The entire entropy of the universe at one point in time matters. That is all.
One point in time, or one point in spacetime? There really are no "points" in time.
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How it is measured is completely irrelevent. You moving around doesn't change the entropy of the universe at a point, it changes the entropy you percieve in your limited definition of perception.
How can the measurement not matter? The measure is the meaning -- not the particular technique of measurement, but the nature of the survey of the universe that's supposed to go into that measurement. This is more than a matter of "mere" perception.
You have some function E which represent the entropy of the universe. E(t) is the entropy of the universe at time t.
So, E(t) = ... what? How t is involved in the terms that follow that equals sign makes all the difference. Does it involve all events in the universe where time equals t in a particular observer's frame (which are, all but one, non-local, events out in the absolute elsewhere)? Does it involve all points in the absolute past of the observer? If you remove all consideration of an observer, how is t defined?
Can you show me on a spacetime diagram what you mean by a "point in time"? Can you draw a line or a curve, or shade an area, that represents the specific slice of the history of the universe which is going to be said to have a specific amount of entropy at a given time?
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What I am saying is that throw perception aside, fundamentally the laws of thermodynamics apply in all frames which implies that the measure of universal entropy in two different frames at the same time should be the same.
There's only one way "two different frames at the same time" makes any sense, and that's for observers who somehow occupy the same point in space while there's relative motion between the two observers.
There is no meaningful "at the same time" for observers in motion relative to each other who aren't at the same location. Both observers can pick an arbitrary event -- and it would be entirely arbitrary -- and call that "time 0" or whatever, but from that point on both observers consider their fellow observer to have a slow-running clock. Meaningful simultaneity cannot be defined by any "compensation" for slow clocks that either observer tries to make.
If you say perception doesn't matter, and particular observers don't matter, I'm afraid that's even more meaningless. At least two observers can be said to agree on an arbitrary simultaneous event. Frames, as you're happy to point out, can't have properties, including notions of reference events.
The best I can grant you is that "two different frames at the same time" is bad phrasing for some other concept you're trying to convey. You're hanging a great deal of import on that one phrase, and it makes no sense to me.
yeah the "observers" occupy the same space or are so close that it dont matter.
measurement to scientists means actually taking a measurement which is the technique. value of the measurement is different.
you dont say what is the measurement, you say how long is that.
point in space time (the conventional understanding of same time does work, relative time doesnt though, i ain't talking relative since you tossed that out at post 2), yadda yadda yadda. I am being intentionally sloppy with my language because this is an arbitrary task. you want details but are unwilling to accept that what you propose simply cannot work.
S(t)= ....... Radom function whose only requirement is that increases with t and is invarient under relativistic transforms. So ha!
If i can force clocks in an infinite lattice to read the same time, then i can carry an entropymometer on all my lattice points, and i can also consult with another reference frame with its infinite lattice of same time reading clocks/entropymometers anywhere in the universe at any time i want to consult, so as i am talking to bob and i say the event began at time 0 and he says sure. i call him up five minutes later and tell him the event ended at 5 past t=0 (at a different lattice point but no matter they are all connected and read the same time) and he is like no dude you are on crack that must be bad shit you had for lunch. he says it ended at 7.6 minutes past t=0 and your mom smells like ape dung. i say dude dont talk about my mater; dude, did you convert to my time coordinates, and he is like oh shit, you are right yup you would see that the event ended at precisely 5 minutes past t=0. oh man, i was about to freak because mr. e would have been wrong all along. man,i say, you just keep your lattice-o-clocks ticking and i will call you when i see the next event begin.
so we can agree with a beginning and an ending, indeed the beginning and ending of the event occurs at the same time regardless of frame -- do you understand what that means now?
i really dont think you understand. i went through this before. i went through everything before. your system breaks down at conservation of mass energy, m'k?
No, pfflam, there are properties and laws that are invarient under relativistic transformation. entropy is one of them.
My understanding, however limited, was that, at teh quantum level, if you observe from a different perspective you cannot have the exact same results as the observation is itself a fom of energy-drain-relationship-interference etc.
It also seems, from what little I understand, that by claiming to have two frames of reference be the same you are operating on a sort of meta-frame where the two frames are related . .
and then extrapolating from that some idea of Univesal fame . . . could be wrong though . . . but, from where I stand, my point of view-in-space-time, it seems something like that
pfflam, after you measure certain values in quantum there is a redistribution of probabilities for a remeasurement of that value. for instance light polarization, velocity, position. but these effects are microscopic, meaning, if i measure the thermal energy of a mug, the perturbation of that measurement isnt going to affect the remeasurement in a percievable or significant value.
What's really odd when I think about, is that, at least the way you've talked about entropy having to be the same for "two different frames at the same time", is that you're implying seemingly non-relativistic idea. A Universal Entropy Clock.
If entropy is always increasing, it never will have the same value twice over time. Given the equation E(t) = e, there's a one-to-one correspondence between t and e. For any given value of e, you can derive an associated time t.
Now consider this variation on the old twin paradox. A pair of twins synchronize their clocks, and then one takes off on a long space journey at high relativistic speeds. Presumably, in some theoretical sense at least, each twin can take the measure of universal entropy any time he likes, and write down in a journal what value entropy had at a given time.
When the traveling twin returns to Earth, the stay-at-home twin has aged 40 years, but the traveling twin has aged only 10 years. Now in the same place at the same time, the twins measure universal entropy one more time, at the same time, and put down one last journal entry, time-stamped by each twin using his own clock.
The two entropy journals can't possibly match. Certainly, the very last entry will show that the entropy of the universe increased more slowly for the traveler than it did for his twin.
To be fair, we're now talking about accelerated reference frames, not simple inertial frames. Does that account for all of the discrepancy?
To simplify comparison, let's presume the stay-at-home twin stayed close to home, but in Earth orbit, living a zero g life. If we compare a portion of the traveler?s journal from a time when he was coasting freely in space, under no acceleration, will we find a sequence of entries marking the same rate of entropic increase? Will all inertial observers experience the same passage of time between two given values of the universal entropy, only seeing differences if they undergo acceleration?
S(t)= ....... Radom function whose only requirement is that increases with t and is invarient under relativistic transforms. So ha!
If it's random, how can you say a particular thing like a message going non-locally backward in time breaks the invariance? Just make sure non-local events don't affect this magic random number and, voilá, no problem with frame invariance.
Since you say that two observers, both at the same point in space but traveling at different speeds should both get the same value for universal entropy, then a very obvious, non-FTL affected way to generate such a value comes to mind: the past light cone. Every point in spacetime, in a completely frame-invariant way, has the exact same past light cone. The value for universal entropy that both observers are supposed to agree upon could derive solely from events in contained in the past light cone, and you could still have the frame invariance you're looking for, you could still have an ever-increasing value for entropy, and my FTL messages still wouldn't harm a thing.
If this doesn't satisfy you, then there must be some particular way that non-local events are figured into the value for universal entropy, or else I can't see how you can claim with such certainly that the non-local effects of FTL messages change anything.
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If i can force clocks in an infinite lattice to read the same time, then i can carry an entropymometer on all my lattice points, and i can also consult with another reference frame with its infinite lattice of same time reading clocks/entropymometers anywhere in the universe at any time i want to consult, so as i am talking to bob and i say the event began at time 0 and he says sure. i call him up five minutes later and tell him the event ended at 5 past t=0 (at a different lattice point but no matter they are all connected and read the same time) and he is like no dude you are on crack that must be bad shit you had for lunch. he says it ended at 7.6 minutes past t=0 and your mom smells like ape dung. i say dude dont talk about my mater; dude, did you convert to my time coordinates, and he is like oh shit, you are right yup you would see that the event ended at precisely 5 minutes past t=0. oh man, i was about to freak because mr. e would have been wrong all along. man,i say, you just keep your lattice-o-clocks ticking and i will call you when i see the next event begin.
so we can agree with a beginning and an ending, indeed the beginning and ending of the event occurs at the same time regardless of frame -- do you understand what that means now?
All you're accomplishing here is the obvious fact that there's an agreed upon way that observers in two different reference frames can translate between each other's coordinate systems.
Remember, "events" in relativity don't have reference frames. They are simply points in space time. If there are 5 minutes between two events in Alice's frame, and 7.6 minutes in Bob's frame, there's no particular reason for Bob to choose Alice's frame as the frame to translate to. Why not translate to Cindy's frame or David's frame? There is no invariant duration between events in space time.
What is invariant for all observers is interval. As long as all observers use the same units of distance and time, this is what's invariant for all observers (pardon the computer-like math notation -- it's the only thing easy to type):
i = sqrt(dx^2 + dy^2 + dz^2 - (c*dt)^2)
(Where a positive result is a spacelike interval, a zero result a lightlike interval, and an imaginary result is a timelike interval.)
More to come later, however... I think I can get the kind of invariance you're looking (although I'm still not ready to concede any particular problem with FTL and entropy). I had spacetime diagrams floating in my head while driving after work to pick up an iPod mini for a birthday present... some interesting ideas came to me...
All you're accomplishing here is the obvious fact that there's an agreed upon way that observers in two different reference frames can translate between each other's coordinate systems.
. . .I'm pretty sure that I said the same thing . .
but can't tell fer sure\
Shheeesh . . Wish I could afford an iPod mini for givin away *cries in sleeve* or even for havin
More musings on frame-invariant universal entropy...
Since observers at the same point in spacetime are supposed to read the same values on their "entropometers", regardless of frame of reference, you can say that, whatever the correct entropy value is, that this value is a property of a given spacetime coordinate.
For any given value of entropy, there will be a set of points in spacetime that share the same value. Let's call them "isoentropic points". Intuitively, I'm guessing that a set of isoentropic points would be contiguous, forming an isoentropic curve of some sort in a simple two-dimensional (x, t) spacetime.
The isoentropic curve an observer intersects with at a given moment cannot also intersect the observer's past or future light cone -- if it did, it would be possible to have come from, or to later visit, a point in spacetime with an entropy that you had previously experienced -- not possible since you should always experience an ever-increasing entropy.
You should be able to exchange data with other observers, and establish a map of isoentropic points, and the shape of various isoentropic curves. Invariance imposes something on the shapes of the curves you should see when you do this: the shapes have to be invariant too. The curves couldn't be a simple lines, for example, because all straight lines, except for light lines (which can't be isoentropic), change angle when you translate from frame to frame. That angle would not be frame invariant.
I'd have to work out the math, but off the top of my head, I think the basic curve that does the trick is a hyperbola.
Of course, none of this helps me get any deeper into your objections related to entropy and FTL. As long as you don't define a meaningful procedure for how you arrive at the value an imaginary "entropometer" displays, and all you define is the characteristics of frame invariance and an increasing value over time, you could simply imagine a spacetime where each point held a "pre-programmed" value, all neatly laid out in hyperbolic curves or whatever shape is required, and where the "entropometer" does nothing more than fetch the pre-programmed value and report it, utterly and completely unaffected by anything that happens in the universe, be it SLT (slower than light), AFAT (as fast as light), or FTL.
The value for universal entropy that both observers are supposed to agree upon could derive solely from events in contained in the past light cone, and you could still have the frame invariance you're looking for, you could still have an ever-increasing value for entropy, and my FTL messages still wouldn't harm a thing.
....
What is invariant for all observers is interval.
First, FTL messages would appear in certain frames to alter what events occur in the past light cone hence affecting the entropy measured in different frames differently (in the preferred frame for instance this signal will not have occurred in the past light cone but in any frame in which the FTL signal appears to go backwards it will necessarily have).
The interval is invariant -- actually that really should be the metric is invariant but whatever, but since its my call to bob on my dime he has to convert to my frame. the next time he calls, i will convert to his frame, but he never calls.
We use mks metric measurements because of history and not because they are intrinsically easier to use (in fact there are units that physicist that are easier to use (where all constants are set to 1, but i digress)). Because i made my call to bob, he has to convert to my frame. i am simply being didatic but really what is in a calculation? it doesnt matter what units you use, and it doesnt matter what frame you use as long as the two people involved in the measurement use the same frame and the same units to compare. there is no physics here (actually, this is the essence of relativity -- there is no physics here).
You break conservation of mass/energy in at least one frame.
rate of entropy change doesnt have to be constant in all frames. that isnt the invariant property. the invariants are entropy and its always increasing value.
this is why i said a random function that is invariant under transform. i am sure it limits the math to certain functions ( maybe a class of functions).
btw shetline, together we arent idiots and i quote: In 1975, Stephen Hawking and Jacob Beckenstein discovered an astonishing connection between thermodynamical entropy, quantum mechanics, and general relavitity, which has inspired much current work on quantum gravity.
rate of entropy change doesnt have to be constant in all frames. that isnt the invariant property. the invariants are entropy and its always increasing value.
pfflam, maxwell's demon is a theoretical construct. i have a demon that sits at the door to my office and hes a smart one he is. in the summer he opens a weightless shutter (expending no energy) and lets out the highest velocity molecules and lets in only the slowest velocity molecules. as a result my office is cooled for free, and with the money i save on electricity I can support my smack habit that let me come up with such a beast. unfortunately, the police seemed to have caught word that i broke the law, you see it seems that my beast needs a way to keep that information in its head which is fine because there is no net energy loss when he stores the bit. but when my demon's memory is full and he needs to erase his rom, it takes him energy to get rid of it. sad, but you cant beat the second law of thermo.
pfflam, maxwell's demon is a theoretical construct. i have a demon that sits at the door to my office and hes a smart one he is. in the summer he opens a weightless shutter (expending no energy) and lets out the highest velocity molecules and lets in only the slowest velocity molecules. as a result my office is cooled for free, and with the money i save on electricity I can support my smack habit that let me come up with such a beast. unfortunately, the police seemed to have caught word that i broke the law, you see it seems that my beast needs a way to keep that information in its head which is fine because there is no net energy loss when he stores the bit. but when my demon's memory is full and he needs to erase his rom, it takes him energy to get rid of it. sad, but you cant beat the second law of thermo.
Yes but my original point bringing up the demon is that each and every frame demands a different observation, a different relationship to the counting of molecules, and that to string two frames together through telephone calls merely displaces the problem into another frame
It seems that this can't simply keep going until you get to the Arche -frame of reference . . . that seems like a fiction: like a 'God'-frame
the telephone call doesnt string the frames together in any real sense, another way to have put the telephone call is to consider two instruments that record the beginning and ending of an event in two different frames. If i the scientist (sitting in the frame of one of the machines) were to be able to slow the other device down back to my frame, the time it recorded for the length of the event would be different than the time my device recorded, but the space time interval would be the same (using shetline's vocab).
Think of the airplane used to show that general relativity correctly predicted the time dilation of the airplane relative to the ground.
There is no coupling of frames when information is passed between them, just information being passed around.
and that's why i thought that you could't assume an over-arching frame: if each observation records its data and they compare they are not, simply by comparing in an agreed upon way, creating a reference frame that itself does not take energy beyond the innitial observations . . . (which, if remaining uncompared, would also remain only probabilistic(?) potential)
Seems that in each case, of observation and subsequent relating of information, there is a loss of energy and never in the exact same way.
hmm?!?
But what they hey?!?! . . . I'm an artist who studied Philosophy . . . with dyslexia mind you . . mathematics and I are called a truce of nonaggression a long time ago . . . so what the hell am I talking about?!
relating of information probably increases the entropy of the universe -- like a virus replicating in a host, or the host itself replicating or breeding...
I think St. Augustine had the whole "time travel" issue pinned down a long time ago....the only place time actually exists is in our memory. All we have now is the present. Right now...think about it, that's all you have. The past is a set of neurons in your brain. And going into the future is a bit absurd. Even if you did go off in a spacecraft and left the earth behind spinning faster than you, you're already "synchronized" with the proprietary time system given by earth. And if there are differences, it's been seen they're negligble.
Space folding is a very interesting idea, though...
And until we solve the problems of fusion and effectively neutralizing gravity and inertial forces (i.e, create these mystical "force fields"), interstellar travel is very far off.
Comments
Originally posted by billybobsky
The entire entropy of the universe at one point in time matters. That is all.
One point in time, or one point in spacetime? There really are no "points" in time.
How it is measured is completely irrelevent. You moving around doesn't change the entropy of the universe at a point, it changes the entropy you percieve in your limited definition of perception.
How can the measurement not matter? The measure is the meaning -- not the particular technique of measurement, but the nature of the survey of the universe that's supposed to go into that measurement. This is more than a matter of "mere" perception.
You have some function E which represent the entropy of the universe. E(t) is the entropy of the universe at time t.
So, E(t) = ... what? How t is involved in the terms that follow that equals sign makes all the difference. Does it involve all events in the universe where time equals t in a particular observer's frame (which are, all but one, non-local, events out in the absolute elsewhere)? Does it involve all points in the absolute past of the observer? If you remove all consideration of an observer, how is t defined?
Can you show me on a spacetime diagram what you mean by a "point in time"? Can you draw a line or a curve, or shade an area, that represents the specific slice of the history of the universe which is going to be said to have a specific amount of entropy at a given time?
What I am saying is that throw perception aside, fundamentally the laws of thermodynamics apply in all frames which implies that the measure of universal entropy in two different frames at the same time should be the same.
There's only one way "two different frames at the same time" makes any sense, and that's for observers who somehow occupy the same point in space while there's relative motion between the two observers.
There is no meaningful "at the same time" for observers in motion relative to each other who aren't at the same location. Both observers can pick an arbitrary event -- and it would be entirely arbitrary -- and call that "time 0" or whatever, but from that point on both observers consider their fellow observer to have a slow-running clock. Meaningful simultaneity cannot be defined by any "compensation" for slow clocks that either observer tries to make.
If you say perception doesn't matter, and particular observers don't matter, I'm afraid that's even more meaningless. At least two observers can be said to agree on an arbitrary simultaneous event. Frames, as you're happy to point out, can't have properties, including notions of reference events.
The best I can grant you is that "two different frames at the same time" is bad phrasing for some other concept you're trying to convey. You're hanging a great deal of import on that one phrase, and it makes no sense to me.
measurement to scientists means actually taking a measurement which is the technique. value of the measurement is different.
you dont say what is the measurement, you say how long is that.
point in space time (the conventional understanding of same time does work, relative time doesnt though, i ain't talking relative since you tossed that out at post 2), yadda yadda yadda. I am being intentionally sloppy with my language because this is an arbitrary task. you want details but are unwilling to accept that what you propose simply cannot work.
S(t)= ....... Radom function whose only requirement is that increases with t and is invarient under relativistic transforms. So ha!
If i can force clocks in an infinite lattice to read the same time, then i can carry an entropymometer on all my lattice points, and i can also consult with another reference frame with its infinite lattice of same time reading clocks/entropymometers anywhere in the universe at any time i want to consult, so as i am talking to bob and i say the event began at time 0 and he says sure. i call him up five minutes later and tell him the event ended at 5 past t=0 (at a different lattice point but no matter they are all connected and read the same time) and he is like no dude you are on crack that must be bad shit you had for lunch. he says it ended at 7.6 minutes past t=0 and your mom smells like ape dung. i say dude dont talk about my mater; dude, did you convert to my time coordinates, and he is like oh shit, you are right yup you would see that the event ended at precisely 5 minutes past t=0. oh man, i was about to freak because mr. e would have been wrong all along. man,i say, you just keep your lattice-o-clocks ticking and i will call you when i see the next event begin.
so we can agree with a beginning and an ending, indeed the beginning and ending of the event occurs at the same time regardless of frame -- do you understand what that means now?
i really dont think you understand. i went through this before. i went through everything before. your system breaks down at conservation of mass energy, m'k?
Originally posted by billybobsky
No, pfflam, there are properties and laws that are invarient under relativistic transformation. entropy is one of them.
My understanding, however limited, was that, at teh quantum level, if you observe from a different perspective you cannot have the exact same results as the observation is itself a fom of energy-drain-relationship-interference etc.
It also seems, from what little I understand, that by claiming to have two frames of reference be the same you are operating on a sort of meta-frame where the two frames are related . .
and then extrapolating from that some idea of Univesal fame . . . could be wrong though . . . but, from where I stand, my point of view-in-space-time, it seems something like that
If entropy is always increasing, it never will have the same value twice over time. Given the equation E(t) = e, there's a one-to-one correspondence between t and e. For any given value of e, you can derive an associated time t.
Now consider this variation on the old twin paradox. A pair of twins synchronize their clocks, and then one takes off on a long space journey at high relativistic speeds. Presumably, in some theoretical sense at least, each twin can take the measure of universal entropy any time he likes, and write down in a journal what value entropy had at a given time.
When the traveling twin returns to Earth, the stay-at-home twin has aged 40 years, but the traveling twin has aged only 10 years. Now in the same place at the same time, the twins measure universal entropy one more time, at the same time, and put down one last journal entry, time-stamped by each twin using his own clock.
The two entropy journals can't possibly match. Certainly, the very last entry will show that the entropy of the universe increased more slowly for the traveler than it did for his twin.
To be fair, we're now talking about accelerated reference frames, not simple inertial frames. Does that account for all of the discrepancy?
To simplify comparison, let's presume the stay-at-home twin stayed close to home, but in Earth orbit, living a zero g life. If we compare a portion of the traveler?s journal from a time when he was coasting freely in space, under no acceleration, will we find a sequence of entries marking the same rate of entropic increase? Will all inertial observers experience the same passage of time between two given values of the universal entropy, only seeing differences if they undergo acceleration?
Originally posted by billybobsky
S(t)= ....... Radom function whose only requirement is that increases with t and is invarient under relativistic transforms. So ha!
If it's random, how can you say a particular thing like a message going non-locally backward in time breaks the invariance? Just make sure non-local events don't affect this magic random number and, voilá, no problem with frame invariance.
Since you say that two observers, both at the same point in space but traveling at different speeds should both get the same value for universal entropy, then a very obvious, non-FTL affected way to generate such a value comes to mind: the past light cone. Every point in spacetime, in a completely frame-invariant way, has the exact same past light cone. The value for universal entropy that both observers are supposed to agree upon could derive solely from events in contained in the past light cone, and you could still have the frame invariance you're looking for, you could still have an ever-increasing value for entropy, and my FTL messages still wouldn't harm a thing.
If this doesn't satisfy you, then there must be some particular way that non-local events are figured into the value for universal entropy, or else I can't see how you can claim with such certainly that the non-local effects of FTL messages change anything.
If i can force clocks in an infinite lattice to read the same time, then i can carry an entropymometer on all my lattice points, and i can also consult with another reference frame with its infinite lattice of same time reading clocks/entropymometers anywhere in the universe at any time i want to consult, so as i am talking to bob and i say the event began at time 0 and he says sure. i call him up five minutes later and tell him the event ended at 5 past t=0 (at a different lattice point but no matter they are all connected and read the same time) and he is like no dude you are on crack that must be bad shit you had for lunch. he says it ended at 7.6 minutes past t=0 and your mom smells like ape dung. i say dude dont talk about my mater; dude, did you convert to my time coordinates, and he is like oh shit, you are right yup you would see that the event ended at precisely 5 minutes past t=0. oh man, i was about to freak because mr. e would have been wrong all along. man,i say, you just keep your lattice-o-clocks ticking and i will call you when i see the next event begin.
so we can agree with a beginning and an ending, indeed the beginning and ending of the event occurs at the same time regardless of frame -- do you understand what that means now?
All you're accomplishing here is the obvious fact that there's an agreed upon way that observers in two different reference frames can translate between each other's coordinate systems.
Remember, "events" in relativity don't have reference frames. They are simply points in space time. If there are 5 minutes between two events in Alice's frame, and 7.6 minutes in Bob's frame, there's no particular reason for Bob to choose Alice's frame as the frame to translate to. Why not translate to Cindy's frame or David's frame? There is no invariant duration between events in space time.
What is invariant for all observers is interval. As long as all observers use the same units of distance and time, this is what's invariant for all observers (pardon the computer-like math notation -- it's the only thing easy to type):
i = sqrt(dx^2 + dy^2 + dz^2 - (c*dt)^2)
(Where a positive result is a spacelike interval, a zero result a lightlike interval, and an imaginary result is a timelike interval.)
More to come later, however... I think I can get the kind of invariance you're looking (although I'm still not ready to concede any particular problem with FTL and entropy). I had spacetime diagrams floating in my head while driving after work to pick up an iPod mini for a birthday present... some interesting ideas came to me...
Originally posted by shetline
All you're accomplishing here is the obvious fact that there's an agreed upon way that observers in two different reference frames can translate between each other's coordinate systems.
. . .I'm pretty sure that I said the same thing . .
but can't tell fer sure
Shheeesh . . Wish I could afford an iPod mini for givin away *cries in sleeve* or even for havin
Since observers at the same point in spacetime are supposed to read the same values on their "entropometers", regardless of frame of reference, you can say that, whatever the correct entropy value is, that this value is a property of a given spacetime coordinate.
For any given value of entropy, there will be a set of points in spacetime that share the same value. Let's call them "isoentropic points". Intuitively, I'm guessing that a set of isoentropic points would be contiguous, forming an isoentropic curve of some sort in a simple two-dimensional (x, t) spacetime.
The isoentropic curve an observer intersects with at a given moment cannot also intersect the observer's past or future light cone -- if it did, it would be possible to have come from, or to later visit, a point in spacetime with an entropy that you had previously experienced -- not possible since you should always experience an ever-increasing entropy.
You should be able to exchange data with other observers, and establish a map of isoentropic points, and the shape of various isoentropic curves. Invariance imposes something on the shapes of the curves you should see when you do this: the shapes have to be invariant too. The curves couldn't be a simple lines, for example, because all straight lines, except for light lines (which can't be isoentropic), change angle when you translate from frame to frame. That angle would not be frame invariant.
I'd have to work out the math, but off the top of my head, I think the basic curve that does the trick is a hyperbola.
Of course, none of this helps me get any deeper into your objections related to entropy and FTL. As long as you don't define a meaningful procedure for how you arrive at the value an imaginary "entropometer" displays, and all you define is the characteristics of frame invariance and an increasing value over time, you could simply imagine a spacetime where each point held a "pre-programmed" value, all neatly laid out in hyperbolic curves or whatever shape is required, and where the "entropometer" does nothing more than fetch the pre-programmed value and report it, utterly and completely unaffected by anything that happens in the universe, be it SLT (slower than light), AFAT (as fast as light), or FTL.
Originally posted by shetline
The value for universal entropy that both observers are supposed to agree upon could derive solely from events in contained in the past light cone, and you could still have the frame invariance you're looking for, you could still have an ever-increasing value for entropy, and my FTL messages still wouldn't harm a thing.
....
What is invariant for all observers is interval.
First, FTL messages would appear in certain frames to alter what events occur in the past light cone hence affecting the entropy measured in different frames differently (in the preferred frame for instance this signal will not have occurred in the past light cone but in any frame in which the FTL signal appears to go backwards it will necessarily have).
The interval is invariant -- actually that really should be the metric is invariant but whatever, but since its my call to bob on my dime he has to convert to my frame. the next time he calls, i will convert to his frame, but he never calls.
We use mks metric measurements because of history and not because they are intrinsically easier to use (in fact there are units that physicist that are easier to use (where all constants are set to 1, but i digress)). Because i made my call to bob, he has to convert to my frame. i am simply being didatic but really what is in a calculation? it doesnt matter what units you use, and it doesnt matter what frame you use as long as the two people involved in the measurement use the same frame and the same units to compare. there is no physics here (actually, this is the essence of relativity -- there is no physics here).
You break conservation of mass/energy in at least one frame.
this is why i said a random function that is invariant under transform. i am sure it limits the math to certain functions ( maybe a class of functions).
btw shetline, together we arent idiots and i quote: In 1975, Stephen Hawking and Jacob Beckenstein discovered an astonishing connection between thermodynamical entropy, quantum mechanics, and general relavitity, which has inspired much current work on quantum gravity.
Originally posted by billybobsky
rate of entropy change doesnt have to be constant in all frames. that isnt the invariant property. the invariants are entropy and its always increasing value.
Don't you mean t+ ?
ot I'll just shut my trap
Originally posted by pfflam
Don't you mean t+ ?
ot I'll just shut my trap
yes i do... mean t+...
pfflam, maxwell's demon is a theoretical construct. i have a demon that sits at the door to my office and hes a smart one he is. in the summer he opens a weightless shutter (expending no energy) and lets out the highest velocity molecules and lets in only the slowest velocity molecules. as a result my office is cooled for free, and with the money i save on electricity I can support my smack habit that let me come up with such a beast. unfortunately, the police seemed to have caught word that i broke the law, you see it seems that my beast needs a way to keep that information in its head which is fine because there is no net energy loss when he stores the bit. but when my demon's memory is full and he needs to erase his rom, it takes him energy to get rid of it. sad, but you cant beat the second law of thermo.
Originally posted by billybobsky
yes i do... mean t+...
pfflam, maxwell's demon is a theoretical construct. i have a demon that sits at the door to my office and hes a smart one he is. in the summer he opens a weightless shutter (expending no energy) and lets out the highest velocity molecules and lets in only the slowest velocity molecules. as a result my office is cooled for free, and with the money i save on electricity I can support my smack habit that let me come up with such a beast. unfortunately, the police seemed to have caught word that i broke the law, you see it seems that my beast needs a way to keep that information in its head which is fine because there is no net energy loss when he stores the bit. but when my demon's memory is full and he needs to erase his rom, it takes him energy to get rid of it. sad, but you cant beat the second law of thermo.
Yes but my original point bringing up the demon is that each and every frame demands a different observation, a different relationship to the counting of molecules, and that to string two frames together through telephone calls merely displaces the problem into another frame
It seems that this can't simply keep going until you get to the Arche -frame of reference . . . that seems like a fiction: like a 'God'-frame
Think of the airplane used to show that general relativity correctly predicted the time dilation of the airplane relative to the ground.
There is no coupling of frames when information is passed between them, just information being passed around.
and that's why i thought that you could't assume an over-arching frame: if each observation records its data and they compare they are not, simply by comparing in an agreed upon way, creating a reference frame that itself does not take energy beyond the innitial observations . . . (which, if remaining uncompared, would also remain only probabilistic(?) potential)
Seems that in each case, of observation and subsequent relating of information, there is a loss of energy and never in the exact same way.
hmm?!?
But what they hey?!?! . . . I'm an artist who studied Philosophy . . . with dyslexia mind you . . mathematics and I are called a truce of nonaggression a long time ago . . . so what the hell am I talking about?!
Space folding is a very interesting idea, though...
And until we solve the problems of fusion and effectively neutralizing gravity and inertial forces (i.e, create these mystical "force fields"), interstellar travel is very far off.