The Flux Of Time, A Modern Perspective Of Time Physics

[Aethelwulf]

This idea would seem to indicate that time exists outside what we think of as our universe.

 

http://wwwphy.princeton.edu/~steinh/npr/

 

 

Yes, I do believe the Ekpyrotic Theory to be a ''promising approach'' to explore new idea's. Any way, I haven't finished the OP exactly, or the conclusions drawn later. I made some mention about ''worldlines'' and cutting up moments in time and using a similar approach as Barbour makes in his paper where he is able to describe time itself by simply the displacement of bodies inside a universe.

 

So how do we do this? I have some latex to write out and will begin to attempt to justify the mass flow equation I created [math](\dot{m} - \hbar \nabla^2)\psi = 0[/math].

Edited July 13, 2012 by Aethelwulf

[Aethelwulf]

First of all it seems best to explain why the term [math]\frac{\partial \mathcal{L}}{\partial \dot{q}}[/math] is important when describing world lines.

 

Consisder a simple spacetime interval as:

 

[math]d\tau^2 = dt^2 - d\vec{x}^2[/math]

 

Where we have set [math]c=1[/math] in this case. You actually calculate the length of a worldline by taking into consideration the integral

 

[math]L(W) = \int_W d\tau[/math]

 

You can, it was shown to me a while ago now, that worldines can be written in terms of time by the chain rule. Doing so, you can rewrite the time derivatives as dots on your variables and can end up with

 

[math]L(W) = \int_{t_0}^{t_1} \sqrt{1 - ||\dot{x}||^2}\ dt[/math]

 

From here, you would calculate the Langrangian by simply multiplying mass into the equation, so we would have

 

[math]\mathcal{L} = -M\sqrt{1 - ||\dot{x}||^2}[/math]

 

Now in my equation, we have been using the generalized velocity, and can be freely exchanged now to make the above equation into

 

[math]\mathcal{L}(\dot{q}\dot{q}) = -M\sqrt{1 - \dot{q}\dot{q}}[/math]

 

Now, the canonical momentum part in my equation can be written as

 

[math]\frac{\partial \mathcal{L}}{\partial \dot{q}} = \frac{M\dot{q}}{\sqrt{1 - \dot{q}\dot{q}}}[/math]

 

This is relativistic and is incomporated as one can see, into the idea of worldlines. Now, in my equation, I decided to multiply the momentum with distance. Of course, this was just the quantum action [math]\hbar[/math], but ignoring that fact for now, we wish to calculate the distance really as a displacement of all the particles in the universe [math]d_i[/math] using Barbour's approach. Doing so, will require an integral.

 

Taking the integral of the equation, which ''cuts up'' or ''slices'' a worldline for a particle, then the distance will be small [math]\delta d[/math] for a particle which is the way elluded to in the OP for how to calculate displacement of particles instead of distance exactly.

 

Remembering that

 

[math]\frac{\partial \mathcal{L}}{\partial \dot{q}} = \frac{M\dot{q}}{\sqrt{1 - \dot{q}\dot{q}}}[/math]

 

then my equation

 

[math]\frac{\partial \mathcal{L}}{\partial \dot{q}_i} d_i \nabla^2\psi = \dot{m}\psi[/math]

 

Can actually be rewritten (including the integral this time) as

 

[math]\int \dot{m}\psi\ dt = \int (\frac{M\dot{q}}{\sqrt{1 - \dot{q}\dot{q}}}) \delta d_i \nabla^2\psi\ dt[/math]

 

So as you can see, the integral not only ''cuts'' up the worldline of a particle appropriately, but making the interval short enough will ensure that your distance is really just a very small displacement on a system of particles.

Edited July 13, 2012 by Aethelwulf

[Aethelwulf]

So, if the final equation is taken seriously, we actually have a type of relativistic mass flow equation which can describe the wordlines of each particle as a flow of mass in the universe. There is of course, not just one matter field in the universe, there are a few so one might change the mass sign for a matter field sign we can give as

 

[math]\int \dot{\Xi}\psi\ dt = \int (\frac{\Xi \dot{q}}{\sqrt{1 - \dot{q}\dot{q}}}) \delta d_i \nabla^2\psi\ dt[/math]

 

Each slice of a worldline has something to say about this thing we might call ''the arrow of time.'' As explained in the OP, my investigations have led me to believe there is no such thing as an arrow of time, that time itself is not a continuous thing but rather momentary fleeting flashes of existence of beginnings and ends. This nature is expressed in it's fullest when you consider that the sliced worldline view has basically tried to sum up very small displacements of particles in any given instant of time. If you want to measure the entire worldline, you need to piece these instances together like a jigsaw puzzle. Again, the nature of quantum mechanics would begin to take place if you wanted to know more than simply the momentum of these particles, say if you tried to measure their positions as well, the uncertainty principle is bound to take effect.

Edited July 13, 2012 by Aethelwulf

[Aethelwulf]

Now assuming my approach has been ok, how would one describe the energy then of a single particle in context of the previous equation? The energy of a single particle can be thought of as

 

[math]E\psi = c^2 \int \dot{m} \psi\ dt[/math]

 

And perhaps even then, a simple Langrangian might have the form

 

[math]\mathcal{L} = (\frac{1}{2}\dot{r} \cdot \dot{r}\int \dot{m}\ dt - V)\psi[/math]

Edited July 13, 2012 by Aethelwulf

[Aethelwulf]

And so, as I fiddled about with the form of my equation

 

[math]\dot{m}\psi = \hbar \nabla^2 \psi[/math]

 

(the [math]\hbar[/math] arising from knowing it was the quantum action) let us multiply both sides by the frequency - doing so gives you the equation

 

[math]\dot{m}f\psi = E \nabla^2 \psi[/math]

 

Multiplying both sides by time gives

 

[math]mf \psi = Et \nabla^2 \psi[/math]

 

Mass times frequency is not something you may see often in physics, I do know of a ''damping constant'' which has these dimensions. Anyway, notice on the right that [math]Et = \hbar[/math] (our action again) and that becomes obvious when you realize the frequency is simply [math]1/T[/math] where [math]T[/math] is the time. There for it satisfies the mass over time dimensions again.

Edited July 13, 2012 by Aethelwulf

[Rade]

A slice of time is different though than saying there is no time at all? It's just an instant of time, a single frame no?

I need to be sure I understand what you mean by "slice of time" and "instant of time".

 

Here is my understanding. Consider time is like a loaf of French bread of infinite length, [...<----------->...], and we can then make slices of the time loaf of different duration, such as [<-->]+[<--->]+....and so on to form "single frames of time" of different duration. Is this your concept of an instant of time, a single frame, a slice ? If no, please explain.

 

If yes, notice that this means that time is not composed of "moments" [{0}], that is, any single slice of time [<-->] is that which is intermediate between any two moments, such as this picture showing three moments and two slices of time....{01}[<-->]{02}[<--->]{03}..... By 'moment' I mean the 'now' or the 'present' as relates to the past and future of things with potential for motion.

 

So, look at the three 'slices of time' that are intermediate between the moments in this picture...[<->]{01}[<-->]{02}[<--->]{03}...

 

Here we see what it means to be called "a moment in time", for example, we study moment {02}. We see that the moment in time {02} requires that at minimum two 'slices of time' must exist...that is, the end limit of one 'slice of time' -->]{02, and simultaneously the begin limit of a second 'slice of time' 02}[<--- As we see, if slices of time do not exist, then neither can moments in time exist, and thus neither can things that have motion at different moments in time exist. Likewise, if moments in time do not exist then neither can slices of time exist, for each slice of time must be the limit of something that differs from itself, in the same way that a line is not composed of points (that is, a line is composed of an infinite number of slices of smaller lines).

 

Here we also see what it means to say that two slices of time are simultaneous, that is, simultaneous times are always the limits of any single moment in time.

 

Not sure if this is what you mean by the concept 'slice of time', relationship to 'moments in time', and what it means to say that two slices of time are simultaneous ?

 

==

 

[EDIT] Using the above picture with time arrows <->, it is important to understand that I follow the suggestion of Feynman that matter is that which moves one direction in time -->, while antimatter is that which moves in the opposite time direction to matter <--. I am not aware that anyone has falsified the mathematics presented by Feynman that this is an accurate understanding of relation of antimatter and matter to "time".

[Aethelwulf]

I need to be sure I understand what you mean by "slice of time" and "instant of time".

 

Here is my understanding. Consider time is like a loaf of French bread of infinite length, [...<----------->...], and we can then make slices of the time loaf of different duration, such as [<-->]+[<--->]+....and so on to form "single frames of time" of different duration. Is this your concept of an instant of time, a single frame, a slice ? If no, please explain.

 

If yes, notice that this means that time is not composed of "moments" [{0}], that is, any single slice of time [<-->] is that which is intermediate between any two moments, such as this picture showing three moments and two slices of time....{01}[<-->]{02}[<--->]{03}..... By 'moment' I mean the 'now' or the 'present' as relates to the past and future of things with potential for motion.

 

So, look at the three 'slices of time' that are intermediate between the moments in this picture...[<->]{01}[<-->]{02}[<--->]{03}...

 

Here we see what it means to be called "a moment in time", for example, we study moment {02}. We see that the moment in time {02} requires that at minimum two 'slices of time' must exist...that is, the end limit of one 'slice of time' -->]{02, and simultaneously the begin limit of a second 'slice of time' 02}[<--- As we see, if slices of time do not exist, then neither can moments in time exist, and thus neither can things that have motion at different moments in time exist. Likewise, if moments in time do not exist then neither can slices of time exist, for each slice of time must be the limit of something that differs from itself, in the same way that a line is not composed of points (that is, a line is composed of an infinite number of slices of smaller lines).

 

Here we also see what it means to say that two slices of time are simultaneous, that is, simultaneous times are always the limits of any single moment in time.

 

Not sure if this is what you mean by the concept 'slice of time', relationship to 'moments in time', and what it means to say that two slices of time are simultaneous ?

 

==

 

[EDIT] Using the above picture with time arrows <->, it is important to understand that I follow the suggestion of Feynman that matter is that which moves one direction in time -->, while antimatter is that which moves in the opposite time direction to matter <--. I am not aware that anyone has falsified the mathematics presented by Feynman that this is an accurate understanding of relation of antimatter and matter to "time".

 

 

Right, this is my understanding.

 

Yes, I think that a ''slice of time'' means as you have elaborated on, '' single frames of reference'' however these slices are made so precise (or as precise as we could theoretically make them) that I don't like to think of slices as ''different durations'' which you seem to be thinking of. Instead, time really is cut up into equal segments - very small moments in time, like [math]\delta t[/math] or maybe even on orders of Planck Time? The latter here would make sense for a true quantized kind of theory.

 

'' We see that the moment in time {02} requires that at minimum two 'slices of time' must exist...that is, the end limit of one 'slice of time' ''

 

Well, this isn't quite what I had in mind, however, start points and end points are very important in the idea of slices of time. A slice of time must have a beginning and end point. If we are bringing in another slice of time, that is a new beginning and end. You can only make sense however of a larger picture of dynamics by gluing these slices together again.

[Rade]

Right, this is my understanding.

Great, then I understand what you are saying, and it appears to me that your mathematics could be applied to my simplistic "picture" example of relationship of slices of time (with begin and end points, [<-->]) and moments in time {0}.

 

...these slices are made so precise (or as precise as we could theoretically make them) that I don't like to think of slices as ''different durations'' which you seem to be thinking of. Instead' date=' [b']time really is[/b] cut up into equal segments - very small moments in time, like [math]\delta t[/math] or maybe even on orders of Planck Time? The latter here would make sense for a true quantized kind of theory.

I think the key words you used I have put in bold... "time really is". I would agree that from the reference frame of the universe, that is, how the fundamental laws of the universe work together in Reality, what time "really is" is a summation of very small "slices of time" of identical duration that are mathematically the duration of Planck Time (the quantum measurement limit). But, Planck Time is NOT a "small moment in time" because there is no time within a moment (by definition that is what differentiates time from moments). Also, this does not mean that Planck Time could not be divided, only that it cannot be divided in the universe in which humans experience. There is no reason in theory that, in another universe, what we call Planck Time represents a very long duration relative to other experiences.

 

So, I would agree with you that representing slices of time as having different durations is but a human construct and not how time "Really Is".....I think this would agree with what you are saying, please let me know if I error.

 

Well' date=' this isn't quite what I had in mind, however, start points and end points are very important in the idea of slices of time. A slice of time must have a beginning and end point. If we are bringing in another slice of time, that is a new beginning and end. You can only make sense however of a larger picture of dynamics by gluing these slices together again.[/quote']Yes, but in my way of thinking, it is never the situation where two slices of time are adjacent to each other, with nothing between them. So, this picture of time is not possible ...[<-->][<-->][<-->]... the picture always must be ...[<-->]{0}[<-->]{0}[<-->]...., with {0} = a moment in time. Why ? Because for me, by definition, time is that which is intermediate between moments. And from this definition of time all classical and quantum theory can be derived. Please let me know if this is your understanding.

 

Finally, for me, time can be considered to be discrete only in the sense that any number (1,2,3..) is discrete, for each slice of time is nothing more than the measure of motion that is intermediate between two moments. This measure can be given a number label that differs from the reference frame of the universe (that is, the measure is = Planck Time) as opposed to human experience reference frame (e.g., it took Mary a larger slice of time to travel distance x between two moments than John).

Edited July 13, 2012 by Rade

[Aethelwulf]

Great, then I understand what you are saying, and it appears to me that your mathematics could be applied to my simplistic "picture" example of relationship of slices of time (with begin and end points, [<-->]) and moments in time {0}.

 

I think the key words you used I have put in bold... "time really is". I would agree that from the reference frame of the universe, that is, how the fundamental laws of the universe work together in Reality, what time "really is" is a summation of very small "slices of time" of identical duration that are mathematically the duration of Planck Time (the quantum measurement limit). But, Planck Time is NOT a "small moment in time" because there is no time within a moment (by definition that is what differentiates time from moments). This does not mean that Planck Time could not be divided only that it cannot be divided in the universe in which humans experience. There is no reason in theory that, in another universe, what we call Planck Time represents a very long duration relative to other experiences.

 

So, I would agree with you that representing slices of time as having different durations is but a human construct and not how time "Really Is".....I think this would agree with what you are saying, please let me know if I error.

 

Yes, but in my way of thinking, it is never the situation where two slices of time are adjacent to each other, with nothing between them. So, this picture of time is not possible ...[<-->][<-->][<-->]... the picture always must be ...[<-->]{0}[<-->]{0}[<-->]...., with {0} = a moment in time. Why ? Because for me, by definition, time is that which is intermediate between moments. And from this definition of time all classical and quantum theory can be derived. Please let me know if this is your understanding.

 

 

Bolded by me.

 

Well, I agree... and even in these slices of time, even if it was not the Planck Length, I still believe them to be traditionally out-side of conscious experience. We have our own speed in which we compute things. This is called the ''speed of consciousness''.

 

You may be able to find some scientific papers online concerning this ''speed''.

 

As for the last part, if we want to think of frames of time which have starts and stops, and knowing that only the present time exists, then what we have is quite possibly, an infinite amount of presents times to consider. However, in an intuitive sense, one can think about pasting ''events'' or ''frames of time'' together in such a way, that we can perhaps piece together what we once spliced up.

[Aethelwulf]

As I have said before, there is no past or future. If anything, there is only an eternal present.

[Rade]

As I have said before, there is no past or future. If anything, there is only an eternal present.

I do not agree as concerns 'moments in time'. There are possible both past and future 'moments in time' because we use terms such as long-ago (e.g., Newton lived long-ago) and presently (e.g., when will you leave for the airport? I will leave presently) in relation to a present 'moment'. So, clearly there are possible both past and future moments relative to the present moment (the now).

 

Concerning time, I took a look at what you said in the OP and found this:

 

Another feature to keep in mind' date=' that really all there is, is a present time. If we could think of time as a sphere that encompasses us (but does not move or flow) then we are always stuck inside this ''present sphere''. The notions of past and future become meaningless because things don't happen in any past or future, everything was always in the present time frame. This is another reason why we may think that our sense of time is not as it seems and perhaps distinction of past and future lead to illusions as well.[/quote']

 

My problem with what you claim is that, given that I define time as that which is intermediate between moments, there is not possible any concept of 'present time' that you discuss. For me there is only a concept of 'present moment' (the now) that simultaneously is the extremity of a past time (where no part of the future exist) and the extremity of a future time (where no part of the past exists). From previous post, ..[<-->]{01}[<-->]{02}[<-->]..

 

The reason there cannot be a 'present time' is due to the definition of 'present', the present in a primary sense is always indivisible, whereas time in a primary sense is always divisible (the concept of slices of time). To use the term 'present time' would then result in a logical contradiction of terms. However, the term 'present moment' is allowed because both terms are indivisible.

 

I understand that you likely will not agree with what I say above, and would be interested in future dialog on the topic. For me this is the fun aspect of the forum, to learn and understand.

[Aethelwulf]

I don't think you actually realize, there is nothing outside the present moment. Nothing exists ''now''' without a good definition of ''now things''.

[Rade]

I don't think you actually realize, there is nothing outside the present moment. Nothing exists ''now''' without a good definition of ''now things''.

OK, I see I am not making myself clear. Let us take the concept "present moment" you use. Recall that by definition time (hence also motion of things) is that which is intermediate between moments, thus there cannot be either time or things with potential motion within any moment, including your concept of 'present moment'. Therefore, all that exists by nature (that is, having internal motion) can only exist within a "slice of time", given that each moment is outside of time. Recall also that slices of time have potential to have different durations when viewed from the human reference frame. Thus, I agree with you that nothing exists "now" (or in the moment) and it makes no sense to try to define "now things", which is a contradiction in terms given that no things exist within the now (except perhaps those things that are forever and have no beginning or end or mass, perhaps for example the photon and gluon).

 

Consider a single "slice of time" that includes two moments, the first a present moment. So, we have a runner that at a present moment {A} begins to move (e.g., to transition) and reaches end point at future moment {B} with immediate stop of motion. Clearly the action is that which is between the two moments (time), where motion of the thing that exists (the running) is in play. So, in my way of thinking, each "slice of time" is where things that exist are either in motion or at rest, and nothing exists within any moment, past-present-future, because each moment is nothing more than where past time and future time undergo transition (that is, just as there is no motion within a moment, neither is there any rest, because both motion and rest are measured by time).

 

I believe we use terms differently by definition and this results in misunderstanding, but I am very interested in your mathematical presentation because I think (?) I can apply it to my way of thinking about time (with your concepts of start and stop limits for time). What you claim about "present moments" may be true using your definitions of time and moment (which I must say is not clear to me yet), but it does not agree with the definitions I follow.

 

[Edit] I have read that some call the "present" to be the combination of: (1) a period of time, including (2) a present moment. Using this type of definition of present would agree with your position (that everything must be within the present moment), but, this is not what I am referring to. I refer to the primary sense of the term present, how it is inherent within all time, not how it is part of time. Again for me, the present is within time as odd and even numbers are within the number line, the time-line being that which is intermediate between the numbers.

[Aethelwulf]

OK, I see I am not making myself clear. Let us take the concept "present moment" you use. Recall that by definition time (hence also motion of things) is that which is intermediate between moments, thus there cannot be either time or things with potential motion within any moment, including your concept of 'present moment'. Therefore, all that exists by nature (that is, having internal motion) can only exist within a "slice of time", given that each moment is outside of time. Recall also that slices of time have potential to have different durations when viewed from the human reference frame. Thus, I agree with you that nothing exists "now" (or in the moment) and it makes no sense to try to define "now things", which is a contradiction in terms given that no things exist within the now (except perhaps those things that are forever and have no beginning or end or mass, perhaps for example the photon and gluon).

 

Consider a single "slice of time" that includes two moments, the first a present moment. So, we have a runner that at a present moment {A} begins to move (e.g., to transition) and reaches end point at future moment {B} with immediate stop of motion. Clearly the action is that which is between the two moments (time), where motion of the thing that exists (the running) is in play. So, in my way of thinking, each "slice of time" is where things that exist are either in motion or at rest, and nothing exists within any moment, past-present-future, because each moment is nothing more than where past time and future time undergo transition (that is, just as there is no motion within a moment, neither is there any rest, because both motion and rest are measured by time).

 

I believe we use terms differently by definition and this results in misunderstanding, but I am very interested in your mathematical presentation because I think (?) I can apply it to my way of thinking about time (with your concepts of start and stop limits for time). What you claim about "present moments" may be true using your definitions of time and moment (which I must say is not clear to me yet), but it does not agree with the definitions I follow.

 

[Edit] I have read that some call the "present" to be the combination of: (1) a period of time, including (2) a present moment. Using this type of definition of present would agree with your position (that everything must be within the present moment), but, this is not what I am referring to. I refer to the primary sense of the term present, how it is inherent within all time, not how it is part of time. Again for me, the present is within time as odd and even numbers are within the number line, the time-line being that which is intermediate between the numbers.

 

 

I think you are mistaking what I have meant myself, I certainly don't mean to say that there is no ''now'' - only that the past and future don't exist and all there is, is the ''now''. Maybe I was writing a bit unclear, for that I apologize. You can define the ''now'' as an ''instant of time''. Does the past exist ''now''? If there is only the present moment, then the answer is no. You also make some mention about the ''slices'' moving at different durations for human observers. Yes, this is true, but it's not encompassed in my view of world line slice. What I was trying to say, when I cut up a world line I want to do it for the shortest available time so displacements of particles are actually very simple short distances - (this in all practicality would be outside of the speed of consciousness and perception).

 

And yes, some might call the present moment a record of the past, or rather as you said, the period of time including a present moment. So one way to write this is by saying, the present [math]t_1[/math] is the past [math]t_0[/math] plus a time delay [math]\Delta t[/math] as

 

[math]t_1 = t_0 + \Delta t[/math]

 

abstractly this is ok. It makes sense to think of the present moment in this case as some present moment that once existed in the past and which then a small change in time led up to the present moment we recognize as ''now''. Just keep in mind, that the past [math]t_0[/math] can't have any physical relevance. I use past and future here as [math](t_0,t_1)[/math], notation may vary.

 

Using the above equation, one could argue the future [math]t_2[/math] is the present plus a change in time as

 

[math]t_2 = t_1 + \Delta t[/math]

 

But how does one make sense of the future in a physical sense? The future has not happened, and in fact, never happens. This is the paradox of our experience of time - all there is is the present moment nothing exists outside of it, nothing flows into the present moment or out of it.

Edited July 15, 2012 by Aethelwulf

[Rade]

You can define the ''now'' as an ''instant of time''

OK, this is not how I define it, thus clearly we are not discussing the same event. I define 'now' = 'moment' and I put both of them outside of time. For me, an 'instant of time' = Planck Time and, because it is a time measure, it is outside the 'now'.

 

how does one make sense of the future in a physical sense?

OK, using your mathematical example, let me suggest this:

 

For moments, there are three possible, past (M1), present (M2), future (M3).

For slices of time there are two possible, past slice of time (t1) and future slice of time (t2)

 

You said

It makes sense to think of the present moment ...as some present moment that once existed in the past and which then a small change in time led up to the present moment we recognize as ''now''

(e.g. now = an instant of time)

 

So' date=' if we apply my symbols to translate your text, then M2 = present moment, M1 = moment that existed in past, [math']\Delta t1 [/math] = change of state during time in the past that led to the present moment M2, and we get this equation:

 

present moment:

 

[math] M_2 = M_1 + \Delta t_1[/math] , eq. 1

 

and this for past moment:

 

[math] M_1 = M_2 / \Delta t_1[/math], eq. 2

 

Then, using the same logic in opposite direction of time line, the future moment for M2 would be:

 

[math] M_3 = M_2 + \Delta t_2 [/math], eq 3

 

substitute present moment from eq 1 into eq 3:

 

[math] M_3 = (M_1 + \Delta t_1) + \Delta t_2[/math] eq 4

 

Rearrange:

 

[math] \Delta t_2 = M_3 / (M_1 + \Delta t_1)[/math] eq 5

 

 

==

 

How to apply to the "future in a physical sense" ?

 

==

 

Eq. 4 suggests that the physical sense of any future moment for a system state requires knowledge of the physical sense of a past moment of the system state at some time duration in the past, how that system state actually changed during that past time duration, and how it potentially will change during the time duration that leads from the present moment to a hypothetical future system state.

 

Comments welcome.

Edited July 16, 2012 by Rade

[Aethelwulf]

 

OK, using your mathematical example, let me suggest this:

 

For moments, there are three possible, past (M1), present (M2), future (M3).

For slices of time there are two possible, past slice of time (t1) and future slice of time (t2)

 

You said (e.g. now = an instant of time)

 

So, if we apply my symbols to translate your text, then M2 = present moment, M1 = moment that existed in past, [math]\Delta t1 [/math] = change of state during time in the past that led to the present moment M2, and we get this equation:

 

present moment:

 

[math] M_2 = M_1 + \Delta t_1[/math] , eq. 1

 

and this for past moment:

 

[math] M_1 = M_2 / \Delta t_1[/math], eq. 2

 

Then, using the same logic in opposite direction of time line, the future moment for M2 would be:

 

[math] M_3 = M_2 + \Delta t_2 [/math], eq 3

 

substitute present moment from eq 1 into eq 3:

 

[math] M_3 = (M_1 + \Delta t_1) + \Delta t_2[/math] eq 4

 

Rearrange:

 

[math] \Delta t_2 = M_3 / (M_1 + \Delta t_1)[/math] eq 5

 

 

==

 

How to apply to the "future in a physical sense" ?

 

==

 

Eq. 4 suggests that the physical sense of any future moment for a system state requires knowledge of the physical sense of a past moment of the system state at some duration in the past for some duration of time that leads to the future from the present.

 

Comments welcome.

 

A very intelligible response.

 

Let me concentrate on the bolded part. The reason why I asked, ''what is a physical interpretation of a future'' is because there doesn't seem to be one.Your answer is good however, but its based on the faulty premise that the past and future exist outside of the present moment. The point I have been trying to get across is that nothing exists outside the present moment. We are all stuck inside it like flies stuck in amber. Therefore, scientifically-speaking, it makes little sense to think about the past or future with any kind of true meaning, other than some illusory experience that we some how flow throughout time - but this has been shown to be incorrect within the framework of experimental physics.

[Rade]

Your answer...its based on the faulty premise that the past and future exist outside of the present moment. The point I have been trying to get across is that nothing exists outside the present moment.

Well, I am confused because this is exactly what I was showing with my equations of the past, present, future moments. So,if you look again (shown below) you will see that the past and future moments require that the 'present moment' (M2) exists, so, in fact my equations agree with the point you have been trying to get across. Again, I suggest:

 

 

past moment:

 

M_1 = M_2 / \Delta t_1, eq. 2

 

future moment:

 

M_3 = M_2 + \Delta t_2 , eq 3

 

==

 

Note that both past and future require that the present moment M_2 exists, that is, nothing is outside the requirement that the present moment exists. Of course, we assume that the present moment M_2 does exist.

 

Therefore' date=' scientifically-speaking, it makes little sense to think about the past or future with any kind of true meaning [/quote']But, this does not agree with your statement from two posts ago that what you call the 'present moment' can be thought as resulting from a [math]\Delta t_1[/math] concept, which does has a clear meaning of being a past time leading to a moment in the present. Thus, it does make sense to think about a concept of the 'past' if we are to accept your concept of a 'present moment'. Well, I hope you can see my confusion.

Edited July 16, 2012 by Rade