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cshalvey
Discussion on Time as a Concept/Theory
Basically trying to capture the discussion that's been going on in chat regarding Time. I'm totally behind and just catching up, but I love hearing about this sort of stuff. (BTW I *know* it's not a question, but hey, I get to bend the rules *sometimes* right?)
We're kind of jumping in halfway through the discussion, so converting to this format might be a bit messy, but here is my assertion summarized. Time is a dimension of reality, along with the three spatial dimensions. We can define forwards in time as the direction in which total entropy increases. Correspondingly, then, backwards in time is the direction in which total entropy decreases. This produces a coherent system and axiomatization of the notion of time.
The real question that there actually is concerns consciousness moreso than time itself. We recognize that we are consciousness put into a particular narrative, that combination of space and time that we view as our reality. It is arguable that consciousness could exist independent of that narrative, but then you're talking more about philosophy than you are about physics.
The debate began here: nbouscal: color is just a human construct agentx5: I agree, nbouscal nbouscal: because we just happen to be able to visually interpret a particular slice of the electromagnetic spectrum agentx5: As is time itself Alternate point of view: Time is an abstract concept, non-real. It is a measured value, it's an extrinsic property, sure I can agree with that. But to say time is concrete is something I strong disagree with. Why? Goes back to the definition of the word first: 1: naming a real thing or class of things 2: formed by coalition of particles into one solid mass 3: or... a): characterized by or belonging to immediate experience of actual things or events b): specific, particular <i.e.: a concrete proposal> c): real, tangible <i.e.: concrete evidence> What is not concrete, is abstract is it not? "Backwards in time := Direction in which entropy decreases." -- my distinguished colleague, @nbouscal's , in describing his point of view This is a concept I disagree with. Entropy is defined by the Gibbs Free Energy Equation as: \(\Delta G = \Delta H - T \Delta S_{intial} \) where \(\Delta G < 0 \), "Spontaneous" \(\Delta G = 0 \), "Equilibrium" \(\Delta G > 0 \), "Nonspontaneous" \(\Delta H =\) change in heat energy (in Joules, BTU, etc.) In layman's terms I could said -\(\Delta\)H means a release of heat from the system/reaction/etc out into the environment (heat release by a fire, steam condensing into water, etc.), +\(\Delta\)H is heat energy taken out of the environment by the system (energy put into boiling water to steam, chemical coldpacks that you administer as First Aid to reduce swelling). T is temperature (average thermal kinetic energy) and \(\Delta\)S is what is known as entropy. Other ways of writing the metric standard for energy (the Joule), in US units it's ft-lbs or BTU: \(\rm 1 \ J = \rm 1\ \frac{kg \cdot m^2}{s^2} = 1\ N \cdot m = \rm 1\ Pa \cdot m^3={}\rm 1\ W \cdot s \) How is time measured? The base unit of time (in all systems we use) is the second. The official defintion since 1967, the second has been defined to be: "The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 (\(\large {}^{133}_{55}Cs\)) atom." It's measured as an abstract unit of change. Change itself is what's being measured, not time. Finally I'd point to why "time travel" is bogus: * Special Relativity shows us that time should slow for the traveler as they travel at a faster speed (magnitude of velocity), and indeed this had held true in experiments so far. * Distance = | Displacement | or Distance = \(\large \sum_{1}^{n}\) | Displacement\(_n\) | In the same way that distances can't be negative, neither can time. You cannot therefore say that just because relative entropy is negative that this represents a change back in time! In fact I can show that with a simple equation: 2n CO\(_2\) + 4n H\(_2\)O + photons → 2(CH\(_2\)O)n + 2n O\(_2\) + 2n H\(_2\)O This is better known as the general reaction equation for photosynthesis, which is endothermic. There is no space time distortion or reversal going on where leaves are. Metaphor: "Burn a forest to ash and it can be regrown, but it will never be like it was before" Even if you CAN reverse everything exactly, it still doesn't change the fact that change occurred. Change occurred and TIME is said to have passed. There are in fact many instances in nature that would make the case that time moves in spiraling cycles, a combination of both linear and cyclical behaviors. This would agree with the notion of time having an "arrow", a direction if you will, but it would not PROVE time as concrete as my college claims.
Thank you for making this topic/question @cshalvey :-) It should prove to be an interesting discussion, as long as it's taken strictly as a matter of logic and philosophy. I would expect that some tempers might flare in this, as this is one of the harder things to explain about the world we perceive as human beings.
@agentx5 Completely agree. Also, in situations where there isn't a universally agreed upon answer, opinions, emotions, and personal philosophy are bound to get involved. For example, I don't see people having these arguments about the conversion equation between Fahrenheit and Celsius ;)
Your definition of second is not an abstract measurement of change, it's a duration. Duration only makes sense within the context of time as a dimension. Duration is a norm defined on that dimension, and the direction is provided by increase in entropy. You can't say that time is an abstract concept any more than you can say that space is an abstract concept. Throughout the discussion you've been talking about reversals, about negative distances, and about a bunch of other stuff that is completely unrelated to anything I've said. I'm not talking about traveling backwards in time. I'm not talking about reversing time. I'm talking about time as a dimensional basis for reality, and defining that basis in terms of entropy. To draw a direct analogy: we can define the x-axis of a coordinate graph in terms of a unit vector. We can then talk about the negative unit vector, which goes in the opposite direction. Despite that definition, we still have the case where all norms are positive. The same thing applies to time. We can talk about what it means to go in the opposite direction of the basis vector for time without needing negative norms.
"Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone. I shall use the phrase ‘time’s arrow’ to express this one-way property of time which has no analogue in space." - Arthur Eddington
I attest time cannot be drawn as a vector. The "arrow of time" Eddington says here is an abstraction. First let's go back to how we define vectors in space in the first place with a little airplane :-) |dw:1342641518710:dw| Now if the airplane flies to one airport an back it's displacement is zero. Using what I said previously: 100 km heading forward to + 100 km heading back from if we use sign conventions letting +x be going to, and -x being heading the other way. 100 km - 100km for a net change (displacement) 0 km But distance? | 100 km | + | -100 km | = 100 km + 100 km = 0 km Question, if this was in distance per time how would it change? See what I mean? Here's another example, a pendulum's period varies only base on the force of gravity and the length of the rotating arm. |dw:1342642271667:dw| It is said to sweep out equal arc lengths in the same time. Think if a metronome if you need a more concrete example. \(\large T \approx 2\pi \sqrt{\frac{L}{g}}\) T = period in units of time L = length of the rod/arm g = local acceleration due to gravity Now, question. According to my interpretation I proposed, are we not REALLY just measuring the effect for the change to repeat itself? This is very hard to put in words, I don't have anything in the English language I can do to properly describe this. But when we said period we're really measuring the effect of gravity to make a sequence of event repeat in a cycle, over and over.
Dimensions should have the ability to draw vectors, magnitudes that have direction. Time only has one direction, as you stated. Therefore I feel it can't truly be a "4th dimension".
Ack I have a typo: | 100 km | + | -100 km | = 100 km + 100 km = 200 km = distance. Forgot to fix when using copy & paste, and I can't edit without deleting the drawings...
First off, a vector is not defined as a magnitude with direction. A vector is defined as an element of a vector space. I know we're on the Physics board, not the Math one, but that distinction is important and it really bothers me when people miss it. Second, every basis vector is unidirectional, time is no different from the standard here. You define the basis vector, and then the opposite direction is derived from the inverse of that vector. It is the same with time. There is no reason to take any issue with the inverse of a vector in the time dimension, we do it all the time in regular speech. "A year ago" refers to a point backwards in time (direction) a distance of one year (magnitude). So even using the inaccurate physics definition of a vector, we're still fine. You're trying to use spatial intuition to argue against time being a vector, which misses the fact that time is a non-spatial dimension. It is distinct and separate from the spatial dimensions. The three spatial dimensions, together with the fourth dimension of time, form the basis of the 'vector space' that we call reality.
Give me a explanation of what you feel defines "vector space"?
A vector space over a field is a set with two binary operations that satisfy certain axioms. Specifically, closure, associative, commutative, inverses, identities, and distributive laws.
Everything I find on vectors says it IS defined as having a magnitude and direction: http://mathforum.org/library/drmath/view/55466.html http://www.physicsclassroom.com/class/vectors/u3l1a.cfm http://en.wikipedia.org/wiki/Euclidean_vector http://mathforum.org/library/drmath/view/55466.html
If you went to the wiki page for Vector instead of the wiki page for Euclidean vector, you'd find the proper definition. Physicists have a habit of defining vectors improperly. It's a systemic problem. There are vectors that do not make sense under that definition.
http://en.wikipedia.org/wiki/Vector_%28mathematics_and_physics%29 <-- lots of options
Lots of options, but the definition is given in the first sentence: "Many special instances of the general definition of vector as \(\mathbf{\text{an element of a vector space}}\) are listed below." (emphasis mine)
Explain to me how vectors in a function space can be accurately defined as objects with magnitude and direction.
Looking at the axioms here: http://en.wikipedia.org/wiki/Vector_space#Definition Show me how time can mathematically work those? Because I see an issue with the units right away (also a common mistake in physics, forgetting to put your units in as you work with the numbers)
What issue? If you have two seconds and add five seconds you have seven seconds. If you have two seconds and multiply by the scalar four, you have eight seconds. There is no issue.
But... You can have 5 m + 5 m = 10 m or 5 m - 5 m = 10 m You can have 5 s + 5 s = 10 s , but you cannot have 5 s - 5 s = 0 s. The "inverse elements of addition" axiom is violated, agreed?
No, not agreed. You can talk about the inverse of a second, a negative second, as being one second backwards in time. We can set the origin as the present moment and talk about positive and negative seconds as forwards and backwards in time from the present moment. So, a vector from the origin (now) to a year ago would be the inverse of a vector from the origin to a year from now.
You're still trying to use physical, spatial notions as the foundation of your argumentation. You have to leave those at the door and argue from axioms.
"being one second backwards in time" How can you say that? It doesn't happen in reality. You cannot go back in time... There's an issue with negative values for time, if you're treating it as a vector. cos(\(\pi\)) = cos(\(180^o\)) = -1 I'm gathering not all vectors have magnitude & direction. Give an example?
To convert your formula into words: "Five seconds before five seconds from now is right now." That is fine, nobody would have a problem with that statement. You can talk about back in time. You can say something happened a year ago. There is no problem here. An example is a vector in a function space. Not sure how you could ascribe direction and magnitude to a vector in a function space.
Then if the axioms for treating time like a vector is true, then the axioms listed should apply to something as complex as this: |dw:1342644420216:dw| But it's non-real, the parametric equations for time in this 2D plane wouldn't even make sense from what I see.
It's easy to argue 5 seconds before 5 seconds have passed is right now, but a bit harder if you want to start treating time has having to obey those properties and still apply meaning to observations witnessed.
You have to recognize the distinction between something being coherent with the axioms and something correlating to your intuitive senses of the world. You can make whatever vector space you want, as long as it adheres to the axioms. Whether or not it will correlate to the real world is a different question. I'm simply asserting that a vector space whose basis is three spatial unit vectors and one time unit vector correlates to the real world. I still don't see any issue, and I don't understand what issue you're having. It's perfectly easy to talk about time as a vector. A year from now is a year from now. A year ago is a year ago. A year before a year from now is today. Two times a year from now is two years from now. All of the axioms hold easily, there is no struggle at all.
But what you're still measuring is the effect of change itself... Any way you want to measure it.
Another example, by the way, that is fun to try to wrap your head around is a vector in \(\mathbb{R}^\omega\). I have been completely unable to figure out how to think of those vectors as having direction, because I don't know how to visualize an infinite-dimensional space. No, what I'm measuring is duration. I'm measuring time. I'm defining a direction on time using entropy as a clock, and I'm defining a magnitude on time using duration.
It's very simple. I'm just defining a basis vector. That basis vector points towards increase in entropy. Everything else just follows naturally.
Within the framework of Einstein's relativity, time is simply one of four local coordinates that can be used to measure the interval between events. For example, if I agree to meet Ilsa at the Gare de Lyon to take the last train to Marseilles on the day the Germans march into Paris, then the time of this event (4.45 PM, 14 June 1940) is just one of the coordinates I need to specify, in my reference frame, the interval between that event and her later walking into my gin joint, of all the gin joints in all the world, in Casablanca in December 1941. The interval has a part that consists of subtracting spacial coordinates -- it's 1,172 miles from Paris to Casablanca -- and a part that consists of subtracting the time coordinate -- it's 18 months between June of 1940 and December of 1941. The math of relativity specifies exactly how you do the subtraction, and add the results up to get an unambigious measure of interval on which all observers will agree. An important fact, however, is that all observers need NOT agree on how much of a given interval is due to spacial separation, and how much to temporal. For Rick, the last time he saw Ilsa can not only seem like yesterday, it can for all experimental purposes *be* yesterday, depending on his frame of reference, while for Ilsa, in another frame, it can be yesterday, last week, 18 months ago, or 18,000 years ago. (The only thing on which both Rick and Ilsa must agree is that Paris came before Casablanca.) In short, time does not have any independent and special existence. It is conceptually no different from a space coordinate. To be sure, we have the odd observational result that time *seems* to be profoundly different than space, to us. Exactly why that is so is still a question that has not been fully answered.
Are we really arguing that time and space are the same thing? x, y, and z can all be changed depending our perspective. We can determine a surface area as being the product of xy, yz, or zx. You can never determine a surface area as being a product of x and t, as it is nonsensical. If time and space are equivalent, m/s is a radian and m/s^2 is a hertz and wavenumber. Time and space are entirely different, and anything saying they're equivalent is nonsense. It's like equating mass and volume as being the same thing.
I'm not presently arguing that time and space are the same thing. I'm simply arguing that time and space are both dimensions and that they both exist, not that they are equivalent. I don't think such an equivalence is quite so nonsensical as you think, though. Carl, your point that all they must agree on is the order is a very interesting one. Now I'm going to spend my whole shift this evening thinking about the topology of time. Thanks :P