Relativity and the question of age

[nitsuj]

I will, but it takes me a long time to think it through and write it out so there is no "holes" in it, I think I may even have to make a definition for aging. (yay wiki defines it pretty well, don't even have to be specific i.e. senescence)

At work right now so in the est. afternoon I can reply much better, and am excited to too..."stupid" work getting in the way of physics musings lol.

About wordlines, Oh, then no not what I meant, we all take different paths through spacetime, which is what leads to the different measures of time/length comparably (less there being no comparative motion). causality is the reason for the interval.

 

[nitsuj]

Surely by now you (wannabeNewton) know I cannot read math. lol

Maybe I need to define a physical occurrence because you(WannabeNewton) keep mentioning separations between objects. A physical occurrence is the moment of interaction between previously separated objects with a “focus” on one of the objects...no concern for the “size” of separation just that there was a separation & that there is a moment when the two objects contact; which could be idealized or actual. This is not about how we measure spacetime and how we plot things differently on our coordinate "charts" if there is relative motion between us. It is strictly about the order of physical occurrences. From a physical perspective anything else is us measuring and plotting on paper i.e. not physical for the objects themselves (less you the observer, measuring tools, yada yada yada)

So there is me in the gym ready for an onslaught of dodge balls to be thrown at me. I'm tough so Ill be sure to be hit by each one. Each one is identified independently...numbered 1 through 10 and thrown at me in an incremental order every minute from 10m away (both measured in my frame). Every observer in the (local) universe will agree on the order the balls hit me. Few will agree on the 10m length & 1 minute time between throwing each ball.

Some will observe little length separation (non zero min.) between me and the ball throwers and a greater then 1 min delay (less then an infinite time path between balls being thrown).

These different observations all see the same order of physical occurrence.

So all that needs to be said is physics (SR) has a causal structure. There are only two mutually exclusive, physically relevant possibilities. The physical occurrence(s) that will occur and the physical occurrence(s) that has (had) occurred. However you measure that separation is up to you and is physically irrelevant. What is not physically irrelevant is the fact there is a separation between the objects. Clearly as we know the length of separation is irrelevant. We could easily make it so the length of separation is less, but that will cause a “delay” for us...which is maintaining the causal structure. Let’s use the dodge ball example.

While I am getting hit by the dodge balls I'm watching you in motion taking observations of the onslaught. Idealize exactly the moment you receive the first lightlike notice of the physical occurrence of ball #5 hitting me, you read your laboratory wrist watch (there cannot be separation between you and clock for this) and it reads 1:00. Note how you receiving the “notice” is it self a physical occurrence. We both agree on that 1:00 o'clock time, despite our independent measure of proper time.
Every observer would agree with that physical occurrence...you receiving notice of ball #5 hitting me when your wrist watch reads 1:00. We can add every observer watching every other observer to note the order each receives the observation of the incremental ball numbering and which order they hit me. All will agree 1-2-3 and on. That's causal ordering. Few will agree on the length/time measures, and that is non-consequential to the physics itself.

But realize that if you are measuring a separation between objects that will never interact (idealized or actual) it is a physically meaningless result/measure, this is actually physically impossible to do but some love diagrams so I mention it idealized. Big deal if you measure a length or a time interval of some sort between objects, sure it's important to you specifically, but the structure of the universe isn't about your measurements of length/time. It's about physical occurrence, and the continuity/order of these physical occurrences, that's it. Even motion is physically meaningless, that’s merely the geometry between physical occurances (who "has" the kinetic energy in comparative motion? Is it even a physical property?) no matter how fast you try to go there will always always always be a length of some measure of 10m or less (but not zero) between me and the dodge-ball ball "throwers" and a time interval of 1min or more (as in longer time path) but less then infinity.

It’s not much of a leap to extend this to differential aging.

In the dodge-ball example, every time the balls hit me I am one minute older; in my frame. In the frames moving compared to the dodge-ball “system” (or would be the case aging of a body) this is happening more slowly than “1 minute older” every time a ball hits me. Let’s say in your frame it’s two minutes between ball throwing/hitting me.

Im going to introduce a magical character named causal system referee. He/she is an observer that makes sure this ordering is maintained. Let’s place this referee far enough away that the field of observation includes the dodge-ball “system” and your frame within a 150 degree or so angle of “view”. This referee is in motion compared to the dodge-ball “system” & you; so that he/she measures one and a half minute time intervals between ball throwing.

This referee will say (as will every other observer) that whether or not you started moving from your position at the moment (any observer’s “moment” of that physical occurrence) ball #5 had hit me you would receive the initial light like notice when your laboratory wrist watch read 1:00, you cannot “speed” away from causal structure. The comparative motion is physically meaningless to the objects themselves.

So for differential aging, the only requirement is causal structure. Regardless of your relative motion, regardless if you measure 1 or 2 minute intervals between ball throwing you get the causal physical occurrence of “notice” when your laboratory wrist watch reads 1:00. For that to happen I must age slower then you from your frame and you must age slower then me from my frame.

So long and short of it is, SR is merely the geometry of physics, not so much physics itself. What’s so intriguing, or what I find so intriguing is that geometry includes a measure of time which leads to geometric “time traveling to another observers future”, equally though it leads to length contracting, not as “exciting” differential aging between twins or what have you.

The only “physics” in SR seems to be “built in” with the mechanical physics postulate. Everything else is geometric “modifiers” to those mechanics. This more or less is saying we live in a continuum, and it’s a causal system.


Trying to reduce it, everything in the (local) universe is in motion. Some are inertial locally by definition, for example my body, a dodge-ball game, the Earth, but that is by definition only. Note we do live in a continuum. So when I say objects assume it’s in motion compared to something else somewhere, we already do but vaguely, here in must be implicit & obvious.

So if everything is in motion, all these things measure length/time between other objects from comparatively different angles across spacetime due to the motion.

So are the simple statements everything is in motion & within a causal structure enough for differential aging. I think so. Ultimately this can be restated as aging (not strictly senescence) is a geometric phenomenon, but the causal structure results in differential aging.

 

[PAllen]

It could be interesting to examine the following:

Both a Galilean universe and an SR universe are causal. However, the the former provides a total ordering of events, while the latter only a partial order (events that have an invariant order are causally connected; those that don't are causally disconnected). Is it possible to come up with a chain of reasoning that leads to differential aging strictly from the causal structure of SR (as distinct from Galilean relativity)? If not, what minimal additional assumption is needed?

I don't have time to think about this in detail now, but I could see a chain of reasoning like: if all world lines between two events have the same clock time, then a global time (and thus time ordering) can be set up, violating the causal structure of SR.

 

[ghwellsjr]

So are the simple statements everything is in motion & within a causal structure enough for differential aging. I think so. Ultimately this can be restated as aging (not strictly senescence) is a geometric phenomenon, but the causal structure results in differential aging.

There's nothing in your post about differential aging in spite of your continual claims.

You are talking about Time Dilation, not differential aging.

Differential aging is when two objects/clocks/observers start out colocated (a physical occurrence, in your terminology) at which point they synchronize their clocks, then they separate and eventually they become colocated again (a second physical occurrence) at which point they compare the accumulated times on their respective clocks and find them to be (possibly) different.

 

[ghwellsjr]

So there is me in the gym ready for an onslaught of dodge balls to be thrown at me. I'm tough so Ill be sure to be hit by each one. Each one is identified independently...numbered 1 through 10 and thrown at me in an incremental order every minute from 10m away (both measured in my frame). Every observer in the (local) universe will agree on the order the balls hit me.
...
We can add every observer watching every other observer to note the order each receives the observation of the incremental ball numbering and which order they hit me. All will agree 1-2-3 and on. That's causal ordering.
...
In the dodge-ball example, every time the balls hit me I am one minute older; in my frame.

This is only true if the balls are thrown at exactly the same speed, an unrealistic assumption, don't you agree?

And, since you didn't specify anything about the speeds of the balls, I'm going to suggest that if some of the balls are thrown at a very slow speed so that they take longer than a minute to traverse the 10-meter distance, then you can't even say that they arrive in the same order in which they were thrown, can you? Of course not.

Furthermore, as I said in my previous post, you didn't provide any example of differential aging. However, if we allow the balls to be thrown at different speeds, then we can use your example to show differential aging of the balls.

I'm going to change your scenario a little bit so that it can be drawn on a spacetime diagram that will fit on one page, but the principles still apply even for your example. I'm going to show you in blue, the ball thrower in green, and then I'm going to show just two balls, the first in black and the second in red.

As I said in my previous post regarding differential aging, the two balls are colocated with the thrower at the beginning (at the Coordinate Time of 1 nsec and the Coordinate Location of 12 feet) and take different paths to you at the end of the scenario (at the Coordinate Location of 0 feet) and we will look at how the age of each ball progresses as shown by the dots indicating 1 nsec increments of Proper Time.

First we have the situation where both balls are thrown at the same speed of 0.6c:

Now if you count the dots from the lower right corner where the first ball is thrown until the upper left corner where the second ball hits you, you will see that both balls age by 22 nsecs.

In the next post, I will show three more examples where the second ball is thrown at different speeds.

After that, I invite you to explain how "the causal structure results in differential aging", ok?

 

[ghwellsjr]

Now I'm going to show the same scenario except that the second red ball will be thrown at a slower speed, 0.479c:

Count the dots again and you will see that the black ball ages by 27 nsecs while the red ball ages by 28 nsecs.

Next, the red ball is thrown at 0.8c:

The black ball ages by 17 nsecs and the red ball by 15 nsec.

Finally, the red ball is thrown at 0.923c:

The black ball ages by 16 nsecs and the red ball by 12 nsecs.

Note also that the order in which the balls hit you is different than the order in which they were thrown.

Also note in these three cases that the time delta in which the balls hit you is not the same as the time delta in which they were thrown.

So now here is your opportunity to explain how "the causal structure", which is clearly apparent in all these diagrams, "results in differential aging".

 

[nitsuj]

This is only true if the balls are thrown at exactly the same speed, an unrealistic assumption, don't you agree?

And, since you didn't specify anything about the speeds of the balls, I'm going to suggest that if some of the balls are thrown at a very slow speed so that they take longer than a minute to traverse the 10-meter distance, then you can't even say that they arrive in the same order in which they were thrown, can you? Of course not.

I was going to retort to your previous reply, but you're changing the post around to make a point. I'm not gunna "play".

No George, it's one minute between ball throwing. the spacetime interval is crucial...

My post does explain differential aging from a causal perspective.

 

[nitsuj]

It could be interesting to examine the following:

Both a Galilean universe and an SR universe are causal.

Show me causal structure in a gallian universe. We will end with infinite speed...does causal structure make sense when we can go infinitely fast? What does infinite fast mean?Geometry in a Galilean universe excludes time as a component (of the geometry). It even hand waved away the speed of gravity saying it's instant. Yea that makes physical sense

When time is a component of geometry, causal structure leads to differential aging & an invariant speed.

a Galilean universe is full of logic "holes", SR is Fort Knox lol

 

[ghwellsjr]

I was going to retort to your previous reply, but you're changing the post around to make a point. I'm not gunna "play".

I didn't change anything that you specified. And I'm trying to help you make your point.

No George, it's one minute between ball throwing. the spacetime interval is crucial...

Then will you agree that my first diagram in post #35 is similar enough to your scenario that you can make your point with it?

And I thought you said you "cannot read math". How do you determine the spacetime interval in your scenario without math? What is its value and what are the two events that you are calculating it between? And if it's so crucial, why didn't you mention it in your very long post?

My post does explain differential aging from a causal perspective.

Where do you mention any differential aging?

 

[nitsuj]

This is only true if the balls are thrown at exactly the same speed, an unrealistic assumption, don't you agree?

And, since you didn't specify anything about the speeds of the balls, I'm going to suggest that if some of the balls are thrown at a very slow speed so that they take longer than a minute to traverse the 10-meter distance, then you can't even say that they arrive in the same order in which they were thrown, can you? Of course not.


After that, I invite you to explain how "the causal structure results in differential aging", ok?

The order the balls hit me as I see it, will be the same order every observer sees the balls hit me. No speed can have it such that ball 5 hits before ball 4. For your charting, this is very clear. If there is no separation between me and the ball there is no way to separate it so ball 5 can "get in there" and hit me before ball 4.

This is NOT about the order they seen traveling, it's the order they hit me The order they leave the Single ball throwers hands will also be invariant, what is not invariant is how they are seen traversing spacetime, which is to your point.

I have explained it, you "distort" the meaning, perhaps unintentionally, but none the less spoils any attempt to discuss it

 

[ghwellsjr]

The order the balls hit me as I see it, will be the same order every observer sees the balls hit me.

You are spending a lot of time "making a point" that everyone already agrees with. Yes, whatever order the balls actually hit you is the order you see them hit you and the order that everyone else sees them hit you. I made no comment about this issue. I only showed one frame, your rest frame. I was not and am not concerned with what other frames or observers might see. This issue has absolutely nothing to do with differential aging. If you would show me the two objects/clocks/observers that you are considering to have aged differently, then I can show you how all frames and observers will agree on their differential aging if you want. But you haven't made any comment about this even though I keep asking you to do so.

No speed can have it such that ball 5 hits before ball 4.

I agree, no speed that is applied exactly to every ball will result in them hitting you in a different order. I already stated this fact.

For your charting, this is very clear. If there is no separation between me and the ball there is no way to separate it so ball 5 can "get in there" and hit me before ball 4.

This is NOT about the order they seen traveling, it's the order they hit me The order they leave the Single ball throwers hands will also be invariant, what is not invariant is how they are seen traversing spacetime, which is to your point.

No, that's not my point. I didn't show any scenario transformed between two different frames. All my diagrams were for the same frame, just different scenarios.

I have explained it, you "distort" the meaning, perhaps unintentionally, but none the less spoils any attempt to discuss it

You aren't discussing the issue you claim to be discussing. That's the problem. You think there is some differential aging going on in your scenario but there isn't. If you think there is, please point it out.

 

[Nugatory]

Justin, back in #29 you say

I have to read what world lines are. I imagine it's the same as saying we each have our own proper time. In other words I don't know the strict definition/concept of worldlines well enough to include in a retort/response.

It's really hard to communicate effectively about causality and time without this understanding. Watching you try makes me feel as if I'm watching someone using Roman numerals to explain long division - the representation is getting in the way.

 

[nitsuj]

Justin, back in #29 you sayIt's really hard to communicate effectively about causality and time without this understanding. Watching you try makes me feel as if I'm watching someone using Roman numerals to explain long division - the representation is getting in the way.

I appreciate that with respect to disusing spacetime between objects. Causality is about the objects themselves and observations of them.

I don't need to draw diagrams representing spacetime, for this point. George says we all already agree on causality.

All that I need to do is assume a "global/local/whatever" causality, which isn't at all about spacetime. And either is differential aging, it's about the objects themselves and how physical occurrences "play out" and how we all agree on the order. If it's conceptually necessary, then include the c postulate (speed limit).

 

[WannabeNewton]

Well for starters, causality is all about causal curves so it involves exactly what Nugatory mentioned, and George's point is that differential aging simply deals with the different integrated proper times along two different space-time "trajectories" that have the same initial and terminal points (I put trajectories in quotes because technically nothing moves in space-time so it's not like we're tracing out a curve following the path of a particle in the Newtonian sense of a trajectory) and what you are saying is not related; I'm not sure you understand what causal structure is (and by the way, Galilean space-time is a known construction so what you said in post #38 is incorrect).

 

[nitsuj]

If you think there is, please point it out.

It is there. I'll try to think of a better way to structure what I wrote so the logic is more apparent.

Like I PM'd you, this is really just making a clear distinction between geometry & physical occurrence.

My perspective is you keep discussing spacetime and making diagrams, which isn't at all what this is about. It's about Physical occurrence ordering being invariant as observed happening to a specific object, and you already said you agree with that. We still don't need diagrams to make the "next step" of how a consequence of this is differential aging.

 

[nitsuj]

Well for starters, causality is all about causal curves

(and by the way, Galilean space-time is a known construction so what you said in post #38 is incorrect).

Yea, I can't make anything of that.

My point which I said explicitly is time is not part of the geometric structure in a Galilean Universe. Speed can be infinite which is a pretty big logical "hole". Who cares if it's "known" it's not "real" /

 

[WannabeNewton]

My point which I said explicitly is time is not part of the geometric structure in a Galilean Universe. Speed can be infinite which is a pretty big logical "hole". Who cares if it's "known" it's not "real" /

At a basic level:
http://ls.poly.edu/~jbain/spacetime/lectures/11.Spacetime.pdf
http://faculty.arts.ubc.ca/ssavitt/Courses/Phil462B/Galilean%20Spacetime.pdf

At a more advanced level: http://arxiv.org/pdf/gr-qc/0211030v2.pdf

 

[PAllen]

Show me causal structure in a gallian universe. We will end with infinite speed...does causal structure make sense when we can go infinitely fast? What does infinite fast mean?Geometry in a Galilean universe excludes time as a component (of the geometry). It even hand waved away the speed of gravity saying it's instant. Yea that makes physical sense

When time is a component of geometry, causal structure leads to differential aging & an invariant speed.

a Galilean universe is full of logic "holes", SR is Fort Knox lol

Completely wrong on all counts. Galilean relativity is simply the c->∞ limit of SR. It is true that there is no (non-degenerate) spacetime metric, but that is the point - space and time are separable. The causal structure is stronger than SR because all pairs events have invariant (under Galilean transforms) causal order. Thus, both theories have causal structure, but not the same one. Obviously SR matches reality, but that is not relevant.

In case you didn't notice, I was wondering whether there is some validity to what you are arguing: Is the specific causal structure of SR versus Galilean relativity (alone) sufficient to require differential aging? I think the answer is probably yes, with maybe a few technical assumptions required, but I haven't put together a rigorous argument for this.

 

[ghwellsjr]

You aren't discussing the issue you claim to be discussing. That's the problem. You think there is some differential aging going on in your scenario but there isn't. If you think there is, please point it out. [Quote expanded to include context.]

It is there. I'll try to think of a better way to structure what I wrote so the logic is more apparent.

It's not a matter of logic, it's simply a matter of stating which two objects/observers/clocks are the ones engaged in differential aging. I already pointed out what you could have answered:

Consider any two of the ten balls. They start out colocated with the thrower. One of them leaves and goes (is thrown) to you. Some time later, the second ball leaves (is thrown) and goes to you at which point those two balls are again colocated. Now we can calculate (if we know their speeds) the amount of aging each ball achieved from the time they were together, then separated, then rejoined.

But you rejected my suggestion, insisting that somewhere else in your scenario is another example of differential aging. I'm just asking where. You don't have to explain how we determine their respective aging, just who (or what) they are.

Like I PM'd you, this is really just making a clear distinction between geometry & physical occurrence.

If you are saying that you have not yet gotten to the differential aging part, then I agree. However, you're going to have to start all over again with a different scenario if you want to demonstrate differential aging in your discussion.

My perspective is you keep discussing spacetime and making diagrams, which isn't at all what this is about.

I'm not the only one discussing spacetime (as if there's something wrong with that):

No George, it's one minute between ball throwing. the spacetime interval is crucial...

And you ignored my request for you to tell me what the value of the spacetime interval is and what two events it applies to. This is a simple request and you shouldn't have a problem answering this question.

If you don't like my diagrams, then just ignore them, I thought they would help you in your explanation.

It's about Physical occurrence ordering being invariant as observed happening to a specific object, and you already said you agree with that. We still don't need diagrams to make the "next step" of how a consequence of this is differential aging.

Ok, I will wait for you to present the "next step". I had no idea your long post was not intended to be an explanation of how "causal structure results in differential aging".

 

[nitsuj]

Completely wrong on all counts. Galilean relativity is simply the c->∞ limit of SR. It is true that there is no (non-degenerate) spacetime metric, but that is the point - space and time are separable. The causal structure is stronger than SR because all pairs events have invariant (under Galilean transforms) causal order. Thus, both theories have causal structure, but not the same one. Obviously SR matches reality, but that is not relevant.

In case you didn't notice, I was wondering whether there is some validity to what you are arguing: Is the specific causal structure of SR versus Galilean relativity (alone) sufficient to require differential aging? I think the answer is probably yes, with maybe a few technical assumptions required, but I haven't put together a rigorous argument for this.

The reality point I suppose could be a matter of opinion. The causal structure is NOT stronger...because it doesn't even exist. It's non sense to compare impossible things to reality and pose it as a point.

Again show me causal structure in that "metric" of infinite speed. I'll just go faster.

In case you didn't notice, you said I was wrong on all counts, that contrasts your agreement with how I described the "metric" as not including time. & the lack of a speed limit. Which are the only two points I mentioned in retort.

This is to your point of SR "breaking" causal connection (spacelike), it has too less the non sense of infinite speed.

If you really feel there is a true & meaningful "causal" structure in Galilean geometry you won't ever agree with what I am saying, if you laugh at that proposed structure as physical non sense then you may see where I am "coming from" with my perspective.

And I hope I don't come across as arguing, if it does I don't want to continue...it's not at all how I wish to "present" a perspective.

 

[nitsuj]

And you ignored my request for you to tell me what the value of the spacetime interval is and what two events it applies to. This is a simple request and you shouldn't have a problem answering this question.

If you don't like my diagrams, then just ignore them, I thought they would help you in your explanation.


Ok, I will wait for you to present the "next step". I had no idea your long post was not intended to be an explanation of how "causal structure results in differential aging".

The interval is important because of it's invariance.

I am at work now, and as much as I want too, I got to refrain from "working" at this lol

I'll reply this E.S.T. evening.

A side note your diagrams are awesome! Just for this it's not really relevant to illustrate spacetime. Just to pose an axiom (and maybe a postulate)

 

[nitsuj]

At a basic level:
http://ls.poly.edu/~jbain/spacetime/lectures/11.Spacetime.pdf
http://faculty.arts.ubc.ca/ssavitt/Courses/Phil462B/Galilean%20Spacetime.pdf

At a more advanced level: http://arxiv.org/pdf/gr-qc/0211030v2.pdf

The temporal & spatial dimensions share the same sign in Galilean Newton whatever, reality is they need to be opposite to be representative of the actual structure of spacetime.

 

[PAllen]

The reality point I suppose could be a matter of opinion. The causal structure is NOT stronger...because it doesn't even exist. It's non sense to compare impossible things to reality and pose it as a point.

Causal structure simply means you can specify between some(all) events which one could have influenced the other (causal connection, with direction). In Newtonian physics, for every pair of events, there is the ability to state which one is before the other and could have causally influenced the other. For SR, there is a different causal structure: for some pairs of events you can say one could influence the other; for others you can say neither could influence the other. Newtonian physics time orders all events; SR contains events that cannot be time ordered.

That Newtonian physics: a) has a causal structure b) it is stronger than SR
are mathematical facts. That Newtonian physics does not match experiments is an observational fact. There may someday be an experiment that falsifies SR. That will not change the causal structure of SR or of Newtonian physics. It may require that the causal structure of a successor theory to SR is different from SR.

Do you understand that that one may speak of the characteristics of a theory, irrespective of whether that theory is falsified by experiment?

Again show me causal structure in that "metric" of infinite speed. I'll just go faster.

I have, multiple times. Causal structure has nothing to do with metric (directly). It is a more primitive structure that can be imposed on a manifold. Given a causal structure, you may or may not be able to introduce a certain type of metric consistent with that structure. For Newtonian causal structure, you cannot introduce a non-degenerate 4-metric (you can introduce a Euclidean 3-metric on each 3-space parametrized by the total causal order) . So what? For SR causal structure, you cannot introduce a Riemannian 4-metric. So what? You can, instead, introduce a pseudo-Riemannian metric.

If you really feel there is a true & meaningful "causal" structure in Galilean geometry you won't ever agree with what I am saying, if you laugh at that proposed structure as physical non sense then you may see where I am "coming from" with my perspective.

See above. There is perfectly meaningful, strong, causal structure in Newtonian physics. It is not 'true' in the sense that it is falsified by experiment, but it is well defined and mathematically consistent.

And I hope I don't come across as arguing, if it does I don't want to continue...it's not at all how I wish to "present" a perspective.

You do come across as argumentative, and you are not succeeding well explaining your perspective.

 

[PeterDonis]

The temporal & spatial dimensions share the same sign in Galilean Newton whatever

No, this is not correct. In fact it doesn't even make sense. For temporal and spatial dimensions to even have signs that can be compared, they have to appear in the same metric. In Galilean/Newtonian physics, they don't; there is no such metric. So you can't even compare the signs of the temporal and spatial dimensions in Galilean/Newtonian physics.

 

[nitsuj]

Causal structure simply means you can specify between some(all) events which one could have influenced the other (causal connection, with direction). In Newtonian physics, for every pair of events, there is the ability to state which one is before the other and could have causally influenced the other. For SR, there is a different causal structure: for some pairs of events you can say one could influence the other; for others you can say neither could influence the other. Newtonian physics time orders all events; SR contains events that cannot be time ordered.

Huh, Then I didn't and still don't understand a causal system/structure. I took it to mean that one thing leads to another and we all agree on that order, and that's it.

I didn't know a causal system was about "could have" & "have had", but thought it was about "will have" & "have had". And I still see no physical significance to "could haves", I see that as merely coordinating / "mapping" positions of objects. Makes me wonder what is a "cause" that never becomes an "effect"?

So with that my perspective was from the object itself. In other words the order of "physical occurrences" as they have happened to an object is invariant. Could be restated as the "historical order" of physical occurrences as they have happened to an object doesn't change.

As those physical occurrences happen to an object the result, or effect propagates to which ever observer cares to observe it. all observers who care to observe this object will see the same ordering regardless of their relative motion. The physical occurrence of the observation itself too is invariant i.e. when the distant observer(s) first receives lightlike information (the effect of what ever cause happened to the observed object). So if all the observers are observing each other they all see this same ordering of these physical occurrences. This is a fundamental "connectedness" (domino / butterfly effect, even determinism) amongst all physical interactions. The fact that there are only two mutual exclusive physically relevant possibilities, will happen , can happen, has motion as implicit. We can measure motion.

From that there is spacetime, which itself isn't physical in the sense discussed above or specifically "involved" in the process. It's just what separates physical occurrences.

Hope that clarifies my perspective in the previous posts, but suppose I wasn't talking about a causal structure at all since that includes the non physical "could have happened".

Thanks for clarifying the definition for me PAllen

And I also see this as more fundamental then the mere metric. The metric isn't much of anything really, but perhaps derived from the physical occurrences, in other words of course there must be time dilation, length contraction, differential aging ect.

I appreciate the importance of theory development, but don't see the physical significance of falsified theories so find it weird to mention them in instances where we are discussing very fundamental physics.

Hopefully there isn't still an argumentative tone to my reply's.

I didn't even know about these things called manifolds and that they are different then metrics ect. This is all making me wish I had gone to school for this stuff (physics). a quick wiki it seems manifold is only spacial.

 

[nitsuj]

No, this is not correct. In fact it doesn't even make sense.

It doesn't make mathematical sense, same way Galilean/Newtonian physics doesn't make physical sense. And here we are not discussing math logic.

temporal and spatial dimensions to even have signs that can be compared, they have to appear in the same metric.

Hey that was my original point to WannabeNewton!

My point which I said explicitly is time is not part of the geometric structure in a Galilean Universe. Speed can be infinite which is a pretty big logical "hole". Who cares if it's "known" it's not "real" /

Let's not play a term game with what is meant by "geometric structure"

 

[WannabeNewton]

No, that is not Peter's point. Read his paragraph again and read the papers I linked you. In galilean space-time we can completely separate the temporal and spatial dimensions and treat them independently but you seem to think that this implies it doesn't have a space-time structure at all, which is false. It just has a structure that is much stronger than that of Minkowski space-time.

 

[nitsuj]

No, that is not Peter's point. Read his paragraph again and read the papers I linked you. In galilean space-time we can completely separate the temporal and spatial dimensions and treat them independently but you seem to think that this implies it doesn't have a space-time structure at all, which is false. It just has a structure that is much stronger than that of Minkowski space-time.

I read it again and guess am still missing the point, I am not saying time doesn't exist in Galilean/Newtonian physics. Of course time is a measure in Galilean/Newtonian physics.

Do you know what I mean by Galilean/Newtonian physics excludes time geometrically?

 

[PeterDonis]

It doesn't make mathematical sense, same way Galilean/Newtonian physics doesn't make physical sense.

No, that's not a valid comparison. Galilean/Newtonian physics is a perfectly valid and consistent mathematical theory; it just doesn't agree with experiment (at least, not if you do a wide enough range of experiments). The comparison you were implying between the signs of the temporal and spatial dimensions can't even be consistently formulated in Galilean/Newtonian physics.

 

[PeterDonis]

Hey that was my original point to WannabeNewton!

Then why are you now taking a position that's opposed to that original point?