What is "spacetime" really?

[Michael Mooney]

A review, of the last four pages, mostly focused on the debate on the ontology of "distance":

 

MM (to Modest):Do you or do you not believe that cosmos exists objectively in and of itself independent of relative observational perspectives?

 

 

Do you believe that the shortest distance between two points is a straight line. If not why not

 

You still have no idea that I am challenging the ontological nature of "spacetime" on the grounds that it makes something out of nothing, that it reifies both space (emptiness) and time (an artifact of measuring "event duration.") Ontologically speaking, neither are actual entities in the real cosmos.

 

Pyrotex:

"It's just that you keep hammering (that's a metaphor) on the idea that observation doesn't change the distance between objects. Or to put it another way, that the act of observing cannot cause a change in the distance between objects.

 

Nobody is saying that it can.

 

Relativity does not say it can.

 

So, WHO are you arguing against?"

 

Me:

OK... Back to basics. Is the average (recognizing orbital out-of round) distance between earth and sun about 93 million miles, the equivalent of just over 8 light minutes (a precise distance measure!) or does it vary with the relativistic effects which Modest keeps "hammering on?"

 

Erasmus:

"I reiterate- if there is no method of determining distance that gives a unique answer, how do we determine a unique answer?"

 

Modest:

"The philosophy of spacetime starts with a very simple premise. Space is the stuff that you measure with a ruler and time is that thing which gets measured by a clock"

 

MM... present:... Which begs the question, "Does the cosmos disappear when its not being "measured?" See my first question above, which Modest invariably dodges, like 'Whadaya mean, objective?'

 

Of course, ultimately, there is no "end of space." (What, a wall... with more space on the other side?...

 

Distance is the "line" between two virtual points or real things. In the real cosmos, this only varies as things move relative to each other. Observation/measurement does not move the things and make the distance between them change. Observational/measurement differences due

different velocities, frames of reference, etc. can be *corrected* by application of the math of relativity to *correct* for the time delay of light travel, which will differ for different observers, as above.

 

MM:

Yes. Time does not slow down. Clocks do. Space does not expand or contract... Things move around *in space.*

 

jedaisoul:

"I agree that time does not slow down, and space does not contract..."

 

MM:

Maybe you missed the way I distinguish the experimental results and the math from the ontology of "spacetime" which is usually taken for granted as a verified "real medium"

 

Pyrotex:

 

Now, that stupid goddam alien is going to measure an entirely different Earth-Sun distance. Seriously. Does that "change" the distance? Absolutely not. He just gets a different value. If he/she/it has any brains, he/she/it will make the appropriate Relativistic correction to counteract the effect of the spaceship's speed. When the corrections are made, the result will be---93 million miles.

 

...When Frames of Reference are whizzing around near the speed of light, this changes or "distorts" what is seen."

 

 

 

MM (On "the shortest distance between two points... and Euclidean "space.):

"So, say my line on flat paper is 10 inches long. (The shortest distance between the dots is a ruler-straight line between them, undoubtedly.) Then, after I bend the paper into an arch and stick a long needle through the dots, the distance between the dots along the straight needle is now, say 8 inches. Now the line on the paper's surface is the long way around, specifically 1.25 longer than the "shortest distance" along the needle. Maybe this example will come closer to the required "proof." I know the math is accurate!

 

MM (to Pyrotex):

"As you can see from my other posts today, I am not arguing (never have!) with the advance of relativity in correcting "observer error" due to lightspeed delay during the process of measurement.

 

How this squares with Modest's constant use of "for observer A" the distance is... whatever... while "for observer B" at different relative velocity, etc, the distance is... (different)... no one has yet answered. He refuses to acknowledge that the "actual distances" are not changing due to these relativistic effects... or even that there is such a thing as "actual distance."...

 

Erasmus:

"1. If "distance" is an objective quantity independent of reference frame, then

a. there should be a way to define "distance" so that everyone can measure and agree on a number. i.e. every person, any where in the universe, should be able to measure the distance between the Earth and the Sun and get the same answer. Its a question of definitions, "what do we mean when we say distance?"

 

b. no such method exists.

 

Conclusion: distance is not independent of reference frame.

 

Where do you disagree?"

 

MM (present):

 

Philosophically speaking (please remember that this is the "Philosophy of Science" section)... the cosmos exists "in and of itself" independent of observational viewpoints and measurements. This means that distances vary between loci only as loci move relative to each other, not as observed from different perspectives with differences in elapsed time for light to convey images. Relativity corrects for these differences to give "actual distance." The latter assumes that human perception creates what is percieved, and in this case observation actually moves loci around, which is an obsurd tenant of subjective idealism... see Berkely, Hume, et.al.

 

Pyrotex:

"If we are in different Frames of Reference (traveling at huge speed relative to one another), our observations may be significantly different (and get significantly different values).

 

THIS IN NO WAY ALTERS THE ACTUAL DISTANCE.

 

There is no acceptable interpretation that would have the actual distance change from one value to the other.

Relativity doesn't claim otherwise.

Nobody on this thread claims otherwise."

 

MM (present): Modest and Erasmus do."It's all relative. There are no 'actual distances.'"

 

Pyrotex:

"If YOU are claiming that the CORRECT INTERPRETATION IS THAT THIS ALTERS THE ACTUAL DISTANCE, then you really need to disabuse yourself of that silly notion"

 

MM (present): Good grief, man! I have been the one here claiming that the cosmos exists as it is idependent of observation and relativistic differences in what is seen and when... which is corrected to "actual distance" by relativity!! Are you having a "senior moment" or what?

 

P: "It is possible for two people in different Frames of Reference to measure the same things and get different distances. However, if they ALSO measure their relative velocities, and make the appropriate corrections for Relativity, they should get the same distance."

 

MM (present): Absolutely! This is what I've been saying all along in my argument with other moderators who disavow "actual distance"... that distance varies with differences in measurement. This argument is going in circles!

 

Watcher:

"if all we can count on is our distorted ability to observe, what's the point of saying there is an actual distance? isn't it obvious that distances are distorted along with observations?"

 

MM (present): NO! A perfect example of the absurdity of "idealism" with observations creating what is observed... and the cosmos has no "reality of its own."

 

jedaisoul:

"When I say all velocities are with respect to what you measure them against, I do NOT suggest that the act of measurement is changing what is measured. I agree that the velocity woul be the same even if there were no intelligent life to measure it.

 

MM(present): Exactly so. This is what I meant by velocity of light is constant, even if there were only one star in the universe as its source... i.e., nothing else to "measure it against."

 

Modest:

"Distance is what gets measured with a ruler"

 

MM (present): So there would be no distance between things which constitute the cosmos without "intelligent life" running around measuring the distance between them with a "ruler??" Or only those distances which get measured count as "actual diatance." There is no "distance without measurement?" It doesn't get any more absurd than this! (No personal offense intended. You are just flat wrong.)

 

Modest:

"So, let’s define some terms. If you, Michael, want to say “actual distances don’t change with velocity” then you should define “actual distance”.

 

Mm (present): That distance between loci which exists independent of whether it is measured or not

.

jedaisoul:

"Hi Modest. Please see my comments above about PROPER distances (and time intervals). These ARE invariant..."

Modest:

"I couldn't agree more, but I'm quite sure you're not going to get Michael to discuss the distance between events, only objects. The idea that there's a spactime distance between an event tomorrow on the moon and yesterday on earth... well, I don't see that working with the philosophy being proposed. But, I'd be ever too happy to be proven wrong."

 

MM: See my comment immediately above.

 

Back later to continue the Euclidean vs non-Euclidean space debate.

 

Michael

[Erasmus00]

Distance is the "line" between two virtual points or real things.

 

What does this mean? We tend to think of "distance" as a number, how do we define that number?

 

If

 

Space is the stuff that you measure with a ruler

 

Then how do we define the ruler? IF distance is the stuff you measure with, say a meter stick, then there is no one distance, because a meter stick can measure the same distance and get a different result.

[Michael Mooney]

Originally Posted by Michael Mooney

Distance is the "line" between two virtual points or real things.

 

What does this mean? We tend to think of "distance" as a number, how do we define that number?

"We", who? Got a mouse in your pocket?:D Basic geometry: Space has three dimensions: line, plane, and volume. A line between two geometric points (or actual objects) is the distance between them. This is true whether you measure it or not. Also true whether you apply a unit of distance and say how many of them there are along the line. BTW, the shortest distance will be a straight line.

 

Quote:

Originally Posted by Michael Mooney (Not!)

Space is the stuff that you measure with a ruler

 

Wrong! Modest said the above. Here again is the quote in my above post:

 

Modest:

"Distance is what gets measured with a ruler"

 

MM (present): So there would be no distance between things which constitute the cosmos without "intelligent life" running around measuring the distance between them with a "ruler??" Or only those distances which get measured count as "actual diatance." There is no "distance without measurement?" It doesn't get any more absurd than this! (No personal offense intended. You are just flat wrong.)

 

Michael

[Erasmus00]

Basic geometry: Space has three dimensions: line, plane, and volume. A line between two geometric points (or actual objects) is the distance between them.

 

This is not true. A line is a 1-d object, a plane is a 2d object, a volume is a 3d object. They are not the actual dimensions of the space (length, width, height, or similar). This is just a vocab issue.

 

This is true whether you measure it or not. Also true whether you apply a unit of distance and say how many of them there are along the line. BTW, the shortest distance will be a straight line. [/b]

 

If distance is a line, what is a "unit of distance." If distance is the line between two objects, what does it mean to be "shortest." If distance isn't a number, how do we make comparisons?

 

Your current definition of distance as "the line between two objects" makes the question "what is the shortest distance between two objects" worthless- a line has no intrinsic notion of length. We have no numbers to compare.

[Pyrotex]

A review, of the last four pages, mostly focused on the debate on the ontology of "distance":...

WOW.

 

:eek::D:eek::):eek:

 

That is one damned fine superlative outstanding great not-bad extraordinary summary of the conversation so far. My hat is off to you.

 

NOW, I understand why you are so confused, Michael. :doh: :lol: :doh:

 

You got half a dozen folks all trying to have a one-on-one conversation with you. Some of them know ALL about what they're talking about; some of them know SOME of what they're talking about. Terms are being used in different ways. Folks are coming from different points of view. Some are trying to give the mathematically correct answers, some the physics conceptual answers. And there's a fair bit of techno-babble sprinkled here and there.

 

Michael, this is Bedlam. :eek_big: :eek: :eek_big: :eek: :eek_big: :eek:

 

:D How do you like it so far? :D

 

Perhaps you should glance over your summary and select two people to help you continue this inquiry. Pick two who seem to be using the same level of terminology. I think that will make everything clearer and easier. And I wish you all the luck you will need with this crew.

 

:hihi: Damn this is fun! Thanks, Michael! :hihi:

[jedaisoul]

Perhaps you should glance over your summary and select two people to help you continue this inquiry. Pick two who seem to be using the same level of terminology. I think that will make everything clearer and easier. And I wish you all the luck you will need with this crew.

I agree. On reflection, I also think that my input is not helpful, because I'm using terms and ideas that are out of context with where Michael is at the moment (conceptually).

 

So I'm happy to bow out, and let others try to explain this.

[modest]

Oh sure. Jumping ship :hihi:

 

I suppose Michael’s ability to maintain his footing while being pulled in so many directions is truly admirable. Then again, relatively speaking, there's not much utility in trying to move something by pulling it 4 different directions ;)

 

Modest:

"The philosophy of spacetime starts with a very simple premise. Space is the stuff that you measure with a ruler and time is that thing which gets measured by a clock"

 

MM... present:... Which begs the question, "Does the cosmos disappear when its not being "measured?" See my first question above, which Modest invariably dodges, like 'Whadaya mean, objective?'

 

No, no, no... In no way does it beg that question. You are connecting the dots assuming something about what I’m saying which I’m in point of fact not saying at all. Now, pick this apart:

If our only knowledge of the universe comes from our observation of it and our ability to reason regarding it, this

does not

imply that the universe ceases to exist without our observation

You consistently confuse the relativist’s argument with that of subjective idealism or phenomenalism. That’s not necessary. Space (or distance) can easily both exist independent of any measurement and alternatively be measured with a ruler. The latter does not need to negate the former without some specific philosophy making it so (like phenomenalism) which I’m not advocating.

 

Do you or do you not believe that cosmos exists objectively in and of itself independent of relative observational perspectives?

 

I believe the cosmos exists independent of human observation. I believe general relativity implies that distance is not a meaningful concept unless there is some mass or some particle with which to reference such a distance. I hesitate to mention this because the reason general relativity implies this is not the reason you think, so this is not going to be helpful... Nevertheless...

In general relativity, the hole argument... is interpreted by philosophers as an argument against manifold substantialism, a doctrine that views the manifold of events in spacetime as a "substance" which exists independently of the matter within it.

 

-

source

What is space? What is time? Do they exist independently of the things and processes in them? Or is their existence parasitic on these things and processes? Are they like a canvas onto which an artist paints; they exist whether or not the artist paints on them? Or are they akin to parenthood; there is no parenthood until there are parents and children? That is, is there no space and time until there are things with spatial properties and processes with temporal durations?

 

These questions have long been debated and continue to be debated. The hole argument arose when these questions were asked in the context of modern spacetime physics. In that context, space and time are fused into a single entity, spacetime, and we inquire into its status. One view is that spacetime is a substance, a thing that exists independently of the processes occurring within spacetime. This is spacetime substantivalism. The hole argument seeks to show that this viewpoint leads to unpalatable conclusions in a large class of spacetime theories. Spacetime substantivalism requires that we ascribe such a surfeit of properties to spacetime that neither observation nor even the laws of the relevant spacetime theory itself can determine which are the correct ones. Such abundance is neither logically contradictory nor refuted by experience. But there must be some bounds on how rich a repertoire of hidden properties can be ascribed to spacetime. The hole argument urges that spacetime substantivalism goes beyond those bounds.

 

-

source

Now... I would think you should find this agreeable. You do not like the reification of spacetime and you do not like giving material or mechanical properties to distance or duration. The argument above supports that position pretty strongly.

 

So... can the cosmos exist independent of human observation? I think yes.

Do space and time exist independent of material particles. I think, most likely, not.

Does the cosmos exit “objectively in and of itself independent of relative observational perspectives”? That question has 2 parts. I believe it does exist “objectively in and of itself” but I do not think it exists independent of relative perspectives. According to relativity it exists *with* relative perspectives and explains those perspectives to result from a 4 dimensional world.

 

If you want to propose a philosophy or ontology absent relative perspectives then you need to explain our observation of relative perspectives. The fact that we observe things relativistically and relativity has and explains relative perspectives is not a problem for relativity... it's just consistent with what we observe.

 

~modest

[Michael Mooney]

Pyrotex:

That is one damned fine superlative outstanding great not-bad extraordinary summary of the conversation so far. My hat is off to you.

 

NOW, I understand why you are so confused, Michael.

Wow! Thanks!... I think?... You really know how to cut both ways! Confused huh? I don't feel confused. I don't think I'm confused. My mind is clear about my challenge of the generally accepted ontology of spacetime in general and the more specific issues of Euclidean vs non-Euclidean space, and even more specific issue of "the distance between" both geometric "points" and actual objects.

 

I get that you say it with a wink, but it still reminds me of the old cliche' assumption:

"Have you stopped beating your wife yet?... Yes or no!"

 

Michael, this is Bedlam.

 

How do you like it so far?

Well, I love a good debate... Great fun!... especially when I know I'm right!:hihi:

 

Perhaps you should glance over your summary and select two people to help you continue this inquiry. Pick two who seem to be using the same level of terminology. I think that will make everything clearer and easier. And I wish you all the luck you will need with this crew.

Nah! I like an open forum without restricted, invitation-only clique/club exclusion parameters. When I feel that someone is just not hearing me, I can always elect not to reply or ask for a specific answer... again and again.

 

Anyway, I just finished reading Modest's post and links (wow! ... an intense study of the "hole argument" and lots of common ground with me on what I've been calling the "reification" of spacetime.

Example from links he so kindly provided:

"What is space? What is time? Do they exist independently of the things and processes in them? Or is their existence parasitic on these things and processes?...

 

"... Therefore the manifold substantivalist advocates an unwarranted bloating of our physical ontology and the doctrine should be discarded."

 

Further, Modest's latest comments shed new light on what had seemed a hopeless communication gap.

I will now turn to a response to him and commentaries on "the hole argument."

 

Again, thanks. Almost too much fun, ain't it!

Michael

[Michael Mooney]

Modest,

First much thanks for the clarification of what you are actually saying... and the "hole argument" links.... very informative!... and a real grind to get through... especially having to look up some of the technical lingo to even know what the hell they were talking about!

 

You wrote:

Now, pick this apart:

If our only knowledge of the universe comes from our observation of it and our ability to reason regarding it, this does not imply that the universe ceases to exist without our observation

Check. Got it. What a relief to hear you say so. (Tho my mystic "seeing" is an "a-priori" form of knowing, epistemologically speaking... tho, granted not emiprical science.)

 

You consistently confuse the relativist’s argument with that of subjective idealism or phenomenalism. That’s not necessary. Space (or distance) can easily both exist independent of any measurement and alternatively be measured with a ruler.

(Please inform Erasmus that distance is not exclusively defined by "numbers and measurement.")

 

The latter does not need to negate the former without some specific philosophy making it so (like phenomenalism) which I’m not advocating.

Good point of clarification.

I believe the cosmos exists independent of human observation. Thank you! I believe general relativity implies that distance is not a meaningful concept unless there is some mass or some particle with which to reference such a distance. Agreed I hesitate to mention this because the reason general relativity implies this is not the reason you think, so this is not going to be helpful... Nevertheless...

 

I"m not clear on what reason you think I think.

---------

(The" hole argument" links: Whew!... a challenging read.)

----------

Now... I would think you should find this agreeable. You do not like the reification of spacetime and you do not like giving material or mechanical properties to distance or duration. The argument above supports that position pretty strongly.

 

Yup. Excellent!

 

So... can the cosmos exist independent of human observation? I think yes.

Do space and time exist independent of material particles. I think, most likely, not.

Does the cosmos exist “objectively in and of itself independent of relative observational perspectives”? That question has 2 parts. I believe it does exist “objectively in and of itself” but I do not think it exists independent of relative perspectives. According to relativity it exists *with* relative perspectives and explains those perspectives to result from a 4 dimensional world.

Good... up to the "but"... Here, I must repeat the question: Does cosmos exist whether or not any *perceivers* ever evolved ,i.e., entities which/who *have those perspectives*? I say, yes, in keeping with what you agreed before the "but."

 

If you want to propose a philosophy or ontology absent relative perspectives then you need to explain our observation of relative perspectives. The fact that we observe things relativistically and relativity has and explains relative perspectives is not a problem for relativity... it's just consistent with what we observe.

Well, again, if cosmos exists independent of all "observation" (loci of "relative perspectives")... which, ontologically, it does, then the latter are merely dependent on lightspeed, etc. for information about it (cosmos) via images conveyed with various time delays, etc.

This point is not philosopically dependent on a "transcendental perspective" (beyond the paradigm of relativity), but it helps!

 

I have a ream of notes on the material you shared... but... Another time for specific commentaries. ... Well... maybe just one, which I can not resist...

 

On the origin of the "hole argument":

In its original incarnation, Einstein considered a spacetime filled with matter excepting one region, the hole, which was matter free. (So in this original form, the term "hole" makes more sense than in the modern version.) He then asked if a full specification of both metric and matter fields outside the hole would fix the metric field within

 

Like Einstein's "fabrication" of "spacetime" (and subsequent reification of it by mainstream science)... this "hole" has no referent in the real cosmos, but remains merely a concept in service to the theory. He then has created an artificial boundary between "outside" and "inside" the "hole."

An aside: Same for the generaly accepted duality of "metric fields" vs "matter fields." The metric is a coordinate overlay (including its math) of actual manifest "stuff" (including matter), and "the map" is not the actual "territory"... the cosmic "stuff" being "mapped."

 

Again, thank you Modest for an excellent clarification post.

Michael

[modest]

Modest,

First much thanks for the clarification of what you are actually saying... and the "hole argument" links.... very informative!... and a real grind to get through...

No prob. Good to hear :singer:

 

You consistently confuse the relativist’s argument with that of subjective idealism or phenomenalism. That’s not necessary. Space (or distance) can easily both exist independent of any measurement and alternatively be measured with a ruler.

(Please inform Erasmus that distance is not exclusively defined by "numbers and measurement.")

Distance between spacetime points will exist if they are measured or not, if we assign a number to them or not. But, if we want to define either the concept of distance or a specific example of distance then we do need to rely on "numbers and measurement".

 

For example, two spacetime points may be a certain distance while two others are twice that distance. We can explain that difference by saying the measurement of one will be twice the measurement of the other. Since our interaction with the universe is via measurement (or observation) and since we use numbers to express relationships then this is only natural.

 

Defining something with a measurement does not mean such a thing cannot exist without the measurement—it simply means that such a thing exists to be measured. Nobody (as far as I know) is saying that the measurement is the cause of the ontology. It is, rather, a necessary result of the ontology. I still think you're slightly misunderstanding us on that.

 

So... can the cosmos exist independent of human observation? I think yes.

Do space and time exist independent of material particles. I think, most likely, not.

Does the cosmos exist “objectively in and of itself independent of relative observational perspectives”? That question has 2 parts. I believe it does exist “objectively in and of itself” but I do not think it exists independent of relative perspectives. According to relativity it exists *with* relative perspectives and explains those perspectives to result from a 4 dimensional world.

Good... up to the "but"... Here, I must repeat the question: Does cosmos exist whether or not any *perceivers* ever evolved ,i.e., entities which/who *have those perspectives*? I say, yes, in keeping with what you agreed before the "but."

No, I agreed that "the cosmos exists whether or not any *perceivers* ever evolved" before and after I said "but". The miscommunication is this: I'm saying "independent of relative perspectives" and you're reading "independent of human relative observation". What I'm saying requires no intelligent life or observation.

 

The relative perspective is a physical fact that will persist regardless of observation. Consider the decay rate of some atoms. If they make different paths through spacetime then their decay rates will differ. The "relative perspective" *is* that difference regardless whether someone is there to observe that difference or not. In this case the decay rate is considered an "observable" because it can be determined physically with observation or measurement which should indicate that it is something that is physically real. But, the measurement isn't what makes it real. Relativity certainly doesn't claim anything like that. The measurement is a property of physical reality—not the other way around.

 

Relativity does not imply subjective idealism! I really think your arguments against subjective idealism are missing the target.

 

In its original incarnation, Einstein considered a spacetime filled with matter excepting one region, the hole, which was matter free. (So in this original form, the term "hole" makes more sense than in the modern version.) He then asked if a full specification of both metric and matter fields outside the hole would fix the metric field within

 

Like Einstein's "fabrication" of "spacetime" (and subsequent reification of it by mainstream science)... this "hole" has no referent in the real cosmos, but remains merely a concept in service to the theory. He then has created an artificial boundary between "outside" and "inside" the "hole."

 

Einstein developed the hole argument and interpreted it in a way that you would find very agreeable. Where you think general relativity reifies spacetime, it in fact demonstrates with the hole argument that the spacetime manifold is most-likely not a physical reality which exists in and of itself. So, once again, it seems like you're missing the target and arguing against a bit of a strawman.

 

The images you see in textbooks of rubber sheets signifying spactime is only an analogy. The fabric of spacetime represents the path of material objects and the distances and durations that such objects experience. The reality or ontology of what those paths and distances and times mean is entirely up to you (so long as it is consistent with observation). It need not be made into something mechanical like a rubber sheet. It represents *whatever* it is that we measure with rulers and clocks whether that something is something physical and malleable or nothing more than a description regarding how matter interacts.

 

~modest

[watcher]

michael,

"the map" is not the actual "territory"... "

 

spacetime interval is the map. what is out there is the territory.

the saying is a caveat not to confuse the two.

but in the end, the map stills represents the territory.

the map has physical meaning and representation.

 

the territory is real. ontology necessitates to have unprovable assumption,

but there is a difference between "mapping" your territory from proven theory and a highly arbitrary subjective higher perspective.

 

now if you have not entirely trashed the equation of spacetime interval,(a non-arbitrary and sensible way to do it is to disprove the constancy of light in an actual experiment . not necessarily the rate itself but its novel characteristic that it refuses to add and subtract with other velocities). so if you can't let me ask you a simple question.

 

does the math of spacetime interval makes distinction between space and time? yes or no?

if no and math makes no distinction, ergo space and time are the same (what is it?) thing and the model that space is absolute and time is imaginary is simply out of touch with the map (equation)

 

further more, you can see the effect of time as a fourth dimension perpendicular to the 3d space. (oh yes, that is the rule in math, the next higher dimension must be 90 deg out of phase with the lower d. that explains why higher dimensions are partly perceptible if not entirely unobservable in lower dimensions, it always appear pointlike).

 

its obvious effect is the seemingly perpendicular to 3d space behavior of gravity force/direction. gravity always go directly to the center of an object occupying 3d space. close your eyes and imagine. its a great insight.

 

i have provided a link where you can visualize what i meant.

see how a 4d object project itself in3d. it will either contract or expand in all 3d space direction when mouse is drag in a perpendicular ( sort of since the pc monitor is still 2d. but a good way to imagine it ).

 

Hypercube

 

if your familiar with autocad, it is the same as clicking the zoom button and drag the mouse anywhere in the drawing plane. (a common feature to all graphic software app). the object will expand and contract in all direction . imo, that is the physical meaning of time as a dimension orthagonal to 3d space. time is physical. don't confuse it with the tick of the clock.

[watcher]

Distance between spacetime points will exist if they are measured or not, if we assign a number to them or not

 

i think it is important to emphasize to be clear for all that the so called "distance" or interval between two spacetime points (which is the absolute distance between two frame of reference) is not spatial distance. the distance represented by the interval are separation of spacetime events, and therefore cannot be considered as actual spatial distance. what is being compared are relative velocities against a known constant velocity c. this is to make sure that if we want to meet halfway the galaxy, we must be at the same place at the same time. but then again if we want to meet in new york, we don't need this crap. LOL

 

if i'm am correct, spacetime as a unified whole is simply an event. in its most fundamental aspect an event can be categorize simply as motion since motion has both the element of distance and time. so this thing that the interval equation says as the same thing could really be simply motion.

 

but then again you can make model of space as discrete granulars, as waves, as tensor, as densities as spin networks and what not. but space as a background emptiness, is best useful only strictly as a coordinate system. imo

[modest]

i think it is important to emphasize to be clear for all that the so called "distance" or interval between two spacetime points (which is the absolute distance between two frame of reference) is not spatial distance. the distance represented by the interval are separation of spacetime events, and therefore cannot be considered as actual spatial distance.

Yes. There is a distinction that may-well cause some misapprehensions. The invariant spacetime distance (or interval) between events is a spacetime construct. It combines space and time and considers the distance through (or across) both. This is not particularly analogous to spatial distance. In particular: spatial distance is relative to velocity while spacetime distance is not.

 

~modest :singer:

[watcher]

spatial distance is relative to velocity while spacetime distance is not

 

yes i think it is the velocities that are relied upon to reconcile two frames of reference.

any space traveler naive enough to use euclidean coordinate system in its navigational system will sure lose its way into the galaxy. for all intents and practical purposes, space must be treated as non-euclidean.

the gps system does. you can't be more ontological than that. LOL

[Pyrotex]

...if i'm am correct, spacetime as a unified whole is simply an event. in its most fundamental aspect an event can be categorize simply as motion since motion has both the element of distance and time. so this thing that the interval equation says as the same thing could really be simply motion....

A "location" is a point in a 3-dimensional coordinate system. For example, X=0, Y=25, Z=-3.

 

An "event" is a point in a 4-dimensional coordinate system, where one of those coordinates is Time. For example, X=0, Y=25, Z=-3, T=April 15, 2009 at 3:30 in the afternoon.

[watcher]

A "location" is a point in a 3-dimensional coordinate system. For example, X=0, Y=25, Z=-3.

 

An "event" is a point in a 4-dimensional coordinate system, where one of those coordinates is Time. For example, X=0, Y=25, Z=-3, T=April 15, 2009 at 3:30 in the afternoon.

 

thanks.

still the the distance between two events are not actual spatial distance.

the two points in space that does not change for all observers is the distance in the spacetime diagram and not in actual spatial distance.

 

so when we say there is an actual distance in space, it is only if you treated space as absolute. in relativity, we are not even allowed to think that way, because the "actual distance between two points" is a spacetime event.

 

and if you take into account the rotations and linear velocities of the frames of reference, then the whole spacetime diagram is simply an expression of motions.

it is the laws of motion that is invariant in all frames of reference.

[Pyrotex]

...so when we say there is an actual distance in space, it is only if you treated space as absolute. in relativity, ... the "actual distance between two points" is a spacetime event.

 

and if you take into account ...frames of reference, then the whole spacetime diagram is simply an expression of motions. it is the laws of motion that is invariant in all frames of reference.

Normally, we DO treat space as absolute. We can get away with it because the relative velocities of our frames of reference are typically very small.

 

The actual distance between two points in space is just a 3-dimensional distance.

The actual distance between two events in space-time is a 4-dimensional "space-time distance". For example the space-time distance between the Declaration of Independance (Philadelphia, 1776) and the launch of Apollo 13 (Cape Canaveral, 1973) is approximately:

[500 miles, 197 years]. The value in brackets is a "space-time distance" between two "space-time events".

 

The invariant laws of motion (as you call them) would correspond to Special Relativity (SR). These are invariant because light apparently cannot be observed (in a vaccuum) as traveling at any other speed than 3X10^8 M/sec. I say "apparently" because this assumption on Einstein's part, leads directly to SR, which is the only Physics model that accurately describes and predicts all high speed motion.