictive power is concerned (Schrödinger and Dirac equations mainly).
It's like... if you have a mathematical function f(x)=y with input set and output set. To be a valid function, every input value must result in one output value, but several input values can have the same output value.
However, the function can only have inverse function f-1(y)=x if each input value has an individual output value.
If there are several input values that produce the same output value, then if you invert the function you end up in a situation where the inverse input set (original output set) has values that would need to produce several output values, and this means the inverse function is not a valid function.
Quantum mechanics sort of has a similar situation. With proper progression of time, you have input set of values that you feed into Schrödinger equation and if you feel particularly masochistic, Dirac equation - and they spit out a wave function that will give you a good idea where the particle will end up. The problem here is that the output is a wave function rather than a discrete value.
Now, it is possible (to some extent) to invert these functions - if you have the actual wave function that you know. However if you look at the situation from inverted time perspective, you'll see some values (with appropriate uncertainties) for a particle's momentum and location, rather than the full wave function of them.
So now it becomes impossible to construct the particle's original input values from its future values, because (to use Copenhagen interpretation terminology) the wave function has collapsed and doesn't exist any more. Knowing a particle's momentum and location makes it impossible to know the actual wave function the particle used to have. If you have several observations for a particle's values, then you can approximate a wave function, but a time-symmetric quantum theory should be able to do the impossible of extrapolating the wave function out of a single observation.
This becomes even more problematic when you consider that a time symmetric quantum theory should be able to, let's say, look at individual photons passing through a double slit in inverted time, coming in from different directions from the shader and converge in their original emitter location.
I understand you were talking about sub-atomic processes but there is no fundamental difference between sub-atomic and superatomic processes, just as there's no difference between microevolution and macroevolution.
As an example, electromagnetic interaction is transmitted via photons (virtual and real); therefore the problems with photon behaviour in inverted time are very much relevant to any process involving electromagnetic interaction...
And same problems would be evident in any quantum model which relies on wave functions rather than discrete predictions...
At least, that is my reasoning. If you can spot any obvious errors in my argumentation, please do point them out, as I'm fairly tired at the moment and ready to go to bed. :nervous:
EDIT: Of course, how much this is apparent depends on the interaction in question. Z- and W-bosons are fairly massive particles, as is gluon; as a result, they may exhibit more particle-like tendencies than wave-like tendencies in most situations - but due to wave-particle duality, they would still have wave-like characteristics to some extent... and that sort of throws a wrench in the time-symmetry thing, as far as I'm concerned.
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Your thinking on the matter is not quite right, but I'm not entirely sure where you're going wrong right now. Here's a quick proof that QED has T-symmetry:
By the CPT Theorem, all interactions in the universe have CPT symmetry. Electromagnetism has both charge and parity symmetry. That is, it behaves exactly the same way if we swapped the label of all charges (which should be obvious), and if we rotate by 180 degrees in ONE spatial dimension (this requires a little more thought to see; consider point charges first, then extend it to diffuse charge distributions via superposition). Therefore, via the CPT Theorem, the EM interaction must have T-symmetry as well, for if it did not, it would break CPT-symmetry, which it does not. QED
Also remember that while QED and QCD might be time symmetric, QFT as a whole is not.
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Your thinking on the matter is not quite right, but I'm not entirely sure where you're going wrong right now. Here's a quick proof that QED has T-symmetry:
By the CPT Theorem, all interactions in the universe have CPT symmetry. Electromagnetism has both charge and parity symmetry. That is, it behaves exactly the same way if we swapped the label of all charges (which should be obvious), and if we rotate by 180 degrees in ONE spatial dimension (this requires a little more thought to see; consider point charges first, then extend it to diffuse charge distributions via superposition). Therefore, via the CPT Theorem, the EM interaction must have T-symmetry as well, for if it did not, it would break CPT-symmetry, which it does not. QED
Also remember that while QED and QCD might be time symmetric, QFT as a whole is not.
OK here's the problem I have with this, because two image tells more than two thousand words.
(http://img339.imageshack.us/img339/9156/quantumproblemnormaltim.png)
Here we have a classic double-slit experiment. Coherent light (or individual photons) are emitted from a light source, travel through double slit that is narrower than photon's wavelength, and an interference pattern emerges. The interference pattern can be characterized by a wave function which tells us the probability for different arrival locations on the shader. It's impossible to know exactly where individual photons emerge, but in statistical analysis the predictive power of the wave function is incredible.
Now, when we reverse the time we have the following situation:
(http://imageshack.us/m/855/3898/quantumprobleminverseti.png)
We have the shader emitting photons into the direction of the double slit, and after they pass through the slit they... somehow should converge to their original location.
In the context of quantum mechnics, this would require a wave function with just one insanely high spike at the middle - probability of each photon arriving at their original location on the emitter should be 1, and I have a big problem with this expectation.
If we assume the model to be time symmetric, then we should expect the model to deal with this dilemma somehow and predict that all the photons coming from different directions will converge to the light source (which, in inverse time, acts as a photon absorber rather than emitter but eh, details). To be time-symmetric, a model needs to be able to be run from status A to status B, and from status B to status A in inverted time, but much like with inverse functions, you run into big problems when you have output values that correspond to multiple input values...
This is impossible and absurd expectation and, in my mind, it is irrefutable proof that quantum mechanics is fundamentally not time-symmetric. Photons are involved in everything where electromagnetic interactions are handled, and if photons can't be handled in a time-symmetric way in such a simple setting, then by the power of greyskull they can't be handled in a time-symmetric way in more complicated settings such as sub-atomic interactions. If anything, in smaller scale these quantum phenomena would be even more prominent.
Now, this is obviously not proof that the universe is not time-symmetric, although there are some pretty strong suggestions that statistical properties of quantum mechanics have it right and the universe indeed does have an element of randomness (which is impossible to reproduce if you invert time).
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Professor Harald Lesch - What is time? (in german :) ) (http://www.youtube.com/watch?v=9OD2uJEy5CU)
This man can explain everything. Could listen to him all day. Maybe someone knows a good translator? :p
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Herr Doktor, think about the number of photons arriving on the shader first! Is the probability that all the emitted photons hit the shader actually 1?
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Herr Doktor, think about the number of photons arriving on the shader first! Is the probability that all the emitted photons hit the shader actually 1?
Technically that depends on the shader's structure - if it's flat shader, then no, but if it's a half sphere...
The wave function spreads to infinity, and when integrated over negative infinity to infinity, it results in probability of exactly 1 (meaning that all the photons go somewhere), but that is really irrelevant for the issue at hand.
The problem is that all those photons that go through the double slit (regardless of where they end up at in real-time) will come back in inverse time and they WILL converge upon the exact point where their journey began. If the inverse time model predicts a different spot for the photons - or, heaven forbid, a wave function, then clearly the model isn't time symmetric in the sense that I understand the term.
And that's the problem here - as far as I'm aware, truly time-symmetric model would require discrete predictive power with exact solution for an exact experiment, rather than statistical prediction of how multiple repeats of the experiment will happen. Quantum mechanics doesn't provide us with that sort of predictions.
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And the absorption by the slit?
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And the absorption by the slit?
...every photon that goes through the slit, goes through the slit.
This is a tautology.
In inverse time, all those photons come back through the slit from the other direction.
The rest of the photons emitted by the emitter are irrelevant. We can run the experiment with single photons if you'd like, and in inverted time, each of those photons will be reverse-emitted from the location where they ended up, travel to the slit, change their course to align with the original emitter, and impact the emitter (visibly changing the energy state of some electron in the emitter source).
If the theory can't predict that this will happen, then it ain't time symmetric. And the best quantum mechanics offers are statistical predictions, so it seems to me that time symmetry in context of QM should just be abandoned as a bad job.
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I'm not sure if I understood what's the problem then.
However, tracing photons from the emitter to the shader loses some part of light on the slit. The setup is not a true reverse system if you don't include those lost on the slit itself (at exact phase, location, direction, time and polarization) when going through it backwards.
Could you explain why a delta spike as a wave function disproves the whole reverse thing?
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I'm not sure if I understood what's the problem then.
However, tracing photons from the emitter to the shader loses some part of light on the slit. The setup is not a true reverse system if you don't include those lost on the slit itself (at exact phase, location, direction, time and polarization) when going through it backwards.
Could you explain why a delta spike as a wave function disproves the whole reverse thing?
Okay, let's analyze a situation where one photon passes through the slit in real time.
It goes through it (this is established in the premise).
It arrives at the shader somewhere, probability of the location predicted by the wave function.
In reverse, the photon emerges from the shader, goes to the double slit and passes through it.
Then what?
Does quantum mechanics in reverse time handle a double slit as a convergent rather than divergent (interference-inducing) element? If so, can it really predict from one single photon's reversed trajectory that it will hit the original emitter, and even the original electron that happened to emit the photon?
A delta spike wavefunction, even with fairly high "spikyness" (narrow arrival area within reasonable probability) the photon technically could end up anywhere in the wave function's area (which by definition should be in range of negative to positive infinity).
In short, the problem I have is that statistical approach doesn't work with something that has already happened. You get one shot at predicting what will happen - giving a wave function that gives you some approximate where the photon probably came from is a cop-out and provides an infinite amount of incorrect answers, situations which clearly didn't happen (as we observed them).
To be time-symmetric, you should be able to run an experiment and record it; then run it in simulation both forward and backward, starting from start and end states respectively, and you should be able to start from observed end values and end up in start values.
Of course, I'll concede that this is only a problem if we consider the past unchangeable (which, for practical purposes of retaining one's sanity is preferable).
If we view the past just as much unpredictable as the future in QM, then we get into an interesting variant of many-worlds situation where infinite amounts of pasts converge into observed present from infinite amount of different states, and diverge into infinite amounts of futures.
I am unsure if this would have any hope of working with Copenhagen interpretation, but I suppose technically a many-worlds interpretation with multiple pasts and futures could satisfy the insufficient predictive powers of QM when run in reverse time.
The philosophical implications are, however, somewhat disturbing.
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An interesting thought experiment you put up there. Let's see where this leads us.
The thing that I'm thinking is that once the location of the photon is known on the shader, its path might be fixed to a quite a large degree. Could it be so that when passing the slit, it is crucial to have all the surrounding atoms and their electrons to behave exactly the same way as earlier in order to get the photon go opposite in the reversed direction?
I wouldn't worry about the resulting delta yet, we can't know exactly where the photon started to begin with (Heisenberg). Then it goes to the scale of the delta.
Just a couple of thoughts for tonight.
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infinite amounts of pasts converge into observed present from infinite amount of different states, and diverge into infinite amounts of futures.
:eek:
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The thing that I'm thinking is that once the location of the photon is known on the shader, its path might be fixed to a quite a large degree. Could it be so that when passing the slit, it is crucial to have all the surrounding atoms and their electrons to behave exactly the same way as earlier in order to get the photon go opposite in the reversed direction?
I believe that could be, but quantum mechanics does not deal with this possibility because it cannot. To remove the probabilistic nature of quantum mechanics would be to completely throw out the theory in exchange for a more complete one, which as of yet does not exist.
By their very nature, the exact position/momentum of the electrons are unknowable without making a measurement that would change them.
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I think there's some misunderstanding of what T-symmetry really means in this thread. Basically, if you set up a new variable t' = -t, insert it into the equation in place of t, and it comes back the same, the equation has T-symmetry. The Schrodinger equation, for example, does not have T-symmetry by this measure. A particle's position in classical mechanics does:
Let x = v(t)*t. Now insert t'=-t; i.e., reverse time. x does not change sign, but t does, as does velocity, since v = dx/dt, and v' = dx/dt' = dx/(-dt) = -dx/dt = -v. So, x = v(t')*t' = -v(t)*-t = v(t)*t. Therefore, a particle's trajectory has T-symmetry in classical mechanics.
Now let's look at electromagnetism. First, we need Maxwell's Equations (http://en.wikipedia.org/wiki/Maxwell%27s_equations). Gauss's Law (for both electricity and magnetism) is obviously time-symmetric. If this is not clear, consider what produces electric fields: charges, which are constant in time. Faraday's and Ampere's Laws are also time-symmetric, though it might not seem this way at first. The dt's change sign, as does the current term in Ampere's Law. That leaves B, the magnetic field. Because B is generated by currents, when the current changes direction, it changes sign as well. Therefore, the signs cancel and Maxwell's equations (and, by extension, EM) are T-symmetric. This extends to quantum EM as well.
Since Herra's thought experiment must incorporate both the QED Lagrangian and quantum dynamics, it will of course not be time-symmetric. Another way of thinking about this is to realize that reversing time is not like watching a movie backwards; you are fully reversing the direction of time, so that the past is now the future, and the future is now in the past. When time reverses, you don't "go back in time," you reverse the whole direction of its propagation!
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Since Herra's thought experiment must incorporate both the QED Lagrangian and quantum dynamics, it will of course not be time-symmetric. Another way of thinking about this is to realize that reversing time is not like watching a movie backwards; you are fully reversing the direction of time, so that the past is now the future, and the future is now in the past. When time reverses, you don't "go back in time," you reverse the whole direction of its propagation!
Exactly! This is precisely why I think quantum mechanics can't be truly time symmetric. It doesn't give discrete predictions when going forwards in time, so how could it possibly do so when going backwards? It's impossible to run the model backwards from a certain state and make sure the progression stays on the path of what actually happened, when the model isn't confined to a single timeline of future in the first place.
I can understand how classical electrodynamic equations can be time-symmetric, as they don't take into account the small quantum differences... but even classical physics gets into serious trouble with certain things as far as time-symmetry goes - mainly, thermodynamics.
Like the example I used before, it would be impossible for classical thermodynamics to be run in reverse and see Zoidberg's ink converge back into Zoidberg's ink pouch, because the information of the ink's original location has been lost. Similar things happen if you have two sections of cold and warm water, separated by a wall... you remove the wall, and water mixes and temperature evens out - but when you run the model backwards, there is no possibility to know that the water wasn't an even temperature block to begin with, and even less hope of deriving the original temperature distributions. You'd see an even temperature body of water stay where it is, and then a wall being lowered into the middle of the pool for no apparent reason.
Similarly, I could accept that the photon experiment I described could be valid - if there was a way to retain each photon's wave function. I'm sure there would be way to run the wave function through the slit and reverse the slit's effect on the photon stream based on that, and that way you would be able to pinpoint the photons' original emitter location - but this is impossible; you don't know the wave function that causes the interference pattern just by observing individual photons emerging from the shader when you reverse the time. You just know that this photon emerged from the shader and is traveling towards the double slit...
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I never said quantum mechanics was time-symmetric. In fact, it is explicitly not so as you noted (neither the Dirac equation nor the Schrodinger equation are time-symmetric). QED, however, as a subset of it, is. Go test it out on the QED Lagrangian if you want. Not a single term changes sign in the end.
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Another way of thinking about this is to realize that reversing time is not like watching a movie backwards; you are fully reversing the direction of time, so that the past is now the future, and the future is now in the past. When time reverses, you don't "go back in time," you reverse the whole direction of its propagation!
This is an excellent comment.
Regarding Herra Tohtori's thought experiment with a single photon and a dual slit, the following might be relevant to it or not. Suppose a diffraction grating optimized for splitting power between zeroth order and the first order, these diffraction orders are separated by some angle. Now when laser sources are placed in the direction of those orders and both of them fire beams back towards the grating, the beams indeed recombine into one beam and travel towards the original source. This is called a grating beam combiner, though there are better methods of doing the same - I could find only one paper related to researching this. But notice that thin slits are diffraction gratings too.
Now if I think the situation from the classical EM perspective, my answer is that at least when you have the same wavefront starting from the shader directed towards the slit, it will recombine into a direct beam back towards the laser source. Should the slit be a more complex grating, the above thing happens. But I find it difficult to think this in terms of probability functions, and after a slight thinking, Schrödinger equation itself doesn't actually work with photons - and as a personal comment, the thought never crossed my mind earlier (or maybe it's just such a long time since I last read it).
Also, if the nature of the photon travel is probabilistic (electron might emit the photon to any direction), I find it difficult to explain to myself how does a mirror or a lens work as well as it does. QED might give the explanation for that, the answer should be applicable on photons passing the dual slit too. Guess I need to check QED stuff again from the optics perspective, but that'll be tomorrow.
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Also, if the nature of the photon travel is probabilistic (electron might emit the photon to any direction), I find it difficult to explain to myself how does a mirror or a lens work as well as it does. QED might give the explanation for that, the answer should be applicable on photons passing the dual slit too. Guess I need to check QED stuff again from the optics perspective, but that'll be tomorrow.
The QED explanation is actually rather similar to the semi-classical one. The first part of the key is the differing path lengths that photons take from emitter to absorber. For a mirror, they have a basically equal probability of being scattered in any direction by the atom they strike. However, if we consider a source S bouncing light off a mirror to a point P, and then draw out all the paths light could take from S to P, it becomes immediately obvious that there is a minimum path length that can be taken, and that the path length varies from path to path. If we assume that the center of the mirror is point for which ai=ar, the optical path length (OPL) is shortest there, and longest at the edges. The phase of each photon also constantly changes as it flies, so photons following different paths will have different phases when they arrive at P. This is the second part of the key. At any given point in time, the probability that you receive a photon from the center of the mirror is higher than of getting one from the edge, due to the differences in travel time. So, if you draw a phasor diagram of the photons coming off the mirror headed for P, the phasors at the center of the mirror are larger than those at the edges. In addition, since larger OPL differences correspond to larger phase differences between photons, the photons coming from the center of the mirror are in phase with each other, while those only a little ways out from it are out of phase with their counterparts on the opposite side of the center. Thus, an observer at P sees an image of S only in the center of the mirror, since the contributions from the other portions of the mirror cancel each other out.
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Also, if the nature of the photon travel is probabilistic (electron might emit the photon to any direction), I find it difficult to explain to myself how does a mirror or a lens work as well as it does. QED might give the explanation for that, the answer should be applicable on photons passing the dual slit too. Guess I need to check QED stuff again from the optics perspective, but that'll be tomorrow.
It's probabilistic but that really only affects things in quantum scale.
Macroscopic optics is all about wavefronts, which are combined effect of insane amounts of photons traveling in a statistically sufficiently similar way. On individual photons, quantum deviations appear, but on large scale, the wavefront formed by the photons appears united, which is why reflections and refractions work in the first place.
In all optics, there is loss of photons from the wavefront, depending on optical qualities of the mediums and reflective surfaces - scattered or non-uniformly reflected photons are not useful in optics, and avoiding them is the key to observing as much of the photons that arrive into the instrument. Statistically, though, we are unlikely to observe the quantum inaccuracies in each individual photon's arrival location. In terms of physically describing what happens is that the delta spike in the photons' probability functions is narrow enough that without very very small scale instruments, we won't notice any difference whether the photon arrives two picometres this direction or that - it'll still hit the same observation instrument with all likelihood: a pixel, or perhaps a cell in your retina.
Or, the expectation value is almost always very close to where the photon will actually end up.
Quantum inaccuracies really only start to become visible when you look at things in a scale that is at least as small as the deBroglie wavelength of the particle. If you're unable to measure things smaller than this, then you'll likely see the particle's behaviour approximate with classical physics - except in situations where it doesn't, such as the double slit interference experiment, which is perhaps the simplest demonstration of wave-particle duality. In this experiment we FORCE the photons to encounter a formation in the scale of their wavelength, and as a result the photons form up in a typical interference pattern.
In refraction and reflection, individual photons don't typically end up in situations where they would go through something like a double slit - although some statistically predictable amount of photons will scatter into statistically more or less predictable directions - predictability of photon scattering angles depending on whether the optical matter is of regular crystalline quality, or something less regular like gas, liquid, particulate suspension or the like. This is used in x-ray crystallography, where the x-ray photons' scattering angles depend on the qualities of the crystal. But I digress.
If you look at a reflection or refraction in quantum terms you'll notice that even if you handle each photon individually, the statistical prediction of how the wavefront will look after reflection or passing through the lens, it'll be largely intact - sufficiently so that we can recognize it as the original image, if projected on a surface. Remember that wavefronts staying intact depends on the quality of surface they are reflected from, and from the quality of the optical border between mediums that they travel through (as well as the transparency of the mediums, how much scattering occurs etc.). Individual photons don't see any difference between different kind of surfaces - say, glass or paper. When photons are reflected from paper, they are diffused into lots of different directions depending on what part of the paper they hit. But when multiple photons are reflected similarly, then their wavefront remains recognizeable, and our optics can work.
After all, photons never interfere with each other - the interference patterns like the one in double slit experiment, or Newton's rings, results from their own wave characteristic interfering with itself, so a wavefront traveling through a medium is safe from collapsing by photons in it interfering each other into oblivion.
Schrödinger equation itself doesn't actually work with photons
It's true that Schrödinger equation isn't ideally suited for photons (you need to jump through some hoops to use it) but in context of the thought experiment, this argument is irrelevant as the photons can be substituted by an electron beam or individual electrons, and the fundamental result is the same (http://www.youtube.com/watch?v=ZJ-0PBRuthc)...
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I'm aware of QED explanation being quite close to Fermat's principle, though the question I actually have about that is that the photon should then see all the possible paths towards any detector, and somehow it explores all the possible routes simultaneously and chooses the shortest one in space time. But never mind, I'm perfectly happy that the Fermat's principle exists, it makes my work considerably easier. But after having relied on it for several years one though starts to think where does this thing actually stem from. This is similar to one of the memorable quotes I heard in a lecture was from a professor in Electrical Engineering, who stated that after 20 years he now starts to understand the deeper meaning of the Ohm's law... A photon is a time like particle, and it would be interesting think the microscopic situation from its perspective. How does it see the microscopic world when it travels through a medium.
The interesting thing here is that superficially macroscopic tests allow for a time reversal. But once somebody evaluates the situation in microscopic level and counts individual photons, that isn't possible anymore. But, it is unclear to me what is the effect of the electrons in the structure of the slit in a double slit experiment.