# Thread: Motion, Duration, and Gravity

1. ## Motion, Duration, and Gravity

Motion, Duration, and Gravity

This topic is started for thorkil2, because of difficulties posting described in an article in topic Is it hard to post in ATM and not hard in other sections? (yet another test).

Take it away, thorkil2.

2. Established Member
Join Date
Sep 2008
Posts
477
Many thanks. I was trying to post an idea about the arrow of time, and some of its implications. I think I will start with just that part and perhaps follow with the rest.

The arrow of time is implicit in the Lorentz-Fitzgerald-Einstein (LFE) contractions. Time and motion are complements. Any change of position in space corresponds to a change of position in time; the temporal change always in one direction only, from present to subsequent present, regardless of the direction of motion in space, its variables subject only to the degree of motion (i.e., speed). The relationship between motion and time is given by the complementary ratios

(v/c)^2+(t_0/t)^2 = 1

from the LFE time dilation equation

t = t_0/√(1-(v/c)^2 )

* * * * *

0< v/c <1

All motion can be expressed in terms of v/c and the range of possible values for v/c encompasses all possible motion.

Every value for v/c is associated with a unique positive (present toward future) temporal interval t (in relation to a designated rest frame interval t_0). There is no possible relative t that is not defined by some value of v/c . Since v/c cannot be greater than 1, and there are no possible negative values for v/c (hence no negative roots for (v/c)^2), the range of all possible motion is bounded by 0 and 1, so there is no negative interval; no possible negative time. Hence the arrow of time and its asymmetry are defined by the fundamental relationship between motion and time.

3. Established Member
Join Date
Sep 2008
Posts
477
What follows here is more speculative, but based on the above:

Duration

Because motion and time are inseparably connected, and because all frames of reference are in motion in relation to some other frames, and all motion creates a calculable positive value for the interval t, then it is simpler and more reasonable to view duration as natural motion through time, as a complement to spatial motion, than to view past, present, and future as co-existent from some higher dimensional frame which requires still higher frames to provide for duration of structure–-ad infinitum. Three-dimensional objects are just that, but they “endure” because they move with the observer through space and time. They don’t “have” a fourth dimension; they move through (along?) the fourth dimension.

This has interesting implications. There is no past, and there is no pre-existing future, though the future can be treated as a destination, whereas the past, as a corporeal structure, does not exist at all. The Universe exists in a constantly moving local “present,” an infinitesimally thin 3-dimensional surface with a 4th dimensional vector. ("Thin" of course, refers to interval. If time is quantized, as it probably is, then the quantum interval would be the thickness of the Universe.) All record of the past exists as the effect of prior causative motion and interaction which cumulatively form the present (and fleeting) state of the Universe. It might be valid to describe “now” as the edge of the universe, but it’s probably more accurate to state that “now” is the Universe (and there is nothing in that statement that is negated by issues of relativity and simultaneity–in fact the “now” Universe fits perfectly into those problems). If this is true, then Entropy is a motion-related marker, not a cause, and Block Time is a myth.

Time and Gravity

I have not pursued this more radical idea beyond this immediate speculation, but it seems to follow from the time-motion relationship, and it should be easy to prove or disprove. Motion establishes a moving object’s orientation in time. All motion dilates, or warps time, only notably at relativistic speeds, but calculably at any speed, per

t = t_0/√(1-(v/c)^2 )

The time-motion complementarity equation,

(v/c)^2+(t_0/t)^2 = 1

which is a simple algebraic transformation of the time dilation formula above, links motion and time as an ontological whole, so if motion warps time, then the converse should be true: any warping of time from a cause other than motion should result in a change in motion. The only sources of time dilation are speed and mass. Because speed and time are complementary, any time warp created by the presence of mass necessarily results in motion or a tendency to motion of any object in the vicinity of the mass (the attraction is mutual, of course, but described here in terms of very small mass in the vicinity of a very large mass for the sake of simplicity). Hence any object entering the range of influence of a mass will tend to move toward the center of that mass and accelerate as the degree of time warp increases in inverse proportion to the distance.

4. Established Member
Join Date
Jun 2004
Posts
617
The Universe is "Now" you said, I am not quite following.

All the effects we experience happen in the past, so how can we say that the past is not real? Even the light from this computer I am looking out left the screen in the past, so the past is very real.

Also, are you saying that gravity is a hydrodynamic event using the warping of time as the attracting variable? If you are I like it a lot and discussed it here years ago.... No math was my limit...help me understand and keep it simple for us amatuers.

5. Established Member
Join Date
Sep 2008
Posts
477
What we experience is a consequence of past events. The light from your computer screen left it some trillionths of a second prior to your awareness of it. Your awareness is the "now;" the time it actually departed was the "now" then, but that is past, and no longer exists. Only the consequence remains, and that only briefly as 3-space moves on through time. Events occur, but are not sustained in some all-persistent past-present-future continuum. You might think of it as a three-dimensional balloon with a fourth dimensional direction of expansion (though the analogy is imperfect, as in this balloon, there is no inside "space," and the rate of movement on the 3-dimensional surface determines a certain orientation in space-time--subjectively, your observed interval, or objectively, relative clock speed). Events occur only on the continuously moving and changing surface, and causality is motion. The thickness of the surface is either a quantum of time, if such exists, or zero if interval is infinitely divisible. The record you see on the surface (yesterday's newspaper, the light from your computer screen, ancient rock strata, etc.) are a consequence of past motion and interaction. But there is no frame of reference in which those past events still exist. There is no destination in the past to get to by time travel, because there is no possibility of generating any sort of negative interval. The past has been, and present is the result of those causal events, but the past does not persist. It may seem to imply the need for consciousness, but in fact that is not my point in this. The departure of photons from your computer screen is a "now" event as it occurs; your consciousness of them is a later "now" event, which is precisely why this idea does not violate relativity or problems of simultaneity.

I almost didn't post the gravity idea because it seems so radical, but in fact, it's such a logical consequence of the complementarity of time and motion that it needed to be stated. I know how to do a proof, I think--or at least to examine the idea mathematically for its viability, but I don't have access to the formulas I need, and I probably do not have the math skills either. I think it's the same gravity, just viewed from a different window.

6. Established Member
Join Date
Sep 2008
Posts
477
Clarification: I don't mean to say the past was not real; just that it doesn't persist.

7. Established Member
Join Date
Sep 2008
Posts
477
To clarify the duration material a bit more: I've been gnawing at this problem for decades, but it all fell together as I was writing a fairly strong critique of Julian Barbour's book "The End of Time," a book that is flawed in its basic premise. Barbour posits a vast landscape in a mathematical "configuration space" that he calls Platonia. Platonia contains all possible configurations of all the matter and energy in the Universe. He has essentially turned the universe into a set of motion picture stills, which when linked together give the impression of time. The flaw is the flaw in all "time doesn't exist" theories. He claims that Platonia is timeless, but fails to observe that any structure must have a quality of persistence to exist at all, which means that for any group of physical dimensions, there must be at least one additional dimension to account for duration. You may have to project the film to get a sense of the sequence of events depicted therein, but the film itself has its own independent persistence whether it's in the projector or not.

If you take the point of view that past, present, and future all exist simultaneously from some higher dimensional frame of reference, that whole becomes a physical structure which must in turn have its own dimension of persistence. That process can be carried on ad infinitum. Every time you trade time for structure, you have to add a dimension for time. So time cannot be eliminated but the number of dimensions must be infinite to account for it, and the theory becomes extremely top-heavy. It makes more sense that there is only one or one set of temporal vectors and that three-dimensional objects move through space and time. They appear to persist because they move with the observer in that same space-time continuum. Again, motion and time are inseparable. There can be no motion without time, and probably no time without motion. The math indicates quite strongly that a reversal from Universal expansion to collapse toward a "big crunch" would in no way reverse time because the change is nothing more than a reversal of physical direction of movement. Length can approach zero, and interval and mass can approach infinity, but none of those can depart the boundaries set by 0 and 1 within the Lorentz-Fitzgerald transformations.

8. Originally Posted by thorkil2
The arrow of time is implicit in the Lorentz-Fitzgerald-Einstein (LFE) contractions.
I don't think that is true. The Lorentz factor, for instance, has v divided by c, so any "negative" of time would cancel.
The relationship between motion and time is given by the complementary ratios

(v/c)^2+(t_0/t)^2 = 1

from the LFE time dilation equation

t = t_0/√(1-(v/c)^2 )
And any negative in t_0 would be reflected in t.
Every value for v/c is associated with a unique positive (present toward future) temporal interval t (in relation to a designated rest frame interval t_0).
Huh?

If v = 150000km/s and c = 300000km/s (approx.), then v/c = 1/2. What unique positive temporal interval t is associated with that?
Originally Posted by thorkil2
To clarify the duration material a bit more: I've been gnawing at this problem for decades, but it all fell together as I was writing a fairly strong critique of Julian Barbour's book "The End of Time," a book that is flawed in its basic premise. Barbour posits a vast landscape in a mathematical "configuration space" that he calls Platonia. Platonia contains all possible configurations of all the matter and energy in the Universe. He has essentially turned the universe into a set of motion picture stills, which when linked together give the impression of time. The flaw is the flaw in all "time doesn't exist" theories. He claims that Platonia is timeless, but fails to observe that any structure must have a quality of persistence to exist at all, which means that for any group of physical dimensions, there must be at least one additional dimension to account for duration. You may have to project the film to get a sense of the sequence of events depicted therein, but the film itself has its own independent persistence whether it's in the projector or not.
There's no need for an independent persistence, though. That's just an attempt to make time "indispensable". "Our time" is already accounted for by the "motion picture stills", once they exist, they're done and not needed. No other "persistence" is necessary.

9. Established Member
Join Date
Sep 2008
Posts
477
Originally Posted by hhEb09'1
I don't think that is true. The Lorentz factor, for instance, has v divided by c, so any "negative" of time would cancel.
And any negative in t_0 would be reflected in t.
You lost me there. v/c is necessarily positive (how can you have negative motion?). t_0/t is implicitly positive in the equation. Can you clarify what cancellation you are talking about. t_0 is your rest frame interval. It can't be negative.

Originally Posted by hhEb09'1
Huh?
There is no way to define negative speed, so every (inherently positive) value for v/c plugged into the time dilation equation generates a single positive value for t. A negative t is impossible unless you can define some way to achieve negative speed. v/c is a scalar value, not a vector, so that can't be done.

Originally Posted by hhEb09'1
If v = 150000km/s and c = 300000km/s (approx.), then v/c = 1/2. What unique positive temporal interval t is associated with that?
For any value of v/c, t is relative to t_0, so if t_0 is 1, then the associated value of t when v/c=1/2 is 1.1547--to quite a few more decimal places. Just plug the numbers into the time dilation equation.

Originally Posted by hhEb09'1
There's no need for an independent persistence, though. That's just an attempt to make time "indispensable". "Our time" is already accounted for by the "motion picture stills", once they exist, they're done and not needed. No other "persistence" is necessary.
I grant that the duration aspect of my post is speculative, but it seems to me to be more logical than the alternatives. Duration is necessary in some form. And I have stated almost exactly the same thing you have, but mine is an alternate definition of persistence. A thing must remain in a timeline to exist. If it isn't there from one moment to the next, then it can't exist at all (its structure, i.e., mass/energy, can't exist in one moment without existing in a subsequent moment unless you can override the laws of conservation of mass and energy). My point is that persistence amounts to movement through time; that there is no 4th dimensional element to the structure of an object, but that a three-dimensional object moves with the observer through time as well as space, and that that movement constitutes duration. There are too many problems with the idea of block time, in which past, present, and future exist simultaneously from some higher dimensional frame of reference.

10. Originally Posted by thorkil2
You lost me there. v/c is necessarily positive (how can you have negative motion?).
If you have negative time, right?

I mean, you can't say "there's no negative motion" and then say that shows that there's no negative time. They'd be equivalent concepts, wouldn't they?
There is no way to define negative speed, so every (inherently positive) value for v/c plugged into the time dilation equation generates a single positive value for t. A negative t is impossible unless you can define some way to achieve negative speed. v/c is a scalar value, not a vector, so that can't be done.
It seems you've got yourself into a situation where you're assuming what you're trying to show.

The equations of Lorentz and Einstein don't help you out at all.
For any value of v/c, t is relative to t_0, so if t_0 is 1, then the associated value of t when v/c=1/2 is 1.1547--to quite a few more decimal places. Just plug the numbers into the time dilation equation.
Ah. You'd said a unique t, but you meant a unique conversion factor. Is that right?
I grant that the duration aspect of my post is speculative, but it seems to me to be more logical than the alternatives.
Some people have the opposite opinion.

I'm not arguing for either one, but that's what the difference boils down to--opinion.

11. Established Member
Join Date
Sep 2008
Posts
477
Originally Posted by hhEb09'1
If you have negative time, right?.
You are assuming negative time. But how do you arrive at a negative interval from the time dilation equation? v/c can't be negative. t_0 is your rest frame interval. How can that be negative unless you assign it arbitrarily? And you can't do that because there's no way to define it. It's your real world baseline. The only remaining value is t, and that's generated by the other two values. There is no way in this math to arrive at a negative t. It's not assumption or opinion, it's right there in the math.

Originally Posted by hhEb09'1
I mean, you can't say "there's no negative motion" and then say that shows that there's no negative time. They'd be equivalent concepts, wouldn't they?
I can say that precisely, because that's what the math says. You can't pull a negative value out of whole cloth. Lorentz-Fitzgerald is an interval machine. The only solutions you can get out of it derive from what you put in. If there are no real negative input values, then there is no possible negative solution. If you want to call it opinion, then you'll have to come up with a definition for negative motion and a negative rest interval, not to mention negative mass and negative dimension (length) for the other equations.

Originally Posted by hhEb09'1
It seems you've got yourself into a situation where you're assuming what you're trying to show.
Not at all. I'm just reading the math. I'm not assuming anything.

Originally Posted by hhEb09'1
The equations of Lorentz and Einstein don't help you out at all.Ah. You'd said a unique t, but you meant a unique conversion factor. Is that right?Some people have the opposite opinion.
No, I didn't mean a unique conversion factor. I meant a unique t. There is a single value for t for any value of v/c you plug into the equation. Show me instead how you would define v/c as negative, or t_0 as negative. I maintain it can't be done.

Originally Posted by hhEb09'1
I'm not arguing for either one, but that's what the difference boils down to--opinion.
No, the difference boils down to the math. It's unequivocal.

I'm actually a bit surprised at this argument. I expected to get considerable flack for the gravity idea, and at least some for the duration idea (as indeed you have taken on), but this part of it is straightforward and fairly simple algebra. The relationship has not been addressed previously in this way to my knowledge (hence its introduction here in ATM), but the concept behind it is mathematically solid--unless Lorentz is true only selectively.

12. Order of Kilopi
Join Date
Nov 2002
Posts
6,235
Originally Posted by thorkil2
No, I didn't mean a unique conversion factor. I meant a unique t. There is a single value for t for any value of v/c you plug into the equation. Show me instead how you would define v/c as negative, or t_0 as negative. I maintain it can't be done.
You do realize that in Quantum Field Theory (QFT) that time operations are symmetric, right? If you have an interaction that creates a electron-positron pair, both moving forward in time, you will get the same answer if you use an electron-electron pair, one moving forward in time, one moving backward in time. In the case of the one moving backward, you have t_0 as negative. Now Special relativity has been included in Quantum Theory since 1928 when Paul Dirac combined the two, so I think it has been covered for quite a while. Any good introduction to Quantum Mechanics should cover it.

13. Originally Posted by thorkil2
You are assuming negative time. But how do you arrive at a negative interval from the time dilation equation? v/c can't be negative. t_0 is your rest frame interval. How can that be negative unless you assign it arbitrarily? And you can't do that because there's no way to define it. It's your real world baseline. The only remaining value is t, and that's generated by the other two values. There is no way in this math to arrive at a negative t. It's not assumption or opinion, it's right there in the math.
No, I'm not assuming negative time. I'm just pointing out the error in your logical progression. By assuming that t_0 cannot be negative, you conclude that t cannot be negative. They both represent "real world baseline". In other words, you are assuming what you wish to prove. That's a logical fallacy.

For instance, you might as well ignore Lorentz, and just use the equation t = t. No one would argue (much) with that, and you can still make the same conclusion--if the right hand side must be positive, then the left hand side is too. No one would let you get away with saying that that equation forces us to accept that time is nonnegative, but that is all you are doing with the Lorentz transformation too.
I can say that precisely, because that's what the math says. You can't pull a negative value out of whole cloth. Lorentz-Fitzgerald is an interval machine. The only solutions you can get out of it derive from what you put in. If there are no real negative input values, then there is no possible negative solution. If you want to call it opinion, then you'll have to come up with a definition for negative motion and a negative rest interval, not to mention negative mass and negative dimension (length) for the other equations.
But, it has absolutely nothing to do with Lorentz or Fitzgerald.
No, I didn't mean a unique conversion factor. I meant a unique t. There is a single value for t for any value of v/c you plug into the equation.
What if you used two different values for t_0, but the same v/c. You'd get non-unique t, not just a single value.

Obviously.
Show me instead how you would define v/c as negative, or t_0 as negative. I maintain it can't be done.
I'm not defining t_0 as negative, I'm saying it might be negative, or positive. The Lorentz equation does not limit the possibility of t_0 being negative.
No, the difference boils down to the math. It's unequivocal.
It's as unequivocal in this regard as is t = t_0. Which is, not.
I'm actually a bit surprised at this argument. I expected to get considerable flack for the gravity idea, and at least some for the duration idea (as indeed you have taken on), but this part of it is straightforward and fairly simple algebra. The relationship has not been addressed previously in this way to my knowledge (hence its introduction here in ATM), but the concept behind it is mathematically solid--unless Lorentz is true only selectively.
It has nothing whatsoever to do with Lorentz. Your argument might as well be just about the equation t = t_0

14. Established Member
Join Date
Sep 2008
Posts
477
Originally Posted by hhEb09'1
No, I'm not assuming negative time. I'm just pointing out the error in your logical progression. By assuming that t_0 cannot be negative, you conclude that t cannot be negative. They both represent "real world baseline". In other words, you are assuming what you wish to prove. That's a logical fallacy.
I am assuming nothing, but looking relationships. You are sitting at your computer watching time pass. Your rest frame interval is positive. There is no way you can turn it around, or devise a condition in which it could be negative. There's no assumption involved in that. It's a real condition. Unless you can state a condition in which t_0 could have a negative value, it has to stand as positive, so long as your clock continues to run forward.

Originally Posted by hhEb09'1
For instance, you might as well ignore Lorentz, and just use the equation t = t. No one would argue (much) with that, and you can still make the same conclusion--if the right hand side must be positive, then the left hand side is too. No one would let you get away with saying that that equation forces us to accept that time is nonnegative, but that is all you are doing with the Lorentz transformation too.But, it has absolutely nothing to do with Lorentz or Fitzgerald.What if you used two different values for t_0, but the same v/c. You'd get non-unique t, not just a single value.
One of the hazards of this kind of presentation is haste. Your last sentence is the kind of feedback I was hoping for to be sure I wasn't mis-stating any of this, and obviously here I have. So this should read "for any given value of t_0 and any given value of v/c there is a unique t" or "the ratio t/t_0 is unique for any value of v/c." Thanks for that correction, but so far I see no cause to abandon the overall reasoning.

Originally Posted by hhEb09'1
Obviously.I'm not defining t_0 as negative, I'm saying it might be negative, or positive. The Lorentz equation does not limit the possibility of t_0 being negative.
The Lorentz equation does not limit the possibility of t_0 being negative (and I don't believe I've said that). The real world does. If you want to say it might be negative, then you have to show how it could be. I'm simply saying there is no real world condition in which the rest frame interval can be negative. If you still believe that is an assumption, then show me an example of a negative rest interval. What I have said is that given a value of v/c, which is by default positive, and a value of t_0 which is also by default positive, then t must be positive.

It's as unequivocal in this regard as is t = t_0. Which is, not.[/QUOTE]

With corrections noted, I stand by my original statement.

Originally Posted by hhEb09'1
It has nothing whatsoever to do with Lorentz. Your argument might as well be just about the equation t = t_0
I think this is answered by the correction above.

15. Originally Posted by thorkil2
The Lorentz equation does not limit the possibility of t_0 being negative (and I don't believe I've said that). The real world does.
You said, in your OP
Originally Posted by thorkil2
The arrow of time is implicit in the Lorentz-Fitzgerald-Einstein (LFE) contractions.
and the OP seems to focus upon that Lorentz implication in the entirety of the post.

I'm saying that the Lorentz stuff has nothing to do with your claim. But then without it, all your claim is, is your personal opinion, nothing more.

16. Established Member
Join Date
Sep 2008
Posts
477
Originally Posted by hhEb09'1
You said, in your OP... and the OP seems to focus upon that Lorentz implication in the entirety of the post.

I'm saying that the Lorentz stuff has nothing to do with your claim. But then without it, all your claim is, is your personal opinion, nothing more.
I think you are twisting my words. t_0 is an input variable, like v/c, and its polarity is not demanded by the equation but by its real world state. t is the output from the equation, determined by the v/c and t_0 input variables. My focus on the equation remains the same. Because v/c cannot be negative, and you haven't shown me any way that t_0 can be negative, the output value for t is implicitly positive, so Lorentz can generate no negative interval: hence the arrow of time is implicit in Lorentz. The possible inputs are limited in their range, and the output is limited as a consequence of the input limits. Positive in, positive out. Again, if you can find a way to establish a non-arbitrary real-world negative value for t_0, then my whole thesis falls apart, and I'm game for that, but I don't think you can do it.

17. Originally Posted by thorkil2
I think you are twisting my words.
I take such a charge seriously. Where have I done that?

I am trying hard to understand your contention.

18. Established Member
Join Date
Sep 2008
Posts
477
Originally Posted by hhEb09'1
I take such a charge seriously. Where have I done that?
I'm sorry if that sounded like an attack. It wasn't meant to be. But you have thrown statements back at me that I don't believe I've made. I never said, for example, that the Lorentz equation forced t_0 to be negative. I said a negative value for t_0 was not possible. You're right. That has nothing to do with the equation. It's an ontological state that affects the outcome of the equation.

Originally Posted by hhEb09'1
I am trying hard to understand your contention.
And I appreciate that. You are doing exactly what I wanted to see done with this when I posted it. I'm happy to defend (or accede, if necessary) to any criticism of the idea. You've already helped me refine the wording so that it's less carelessly stated, and you've kept me thinking hard about it.

19. Established Member
Join Date
Sep 2008
Posts
477
Originally Posted by Tensor
You do realize that in Quantum Field Theory (QFT) that time operations are symmetric, right? If you have an interaction that creates a electron-positron pair, both moving forward in time, you will get the same answer if you use an electron-electron pair, one moving forward in time, one moving backward in time. In the case of the one moving backward, you have t_0 as negative. Now Special relativity has been included in Quantum Theory since 1928 when Paul Dirac combined the two, so I think it has been covered for quite a while. Any good introduction to Quantum Mechanics should cover it.
Sorry, I missed your post in the midst of the discussion with hhEb09'1. Yes, I am aware of that, but would not quite agree with the statement that time operations are symmetric, only that they give the appearance of and can be interpreted as being symmetric. That same apparent symmetry is broken by the T-asymmetry of Kaon creation/decay. I don't think any physicist would allow the electron-positron relationship as very conclusive or convincing evidence in the problem of the arrow of time, since the apparent symmetry is contradicted by other phenomena, and contra-indicated (but not yet fully substantiated by experiment) in the standard model, which predicts a degree of T-asymmetry at the quantum level. The issue remains under scrutiny. You might also interpret the electron-positron pair to be exclusively what they appear to be: an electron-positron pair, without temporal symmetry. Because of their opposite properties, they would look like electrons moving in opposite temporal directions, even in a world that does not permit that opposite motion. I'm simply suggesting an alternative way of looking at it that might (or might not) shed light. I take issue with the idea that T-reversing reactions are time-symmetric. A reversible chemical change, for example, experiences its three states at three distinctly different points in space-time: original state at T_1; altered state at T_2, and re-established original state, not at T_1, but at T_3. It may look like time-reversal, and it may be convenient for the sake of calculation, but in fact, T_3 is not positionally equivalent (in space-time) to T_1, and the reaction proceeds in a positive time line. In other words: the clock keeps on ticking, and it never goes kcot-kcit.

20. Established Member
Join Date
Sep 2008
Posts
477
I've been analyzing this discussion for several days since it stopped and thanks to hhEb09'1 see that there are problems with my own exposition of the idea. I am close enough to this that I have made the error of assuming the "obvious," i.e., that others would read what I see, and I failed to catalog some of my own assumptions. There are corrections to be made, and the addition of things left unsaid that are needed to state the idea more precisely, but I think the idea is still sound. So, let me try this again, and hope I can state it more clearly, and more correctly. I want to emphasize that it is not a revision of the idea, but only a refinement of my exposition of the idea.

The arrow of time is implicit in the Lorentz-Fitzgerald-Einstein (LFE) contractions when the natural limits on input values are considered. Time and motion are complements. Any change of position in space corresponds to a change of position in time; the temporal change is always from present to subsequent present, regardless of the direction of spatial motion, its variables subject only to the degree of motion (i.e., speed). The relationship between motion and time is given by the complementary ratios

(v/c)^2+(t_0/t)^2 = 1

which is a simple algebraic transformation of the LFE time dilation equation

t = t_0/√(1-(v/c)^2 )

* * * * *

0 < v/c < 1

0 < t_0

All motion can be expressed in terms of v/c and the range of possible values for v/c encompasses all possible motion. Input values for v/c are limited to positive values because c is a positive constant, and it is impossible to define a negative v in relation to c.

The value for t_0 is limited because t_0 is the reference interval, measured within the designated rest frame of reference, from which t is calculated. There is no definable negative rest frame interval, so no negative rest frame value for t_0, hence t_0 > 0.

Consequently, all input values used to derive t are greater than 0, so t must be greater than 0.

For any t_0, every value for v/c is associated with a unique value for t, and there is no possible t that is not generated by some value of v/c. These relationships account for all possible motion and all possible relative interval, so negative interval is impossible. Hence the arrow of time and its asymmetry are defined by the fundamental relationship between motion and time.

I welcome comment, evaluation, and/or criticism. I am reasonably certain that the idea is valid, but if I have failed again in any way in expressing it, I welcome comment, and if there is something I've missed that invalidates it, I would like to know that too. My thanks to hhEb09'1 for the earlier comments.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•