What is "spacetime" really?

[modest]

It may be blatantly obvious to you, but my point is that the meaning of the spacetime interval is not blatantly obvious to many people...

 

They have little interest in the maths, but they may be interested in the philosophic meaning of spacetime...

 

The trouble is, I don't think that anyone not familiar with the mechanics of spacetime would find that satisfactory...

 

Oh—ok :Glasses:

 

-----EDIT-----

The following is a parody of an educational/entertainment video that tires to make learning fun. Writing odd stories is something I’ve been known to do. It's obviously not meant to offend anyone.

 

:doh:

-----EDIT-----

 

Let’s say Alice and Bob are making a model of Earth and they want it to be really good. Perhaps it’s a homework assignment... Alice and Bob have a homework assignment to model the Earth. They have a really strict teacher, and they’re flunking the class, so they want to make it really good.

 

Alice draws an outline of the united states on some paper (she’s the artistic one). She draws a little heart near the California area of the map. You see, her boyfriend lives in Los Angeles where he’s between jobs trying to get a gig with a band. He doesn’t realize bands in LA suck.

 

She draws another heart around the New York area... Bob raises an eyebrow... Changing the subject, Alice asks “So, I was wondering, how far is Los Angeles from New York?”

 

Bob considers the proper answer to this most-difficult question. He is, after all, failing this class and needs to do a good job. He also wouldn’t mind impressing Alice with a beautifully constructed and factually accurate answer. Weighing his options, he says, “About four inches, Yeah—I’d reckon LA’s about four inches from New York.”

 

Alice considers that Bob was most likely kicked in the head by a horse as a child before Bob clarifies, “I mean, on the map. Los Angeles isn’t really 4 inches from New York. I was talking about on the map.” Alice is satisfied and pulls a ruler out of her back pocket and... (wait, that isn’t very realistic. Why would she have a ruler in her back pocket?) Alice pulls a ruler out of her desk drawer and starts measuring.

 

Bob continues his pathetic attempt to impress Alice with a bit of obscure knowledge, “Did you know the distance between New York and Los Angeles could be four inches if you were going really, really fast?” Alice rolls her eyes, “Yes, I’m not an idiot. I know about relativity.”

 

Alice counts the inches between her hearts, “1, 3, ... I mean... 1, 2, 3”, before looking up in astonishment. She takes bob by the shoulders, eyes open wide, jaw hanging, a look of epiphany on her face. “Bob, think about it, how far is it really, I mean really, between New York and Los Angeles?”

 

Bob looks shocked—not so much by the question—he quite frankly wasn’t expecting Alice to grab him by the shoulders and start interrogating him. He calmly answers, “I don’t know Alice. I’m sure there’s a reasonable answer. We just need to calm down and we can figure this out.”

 

But, Alice and Bob clearly aren’t going to figure this one out. Did I mention they were flunking this particular class? But, not to worry...

 

Right then, Morgan Freeman walks into the room. He’s wearing glasses, so we know he plays the scientist in this movie. Dr. Freeman says in a deep and reassuring voice that would hypnotize a jackal, “Hello Children. I am here to unravel the mysteries of the universe. Won’t you join me?”

 

Bob, not at all thinking it odd that Morgan Freeman just walked into the room, says, “Dr Freeman, we’re trying to figure out how far it really, really is between New York and Los Angeles.” Dr. Freeman removes his glasses and sits down in a conveniently-placed chair adjacent to Bob and Alice which had previously gone unnoticed by the narrator. He pulls some folded-up pages of the script out of his pocket and begins to read aloud.

 

“This is an excellent question children. The answer shall surely take us into the caverns of enlightenment, beyond which...” Freeman flips over a couple pages of the script considering how verbose his character is... “Before I answer, I must ask you a question. How far is it between today and tomorrow?”

 

Alice pulls a calculator out of her back pocket (I mean desk drawer) and pushes way too many buttons before concluding, “24 hours. It’s 24 hours” Freeman smiles, “But, what if two people are going two different speeds? If they both measure how long it is between this morning and tomorrow morning in some place like Los Angeles they will get different answers.”

 

Bob realizes that this means space and time are both relative—nothing is absolute, everything is relative! He, unable to handle the awesomeness of the revelation, throws himself out the window. Dramatic music plays.

 

Alice also realizes the implications, but her character was deemed more likeable by study groups, so, she doesn’t throw herself out the window. She says, “Dr. Freeman, if nobody can agree on the measurement of time and nobody can agree on the measurement of distance, then how can we know how far it really is between an event in New York and another event in Los Angeles? I have to know. I have a model to make for homework and Bob isn’t going to be any help—he most-likely died in the fall”

 

Bob is heard in the distance moaning in pain.

 

“He most-likely was mortally injured in the fall”, adds Alice. Freeman stands up and puts his glasses back on. He pauses a beat before sitting back down in Bob’s seat and taking his glasses off even more dramatically than the first time. The narrator remarks that Morgan Freeman has to be one of the ten greatest actors of all time. Freeman says softly, “Alice, there is a way to do this. I will reveal this secret to you in memory of your fallen comrade.”

 

Bob’s moans grow louder.

 

“In memory of your nearly-fallen comrade,” continues Freeman. “These observers need merely subtract their measure of distance from their measure of time. In doing this, each observer will get a value of space combined with time which all shall agree to.”

 

Alice asks persistently, “Will this be the true value of distance between these two events? Will this be the real distance?” Freeman puts the folded up pages of the script back in his pocket and places his hand on Alice’s knee. “I’m afraid I don’t have that answer, Alice. All I know is it’s the best answer we have, so it'll have to do.” He looks into the camera and repeats a line he delivered playing the President on Deep Impact, “Life will go on, we will prevail.”

 

Bob dies.

 

~modest

[jedaisoul]

Well, thats not the reply I expected, and I hope that you will reconsider how appropriate it was. But that's up to you.

 

The message I get from this is "If you can't be bothered to learn the maths, you don't deserve to understand the universe". I'm not saying that is what you said, nor what you meant, but I would suggest that such a message might be deemed deeply offensive by quite a lot of intelligent people. And I'm not talking about teenagers flunking class.

[modest]

I honestly meant for it to be a fun and entertaining story that offends nobody. I’m sorry if you took it otherwise. I was poking fun at the instructional/educational videos I had to watch in high school. I didn't mean to compare Alice and Bob to anybody in this thread. I didn't even consider that.

 

In case you missed it, I wrote a very direct post just yesterday in this very thread regarding my feelings on people such as myself with math skills that need improvement. It is post #60.

 

~modest

[Michael Mooney]

Your six questions involved the reification of

 

spacetime, non-Euclidean space, parallel lines, emptiness, the "end of

 

space", and reification again.

 

I addressed all of these (with the exception of the "end of space") at

 

length in post #37 right after you asked them. But,

 

I'm not trying to debate you. Many of your questions are based on

 

misconceptions and bad assumptions regarding scientific theories that I

 

think need responding to directly. In other words, I'm answering you

 

the best I know how.

 

~modest

Modest,

I'm still trying to catch up to unanswered posts, like the above.

You don't seem to realize that I am questioning the fundamental

 

assumptions behind the leap from Euclidean space to non-Euclidean,

 

specifically the assumption that space has shape. (I studied several of

 

the links you gave in a subsequent post and all of it is based on the

 

assumption of curved space.

 

You insistence that science has gone beyond Euclidean space, that the

 

math proves it, and that If I can't go toe to toe and eye to eye with

 

you on the math, I am living in the past without a serious leg to stand

 

on re: "The Philosophy of Science." (Again, I am not debating the math

 

per-se, as I haven't the expertise, but I am welll studied in

 

epistemology as it applies to science, and you are insisting on the

 

a-priority assumption that space is curved, and that the math proves

 

it.

Still working on deleting redundancies... second edit... not finished but must go. I invite you to delete what I have missed, Modest. Sorry... but also have lost patience with this site, as per my last statement. It must be "timing me out" then running me in circles to log in again, arrow back only to find no post just composed, then back to log-in and "re-direct." Will compose all on notepad hereafter without the redundancies. Bye.

 

You continually assert that space is just emptiness and therefore

 

cannot have properties such as being curved. This is wrong (or at least

 

unsupported) for a few reasons.

 

General relativity is not the only theory of physics that demands space

 

is not just emptiness. QFT (quantum field theory) also describes fields

 

that are present in all of space. This culminates in theories such

 

quantum electrodynamics which have enjoyed enormous success. QED is

 

tested accurate to ten parts in a billion. As wikipedia says: "This

 

makes QED one of the most accurate physical theories constructed thus

 

far". For you to declare that space is "just emptiness" is not just

 

disagreeing with General Relativity—it's disagreeing with many physical

 

theories in modern science.

 

Please examine your assumption that forces (fields) can not traverse

 

"empty space" and if not empty, *with what is it filled?* (Computer

 

generated visual aids to not consitute proof of reality of whatever it

 

is that fills it, i.e., precludes space being the emptiness between

 

observable/evidential phenomena.)

 

The nature of emptiness as you envision it is a disconnection between

 

entities. If nothing but emptiness (with no properties) exists between

 

things that are spatially separated then simple thought experiments go

 

awry.

 

You never responded to my proposed thought experiment involving a

 

cosmic scale perspective on the present being omnipresent (everywhere,

 

universally) transcending all thought experiments in relativity, all

 

limited to comparisons of local perspectives by individual observers,

 

all based on the speed limit and constancy of light.

Also, I propose that emptiness imposes *no impediment or obstacle* to

 

the forces which we all know traverse space. In other words,

 

"scientific materialism" is a worldview which insists on a

 

billiard-ball-like tangible "connection" between events/masses, etc.

 

But yet the true nature of this "medium" spacetime (I call it malleable

 

because it is supposed to bend and distort or "wrinkle", as in "frame

 

dragging" take various shapes, as per "open, closed, and flat)" has

 

never been addressed in this thread, but for the insistence that the

 

math proves it out. (I am not disputing the math, but there are other

 

possibilities to explain what is going on between masses that

 

distorted "spacetime.")

 

 

 

Here is the relevant part of your post #37...past your very helpful

 

tech coaching on quotes... again, thanks.

(I'll reply bold in context for easy ref. via proximity):

 

Michael,

 

You continually assert that space is just emptiness and therefore

 

cannot have properties such as being curved. This is wrong (or at least

 

unsupported) for a few reasons.

 

General relativity is not the only theory of physics that demands space

 

is not just emptiness. QFT (quantum field theory) also describes fields

 

that are present in all of space. This culminates in theories such

 

quantum electrodynamics which have enjoyed enormous success. QED is

 

tested accurate to ten parts in a billion. As wikipedia says: "This

 

makes QED one of the most accurate physical theories constructed thus

 

far". For you to declare that space is "just emptiness" is not just

 

disagreeing with General Relativity—it's disagreeing with many physical

 

theories in modern science.

 

Please examine your assumption that forces (fields) can not traverse

 

"empty space" and if not empty, *with what is it filled?* (Computer

 

generated visual aids to not consitute proof of reality of whatever it

 

is that fills it, i.e., precludes space being the emptiness between

 

observable/evidential phenomena.)

 

The nature of emptiness as you envision it is a disconnection between

 

entities. If nothing but emptiness (with no properties) exists between

 

things that are spatially separated then simple thought experiments go

 

awry.

 

You never responded to my proposed thought experiment involving a

 

cosmic scale perspective on the present being omnipresent (everywhere,

 

universally) transcending all thought experiments in relativity, all

 

limited to comparisons of local perspectives by individual observers,

 

all based on the speed limit and constancy of light.

Also, I propose that emptiness imposes *no impediment or obstacle* to

 

the forces which we all know traverse space. In other words,

 

"scientific materialism" is a worldview which insists on a

 

billiard-ball-like tangible "connection" between events/masses, etc.

 

But yet the true nature of this "medium" spacetime (I call it malleable

 

because it is supposed to bend and distort or "wrinkle", as in "frame

 

dragging" take various shapes, as per "open, closed, and flat)" has

 

never been addressed in this thread, but for the insistence that the

 

math proves it out. (I am not disputing the math, but there are other

 

possibilities to explain what is going on between masses that

 

distorted "spacetime.")

 

For example, the earth is spinning compared to the stars in the sky.

 

Either the earth spins and the stars remain fixed or the earth remains

 

still and the stars rotate around the earth. If the earth is an island

 

universe unto itself with no fundamental connection to those stars then

 

there should be no way to determine which is the case. But, the earth

 

does know it's spinning compared to the stars.

 

As I've previously commented, the above absurdities are in no way an

 

argument for a substantial (real/ etheric... whatever) medium

 

"connecting" all masses in the cosmos, as per my comments immediately

 

above. The simple structure of logic as per your "Either/or" and

 

"If/then" does not make an argument logical. For instance the premise "

 

If the earth is an island universe unto itself"... is an absurd

 

premise, to which no intelligent person would subscribe. Your positing

 

it in such a way is an obvious insult one's intelligence, though I do

 

not choose to take it personally.

 

The earth has angular momentum and centrifugal force that is quite

 

real. It is not just a mathematical construct. When things spin

 

compared to the "background stars" or the background of "spacetime",

 

mass is accelerated away from the axis of rotation. But, if such

 

objects were disconnected from the rest of the universe there would be

 

no way for them to know they are spinning or not. They can't very well

 

spin compared to nothing. In the language of General Relativity, mass

 

there affects inertia here. [see Mach's principle]

I have also previously answered this. *Of course* earth has actual

 

angular momentum and centrifugal force. If forces can traverse *empty

 

space* then objects are *connected by the forces themselves* not by

 

some theoretical "space-filler" whether you call it "spacetime" of

 

'cosmic glue.'

 

So, experimentally, we know there is some connection between mass here

 

and mass there. It can't be nothing—it must be something.

 

Yes, the forces themselves are the connection. Your assumptions (as

 

detailed above, philosophically speaking) obviously blind you to the

 

possibility that space can indeed remain nothing, that it need not

 

after all be something... i.e., that forces can act at a distance

 

without a medium between them. (BTW, no answer yet to the "medium" of

 

info exchange between two "entangled particles" in QM experiments?

 

Avoidance of the unknown? Yet no one yet knows *how* these 'dancing

 

partners' "know" when to change direction of spin in perfect synch!

 

 

You also assume incorrectly that if space is "just distance" then it is

 

Euclidean. In other words, if space has no properties then it will be

 

measured in an Euclidean way. But, saying space is Euclidean is giving

 

it a property. Assuming parallel lines will never cross or diverge is

 

no more of an assumption then assuming they will cross or diverge.

 

There's nothing about Euclidean geometry that makes it the a priori

 

first choice in describing how the universe works.

 

Woah! Space as emptiness has no "properties." Space as something

 

curved (sphere-like or saddle/hyperbola-like), i.e., non-Euclidean

 

space is *supposed* to have the properties of curvature as above,

 

either "open or closed" ("Flat" is a reification of empty space based

 

on the erroneous assumption, like yours, that space must have the

 

property of shape.) Your logic is weak in claiming that emptiness

 

is a property rather than a lack of properties such as shape.

 

We certainly do measure distance and duration in a non-Euclidean way.

 

If you emit a laser at the top of a building it will have a different

 

frequency as when you detect it at the bottom. The measurements of

 

distance and duration are different at the top as at the bottom. This

 

was predicted with startling accuracy (and is still described best) by

 

the 10 differential equations of general relativity. [see gravity probe

 

a]

 

I will not go into the arguments about the many possible causes of

 

changes in the wavelength of light.

You have not yet addressed my basic, literally "base line" question

 

about "distance." Again, how can the shortest distance between two

 

points *not* be a straight line. (Please review my previous comments

 

about the straight line *through a sphere* as still shorter than a

 

curved line on the surface. Likewise, how can two paralell lines

 

converge? Remember, curving lines are not straight lines, and the

 

latter describe said parallell lines.

 

No, Modest, you have not in fact answered my questions. More links

 

based on non-Euclidean models of space as a-priori assumptions, like

 

Minkowski's curved space will not be answers either, as they assume

 

that Euclidean space is now obsolete.

 

Therefore, to assume that that rules of the universe demand euclidean

 

space and time is conjecture that appears not to be supported by

 

evidence.

 

I am not making that assumption. After studying relativity and

 

non-euclidean "space, The model of a cosmos based on the universal

 

present (not units of time ruling local perspective of light") and on

 

empty space between observable phenomena simply makes more sense to me!

 

I am asking how it is that Euclidean space has been conclusively

 

disproven. I see no evidence that it has. (Math can be very tricky and

 

its models easily *reified.* If one must be a PhD mathematician to make

 

the cosmology make sense, then it has no observable referents in the

 

real world which can make sense to an intelligent, non-mathematical

 

scientist or philosopher/cosmologist.

 

 

 

Modest:

"This question has been answered in unanimous agreement. Spacetime is

 

not a malleable medium. It is not made of matter and it is not tied to

 

a preferred reference frame. It is non-mechanical in nature. The

 

analogies that you bring up are just analogies. They mean to relay

 

characteristics of the theory in an easily envisioned way. They do not

 

mean to imply anything ontological about any aspect of the theory.

 

In a general sense, the variables of space and time in GR are the same

 

as the variables of space and time in special relativity. They are

 

distance and duration. They are 'whatever' clocks and rods measure. Why

 

these variables function in a way that is described by GR (in a way

 

that is loosely described as curved) is a very interesting and

 

difficult question that is at the heart of our discussion. I think it's

 

a very thought-provoking and interesting topic."

 

I suspect that my use of the term "malleable medium" is different than

 

yours. I simply mean that if *it* is something that can be bent,

 

curved, distorted, etc., then "it" is supposed to be malleable.

 

Still, a straight line is not a curved line and remains the shortest

 

diatance between two points. The only change in the distance is via the

 

actual movement of either or both of the points *relative to each

 

other.* (We all know that the universe is expanding and that there are

 

many scales of perspective... that everything is moving.)

 

You have yet to even acknowledge the cosmic perspctive I have proposed

 

even as a "thought experiment" transcending all local perspectives (the

 

whole universe of discourse in relativity)... transcending "units of

 

time and space" as standardized by lightspeed.

 

Gotta go again. Back when I can.

(Again, I was logged in but got the run-around to log in then retrieve my post via the back arrow then back to the original prompt... over and over. So I exited the site, logged in again and retrieved my post from my notepad. Any redundancy will be over-lap as i composed and "saved." Will edit again after posting.)

 

Michael

[Michael Mooney]

Sorry, I'll clean these redundancies on my notepad and re-post.

[modest]

Modest,

You don't seem to realize that I am questioning the fundamental assumptions behind the leap from Euclidean space to non-Euclidean, specifically the assumption that space has shape.

I do understand where you’re coming from and I will do my best to answer your questions directly.

(I studied several of the links you gave in a subsequent post and all of it is based on the assumption of curved space.

 

I think spacetime is an assumption. The properties that spacetime has and the reality of its existence are both assumptions that have to be tested. The only link I remember saying you should read was The Confrontation between General Relativity and Experiment which sets out in detail what these tests are and what the results have been. While this gives a lot of credibility to the idea of a spacetime gravitational field, it was more directed toward your comment that Newton’s law of gravity is sufficient/equivalent to GR. That is not the case.

 

You insistence that science has gone beyond Euclidean space, that the math proves it, and that If I can't go toe to toe and eye to eye with you on the math, I am living in the past without a serious leg to stand on re: "The Philosophy of Science."

I’m tired of being accused of this, so I’d appreciate you showing me exactly where I said any of this or anything that can be interpreted as what you say here. I’d honestly like to see exactly what I said so I can avoid never being so misunderstood again.

 

I have not once used the word “prove” or “proven” in this thread. I have, on the other hand, said multiple times that “I don’t know” or “I don’t have those answers”.

 

I have never claimed anything like “If you can't go toe to toe and eye to eye with me on the math...”. Nor have I claimed that my math was superior to anybodies. The only thing I’ve said regarding my proficiency with math was “I am honestly neither expert in math nor physics” and that was in response to the same strawman you’re pushing now. When you brought up this math thing before I quoted two sources, saying:

The worst thing that can ever happen for philosophy, and for science, is that people are so overawed by the conventional wisdom in areas where they feel inadequate (like math) that they are actually afraid to ask questions that may imply criticism, skepticism, or, heaven help them, ignorance...

 

Faraday did not speak the sophisticated mathematical language his fellow theorists expected to hear. Beyond rudimentary arithmetic, Faraday had no mathematics; his mathematical methods were about the same as those of Galileo. In Faraday’s time, that may actually have been an advantage for creativity. The field concept was the product of “a highly original mind, a mind which never got stuck on formulas,” wrote a great twentieth-century field theorist, Albert Einstein.

Honestly, Michael, I don’t care about your skills with math. I would rather not give it half a thought. Can I make it any more clear? You have just as much right to ask these questions as a tenured math professor. Math doesn’t prove the subject at hand. Proficiency in that field isn’t a prerequisite for discussing the topic.

(Again, I am not debating the math per-se, as I haven't the expertise, but I am welll studied in epistemology as it applies to science, and you are insisting on the a-priority assumption that space is curved, and that the math proves it.

Again, please—either show me where I said “the math proves it” (or anything of the sort) or stop with this and get to the subject at hand.

Sorry... but also have lost patience with this site, as per my last statement. It must be "timing me out" then running me in circles to log in again, arrow back only to find no post just composed, then back to log-in and "re-direct."

Try previewing your post every few minutes as you’re writing/editing it. It will help you spot errors while also keeping you logged in.

Please examine your assumption that forces (fields) can not traverse "empty space" and if not empty, *with what is it filled?*

My understanding is that space is not completely empty if a field is present. The quote of Faraday that I gave sums it up:

The field, though nearly as ethereal as the ether itself, can be said to have physical reality. It occupies space. It contains energy. Its presence eliminates a true vacuum. We must then be content to define the vacuum of everyday discourse as a region free of matter, but not free of field.”

As I understand your argument (Spacetime is a bendable something which can’t exist because space needs to be “no-thing-ness” which spacetime is not) you are equally ruling out any kind of field. How could, for example, “empty” space have a vacuum expectation value with your objection? I’m very certain it could not.

 

I’m very certain that your objection/view rules out the possibility quantum fields as well as spacetime in general relativity. If you think I’m wrong about this then look at the wikipedia page that I link above or this one on vacuum energy. How could the empty, vacuum of space have energy or any other significant value in accordance with your views?

You never responded to my proposed thought experiment involving a cosmic scale perspective on the present being omnipresent (everywhere, universally) transcending all thought experiments in relativity, all limited to comparisons of local perspectives by individual observers, all based on the speed limit and constancy of light.

That sounds like a very interesting idea. I don’t think it’s necessarily inconsistent with observations, but without more specifics I really couldn’t say. You might be interested that modern cosmology assumes something like what you are saying. What you call “a cosmic scale perspective on the present” might be considered Hubble time (or what the following quote refers to as “natural time”). Hubble time is the age of the universe as viewed by all commoving observers—which are observers who are moving with the Hubble flow or the expansion of the universe and have no other peculiar velocity. This assumption makes the further simplification that the universe is homogeneous, so there is no change in gravitational time dilation between observers.

The simplest universe consistent with SR is one which appears isotropic (the same in all directions) to a set of privileged observers, called co-moving observers because each observer sees the others as moving along with the overall cosmic expansion. (Actually these observers are just a figure of speech - the important thing is that there are sites from which the universe would appear isotropic if there were anyone there to observe).

 

The existence of three or more such observers places very strong constraints on the possible structure of space-time. For a start, there is a "natural" time coordinate: the time as measured by each co-moving observer, equipped with a standard clock. Notice that their clocks all measure the same time because they are all controlled by the same rules of physics, and the observers can synchronize their clocks by agreeing to define t=0 to be some special moment in the life of the universe, for instance its beginning (if it had one). The existence of a cosmic time is an enormous simplification; without it, there is no sensible way of separating space from time in the 4-D continuum of space-time.

 

Robertson-Walker Metric

I can also recommend the thread, 15179, which discusses these ideas (if I recall correctly).

Also, I propose that emptiness imposes *no impediment or obstacle* to the forces which we all know traverse space. In other words, "scientific materialism" is a worldview which insists on a billiard-ball-like tangible "connection" between events/masses, etc.

What tangible connection between masses do you propose is responsible for gravity and the effects of special relativity?

But yet the true nature of this "medium" spacetime (I call it malleable because it is supposed to bend and distort or "wrinkle", as in "frame dragging" take various shapes, as per "open, closed, and flat)" has never been addressed in this thread, but for the insistence that the math proves it out.

“the math proves it out” :shrug:

 

Whatever way you can describe the location of two different events—that’s what spacetime is. It is the height, width, depth, and duration in our universe.

For example, the earth is spinning compared to the stars in the sky. Either the earth spins and the stars remain fixed or the earth remains still and the stars rotate around the earth. If the earth is an island universe unto itself with no fundamental connection to those stars then there should be no way to determine which is the case. But, the earth does know it's spinning compared to the stars... [see Mach's principle]

As I've previously commented, the above absurdities are in no way an argument for a substantial (real/ etheric... whatever) medium "connecting" all masses in the cosmos, as per my comments immediately above.

 

The simple structure of logic as per your "Either/or" and "If/then" does not make an argument logical. For instance the premise "If the earth is an island universe unto itself"... is an absurd premise, to which no intelligent person would subscribe. Your positing it in such a way is an obvious insult one's intelligence, though I do not choose to take it personally.

I’m describing Mach’s principle which is a well-known argument (thought experiment) proposed by Austrian philosopher and physicist Ernst Mach and refined by Einstein. It concludes “mass there influences inertia here". I thought it would be a simple way to impress upon you that there is a necessary connection between masses. You’ve apparently mistaken it for my own personal “absurdity”.

 

It also troubles me that you read a simple summary of a thought experiment and think it is meant to insult your intelligence.

 

Woah! Space as emptiness has no "properties." Space as something curved (sphere-like or saddle/hyperbola-like), i.e., non-Euclidean space is *supposed* to have the properties of curvature as above, either "open or closed" ("Flat" is a reification of empty space based on the erroneous assumption, like yours, that space must have the property of shape.)

Euclidean geometry has 23 definitions, five common notions, and five postulates. The only difference between Euclidean geometry and non-Euclidean geometry is in changing the fifth postulate. There’s no reason to assume (as you have) that the universe somehow has to have Euclidean geometry or that it chooses Euclidean geometry by default. We would have to test and measure to find out something like what geometry the universe has.

You have not yet addressed my basic, literally "base line" question about "distance." Again, how can the shortest distance between two points *not* be a straight line.

If you’re really interested in the answer to this then I’d recommend:

 

The Ontology and Cosmology of Non-Euclidean Geometry

 

It’s written by a modern professor of philosophy of whom I’m rather fond.

 

~modest

[modest]

I've just had another thought. Perhaps the following would be a more meaningful definition of spacetime:

Spacetime is a description of the universe. It is composed of three "spacelike" dimensions and one "timelike" dimension. A distance in spacetime is composed of two intervals:

• A "spacelike" interval. This is the distance in space between two events.
  
• A "timelike" interval. This is the time interval between two events.

The two intervals are combined into two components:

• A "lightlike" component. The "lightlike" component is the amount of spacetime where the "spacelike" interval matches the "timelike" interval between the events.
  
• A "spacelike" or a "timelike" component. This is the remainder (if any) of the "spacelike" or "timelike" interval.

The intervals are combined in this manner because the spatial distance and time interval between two events that will be observed by an observer depends upon the frame of reference in which it is observed.

This definition makes the point that spacetime is not just a mathematical model. It also stresses the "lightlike" component of the spacetime interval. Mathematically this is zero (because the spacelike and timelike intervals cancel), so is ignored mathematically, but is very important conceptually. I think it is the omission of the "lightlike" component in descriptions of the spacetime interval that leads to many misunderstandings.

 

Anyway, what do you (anyone) think?

 

Hello Jedaisoul,

 

I like where you’re going with this spacetime composition. If you don’t mind, I see some sticky points I can point out.

A distance in spacetime is composed of two intervals:

There is only ever one interval between two spacetime points (or events). It is a number that can be thought of as the spacetime separation of the events.

 

Depending on where the events are located with respect to one another in space and time, the interval can be negative, zero, or positive. If the interval is negative it is known as a space-like interval. If the interval is zero it is known as a light-like interval. If the interval is positive it is known as a time-like interval.

 

Note: this follows the Landau-Lifshitz sign convention.

 

Time-like interval: There can be a cause-effect relationship between the two events. Enough time passes for an inertial observer to intersect both events. Therefore, each event is necessarily in the past or future of the other event.

 

Space-like interval: There can be no cause-effect relationship between the two events. They are separated by too much space and not enough time for an observer or light to intersect both events. Therefore, neither event is in the past or future of the other event.

 

Light-like interval: There is exactly equal amounts of space and time between the events which is equal to the speed of light. Therefore, two events with a light-like interval can only be intersected by massless particles such as light. The zero interval describes a light cone.

 

The two intervals are combined into two components:...

 

The intervals are combined in this manner because the spatial distance and time interval between two events that will be observed by an observer depends upon the frame of reference in which it is observed.

I think I see what you’re trying to say.

 

Any given observer can describe two events in their reference frame. When they do this they will have two components: space (spatial distance between the events) and time (duration between the events). By converting the two values to similar units, squaring them, and taking the difference, they find the spacetime interval between the events which is described above.

 

You wouldn't say you're combining two intervals when you do this. The word interval is reserved for the result of the preceding paragraph. It is the invariant that everybody agrees on. It is a single value.

 

~modest

[jedaisoul]

Hi Modest,

 

I withdraw my comments about your metaphor of the flunking students, as it is clear you did not intend the meaning I drew from it.

 

I'm also impressed that you are seriously trying to understand what I'm saying. But I suspect that you have not grasped what I'm trying to say, so I'll have another try:

 

We are trying to understand the meaning of spacetime. To understand that you need to understand the meaning of the spacetime interval. The trouble is, the spacetime interval is a metric, a "magic number". It is meaningful in the sense that you can derive meaningful values from it, but in itself it is largely meaningless.

 

I have illustrated that claim with the zero interval. It is meaningful as an expresssion of how light experiences the universe. As light moves radially along the light cone, the events it passes are co-located and simultaneous in the rest frame of the light. But the zero interval is not, in itself, meaningful as how material objects experience those events:

• They are not co-located.
  
• They are not simultaneous.

So what does the zero interval mean? It means that the spatial interval and the time interval are the same. That's all. They could be any value, so long as they are the same. So the spacetime interval does not fully describe the space-time (spatial and temporal) relationships between two events, It merely allows you to calculate them if you know one of these values. So, if in a given frame of reference you know that two events have a zero spacetime interval and are separated by one second in time, you know they are one light-second apart in space.

 

There is another ways of calculating the space-time relationships between two events. I.e. If you know the relationship between a given frame of reference and the frame of reference in which the spacetime interval between those events is zero, then you can calculate the space-time relationships between those events in the given frame of reference. But the point I'm making remains. The spacetime interval alone does not fully describe the space-time relationships between two events. It's just a "magic number" from which the relationships can be calculated, providing you have further information.

 

So the spacetime interval is not, of itself, sufficient to describe the physical relationships between material objects.

 

Now, I suspect that you are content with that. You may not expect the spacetime interval to be any more meaningful than that. But, to some people, that is not satisfactory philosophically. They want spacetime (and the spacetime interval) to be meaningful in the sense that Eucliean space-time is meaningful. We perceive space and time in Euclidean terms. It is meaningful to us. Even if spacetime is non-Euclidean, we need to translate physical relationships back to distances in space and time (in a given frame of reference) for them to be meaningful to us.

 

So I was seeking to make spacetime more meaningful by suggesting that, philosophically, the spacetime interval is only one of two components that together define the spatial and temporal relationships . It tells you the amount by which the spatial and time intervals differ. The other component is the amount by which the spatial and time intervals are the same. In spacetime terms, that component is always zero, so is ignored. But in space-time terms it is non-zero, and is the misssing information that makes spacetime intervals meaningful.

 

Does that make sense?

[jedaisoul]

I'm still not sure if I've made myself clear, so I'll give an analogy:

 

When stereo recordings were introduced, radio broadcasters had a problem: they wanted to braodcast in stereo, but needed to remain compatible with existing mono receivers. Stereo is composed of two signals: Left and Right, and if you add them together you get mono (the sum). But if you subtract them you get the difference. So the broadcasters went on transmitting in mono, but added a side signal (Left - Right). Stereo receivers then extract the Left and Right signals by combining the sum and difference signals in two ways;

sum + difference = Left

sum - difference = Right

 

Relating this to spacetime, the difference between time and spatial intervals is the spacetime interval. The amount by which they are the same is ignored as it is the "light-like" component which is mathematically zero (because the two intervals cancel in spacetime). But although it is mathematically zero, to material objects there is a real difference between 1 second of time cancelled by a distance of 1 light-second, and 2 seconds of time canvcelled by 2 light-seconds of distance. When you calculate the spatial and temporal intervals experienced by material objects in a given frame of reference they are not the same. This difference is caused by the amount by which the spatial and temporal intervals are the same.

 

So you can ignore the light-like component in spacetime, but not in space-time. In space-time the light-like component has a real magnitude (which is the smaller of ithe the light or spatial interval (i.e. the amount by which they are the same).

[Michael Mooney]

I do understand where you’re coming from and I will do my best to answer your questions directly.

 

 

I think spacetime is an assumption. The properties that spacetime has and the reality of its existence are both assumptions that have to be tested. The only link I remember saying you should read was

 

Tests of Post-Newtonian Gravity

3.1 Metric theories of gravity and the strong equivalence principle

3.1.1 Universal coupling and the metric postulates

3.1.2 The strong equivalence principle

3.2 The parametrized post-Newtonian formalism

3.3 Competing theories of gravity

3.3.1 General relativity

3.3.2 Scalar-tensor theories

3.3.3 Vector-tensor theories

3.4 Tests of the parameter

3.4.1 The deflection of light

3.4.2 The time delay of light

3.4.3 Shapiro time delay and the speed of gravity

3.5 The perihelion shift of Mercury

3.6 Tests of the strong equivalence principle

3.6.1 The Nordtvedt effect and the lunar Eötvös experiment

3.6.2 Preferred-frame and preferred-location effects

3.6.3 Constancy of the Newtonian gravitational constant

3.7 Other tests of post-Newtonian gravity

3.7.1 Search for gravitomagnetism

3.7.2 Geodetic precession

3.7.3 Tests of post-Newtonian conservation laws

3.8 Prospects for improved PPN parameter values

 

Semantics! Seemed like lots of links to me.

 

Originally Posted by Michael Mooney

You insistence that science has gone beyond Euclidean space, that the math proves it, and that If I can't go toe to toe and eye to eye with you on the math, I am living in the past without a serious leg to stand on re: "The Philosophy of Science."

 

 

I’m tired of being accused of this, so I’d appreciate you showing me exactly where I said any of this or anything that can be interpreted as what you say here. I’d honestly like to see exactly what I said so I can avoid never being so misunderstood again.

 

Gimme a break! The whole post leading to the link(s) above was a mathematical presentation. And your whole conversation with Jediasoul is a math argument completely ignoring the title question of this thread. Please review all your replies to me on this thread. You are giving me standard non-Euclidean warped spacetime as per Einstein/Minkowski though I opened with the declaration that I have already studied it... yet you insist on it and say we can not go "backward" into the implied stone-age of Euclidean space/cosmology.

 

I have not once used the word “prove” or “proven” in this thread. I have, on the other hand, said multiple times that “I don’t know” or “I don’t have those answers”.

OK, you offer the math as very strong evidence... etc.,etc... shall we make this about mincing words? I hope not.

 

I have never claimed anything like “If you can't go toe to toe and eye to eye with me on the math...”. Nor have I claimed that my math was superior to anybodies. The only thing I’ve said regarding my proficiency with math was “I am honestly neither expert in math nor physics” and that was in response to the same strawman you’re pushing now. When you brought up this math thing before I quoted two sources, saying:

Honestly, Michael, I don’t care about your skills with math. I would rather not give it half a thought. Can I make it any more clear? You have just as much right to ask these questions as a tenured math professor. Math doesn’t prove the subject at hand. Proficiency in that field isn’t a prerequisite for discussing the topic.

 

Again, please—either show me where I said “the math proves it” (or anything of the sort) or stop with this and get to the subject at hand.

 

"Special relativity works on flat Minkowski spacetime (as I'm sure you know). SR also works (we know, experimentally) in small areas of freefalling space along the gravitational potential of a body. This means the *geometry* of space is somehow fundamentally curved. This is explained in the Wiki for General Relativity from section 2 to section 4."

 

"Spacetime is supposed to be a mathematical representation of the geometry and happenings of our universe."

 

"All physical laws used to be modeled on three-dimensional Euclidean space with universal time. In the beginning of the last century, Einstein demonstrated that time (as is measured by clocks) and space (as is measured by rods) was not universal, but depended on the relative motion of the clocks and rods."

(See my posts on time and space and the universal now. All "used to be" valid but no longer, given the MATH of relativity and the model of distorted SPACETIME.)

 

"In the language of mathematical logic, space and time are axioms of our system."

 

(Aside... just scanning your posts...

"A clock measures time and time is what a clock measures." This precludes investigating what forces might make clocks *run faster or slower.* The "perfect clock" would keep "perfect time." Are there any such? And what is perfect time?" Standardized fractions of an earth rotation cycle? How is this mutable via observers and their clocks traveling at different speeds?.. Just another question that you have totally ignored.)

 

"We certainly do measure distance and duration in a non-Euclidean way. If you emit a laser at the top of a building it will have a different frequency as when you detect it at the bottom. The measurements of distance and duration are different at the top as at the bottom. This was predicted with startling accuracy (and is still described best) by the 10 differential equations of general relativity.

 

"For example, you continually claim that Einstein's spacetime is some kind of malleable medium made of bendable stuff. I (and others) have corrected you on this multiple times, yet you continue criticizing GR on that basis.

 

"It" curves, gets wrinkled, has shape, and is filled is itself a medium which is required to transmit force fields, yet it is *not* malleable? Maybe "malleable" has acquired a special meaning in GR?

 

" however, because of space curvature around the Sun, determined by the PPN parameter , local straight lines are bent relative to asymptotic straight lines far from the Sun by just enough to yield the remaining factor “/2”. The first factor “1/2” holds in any metric theory, the second “/2” varies from theory to theory."

 

" A 2004 analysis of almost 2 million VLBI observations of 541 radio sources, made by 87 VLBI sites yielded , or equivalently, ..."

 

"You are simply incorrect. Every conceivable test of general relativity (as above) has sided against Newton. We have moved past the question of "is general relativity correct" and moved on to "why is general relativity correct".

 

My understanding is that space is not completely empty if a field is present. The quote of Faraday that I gave sums it up:

 

As I understand your argument (Spacetime is a bendable something which can’t exist because space needs to be “no-thing-ness” which spacetime is not) you are equally ruling out any kind of field. How could, for example, “empty” space have a vacuum expectation value with your objection? I’m very certain it could not.

A true vacuum *is* empty space. Maybe words have lost their meaning since a vacuum is no longer empty space. Shall we just re-define out words to suit our theoretical fancy? And a magnet on one side of a "vacuum" will still attract a iron bar on the other side. "How does it do that with nothing in between? Well, it does even if we don't know how.

 

I've gotta go again. Will take it (the rest of your post up when I can.

Oh..., I read the whole piece given in the link at bottom.

Back to that later as well.

 

What tangible connection between masses do you propose is responsible for gravity and the effects of special relativity?

 

Maybe if i say it a few more times.... No tangible connection! Forces effective across *empty space* (no billiard balls conveying kenetic energy one mass to another... actual "action at a distance.

 

“the math proves it out” :evil:

Maybe your eyes can focus on the above examples rather than implying m your impatience with my ignorance.

 

Whatever way you can describe the location of two different events—that’s what spacetime is. It is the height, width, depth, and duration in our universe.

 

That works well with common sense empty space, stuff expanding into it, and the perpetual now everywhere... without non-Euclidian space as having curvature, being distorted, etc.... nor distorted "time."

 

 

 

It also troubles me that you read a simple summary of a thought experiment and think it is meant to insult your intelligence.

 

Like the earth being an island unto itself if one doesn't accept space being filled with something to transmit forces. Yes, no doubt an insult to anyones intelligence.

 

 

Euclidean geometry has 23 definitions, five common notions, and five postulates. The only difference between Euclidean geometry and non-Euclidean geometry is in changing the fifth postulate. There’s no reason to assume (as you have) that the universe somehow has to have Euclidean geometry or that it chooses Euclidean geometry by default. We would have to test and measure to find out something like what geometry the universe has.

 

If you’re really interested in the answer to this then I’d recommend:

 

I studied the contents of the link below in depth. Copious quotes and my commentaries. Next time.

 

Seems you hide behind these complex papers so that you need not, in your own words, reply to the simple question, as the point of departure from Euclidean to non-Euclidean...

""Do you believe that the shortest distance between twopoints is a straight line?"

 

The Ontology and Cosmology of Non-Euclidean Geometry

 

It’s written by a modern professor of philosophy of whom I’m rather fond.

 

~modest

I have twice received the prompt that my post is too short, though it is clearly quite long.

Third try:

Michael

[jedaisoul]

The whole post leading to the link(s) above was a mathematical presentation. And your whole conversation with Jediasoul is a math argument completely ignoring the title question of this thread.

I hope that this comment does not apply to my part of the conversation with modest. I have used the minimum of maths and focussed on the philosophic meaning of the spacetime interval, and hence spacetime itself. I'd be interested to know whether you have grasped the thrust of my argument about the spacetime interval not being meaningful in itself? To me that point is central to the answer to your question "what is spacetime really?".

 

If you have not grasped that, then that does not reflect on you, but on my ability to communicate clearly. Hence I'd like to know what you make of it...

 

By the way, when you embed your comments in the text you are quoting, your comments do not come up when other people reply to you. It is preferable to split the post you are commenting on into separate quotes, and put you comments between the {/quote} and the next {quote}. Note: I've used curly braces in these examples, so they will come out as text. You should use square brackets, then they will be interpreted as the start and end of a quote.

[Michael Mooney]

Jediasoul:

I'd be interested to know whether you have grasped the thrust of my argument about the spacetime interval not being meaningful in itself? To me that point is central to the answer to your question "what is spacetime really?".

I meant Modest's half of the argument. Yes, I understand your side of the argument and agree. If two actual objects are two light seconds apart, they are that *actual distance apart in space,* not at the same place at the same time as the nonsense of spactime math insists, and as you have cogently argued against.

 

I think you put the general principle of spacetime math being unreal very well as follows:

 

But the point I'm making remains. The spacetime interval alone does not fully describe the space-time relationships between two events. It's just a "magic number" from which the relationships can be calculated, providing you have further information.

 

So the spacetime interval is not, of itself, sufficient to describe the physical relationships between material objects.

 

Now, I suspect that you are content with that. You may not expect the spacetime interval to be any more meaningful than that. But, to some people, that is not satisfactory philosophically. They want spacetime (and the spacetime interval) to be meaningful in the sense that Eucliean space-time is meaningful. We perceive space and time in Euclidean terms. It is meaningful to us. Even if spacetime is non-Euclidean, we need to translate physical relationships back to distances in space and time (in a given frame of reference) for them to be meaningful to us.

I have been questioning the reasonability of theory as to *how* "spacetime" became non-Euclidean, and I have studied the history of it in depth, including the last link/paper given me by Modest. The latter will be the subject of my next post. Meanwhile I can't get a straight answer here in this forum as to how empty space became substantial enough to have shape, curvature, wrinkles, etc, as per non-Euclidean theory... which clearly *reifies* "space" into some-thing (as distinct from emptiness between things) and time into some-thing which can slow down or speed up (as distinct from clocks' inability to keep accurate standardized time under the force of inertial change... acceleration/deceleration.)

 

And thank you for the technical advice. I am still quite tech-challenged in computer tech in general and especially by the idiosyncrasies of this site.

 

Michael

[Michael Mooney]

Modest,

Thanks for the link: The Ontology and Cosmology of Non-Euclidean Geometry

 

I compiled extensive quotes and interjected my commentaries, but ended with a very long essay. Will here edit it down as best I can.

(Hope this does not preclude your reply to my last post to you above.)

 

There are still many good questions to ask about non-Euclidean geometry; but in treatment after treatment in both popular expositions and in philosophical discussion, the questions consistently seem pointedly not to get asked

My mission here is to ask them.

 

A good example of this may be found in two articles published in Scientific American in 1976. J.J. Callahan's article, "The Curvature of Space in a Finite Universe" in August, makes the argument that Riemann's geometry of a positively curved, finite and unbounded space, which was used by Einstein for his theory, answers the paradox of Kant's Antinomy of Space, avoiding both finite space and infinite space as they had been traditionally understood

 

The above clearly makes the assumption that space is not emptiness but has shape. As emptiness, the question of "finite or infinite" does not arise. There can be no boundary around emptiness. Any such "spherical cosmos" will have more space, infinite space beyond its outer sphere of expanding *material.* Emptiness has no properties... shape or expansion.

 

Instead, the universe is more likely to be infinite, either with a Lobachevskian non-Euclidean geometry, or even with a Euclidean(!) geometry after all.

For clarity sake, space is infinite, and what it contains, on whatever cosmological scope, has (whatever) shape... I believe it is spherical as per cosmos exploding out from the "Bang" (via whatever dynamic) liker any fireworks display.

 

It is as though everyone is waiting around in the hope that the "missing mass" turns up

 

More normal (baryonic) matter, simply not emitting or reflecting light, is being discovered all the time, and various kinds of strange ("dark") matter

/energy as well. (I don't pretend to understand the "nature" of the latter.) Anyway, my favorite cosmology requires the critical cosmic mass to reverse the expansion and commence the contraction toward the "Crunch"... and the full two phase cycle must be perpetual. (Entropy is not a problem as nothing is "lost", i.e., there is no limit to the reach of gravitation, though of course its strength diminishes with the square of the distance. Thanks, Modest for the technical, 'squared' reminder.)

 

§2. Curved Space and Non-Euclidean Geometry

 

Euclid's parallel postulate, in its modern reformulation, holds that, on a plane, given a line and a point not on the line, only one line can be drawn through the point parallel to the line.

.......... There were two ways to contradict the postulate: space could have 1) no parallel lines (straight lines in a plane will always meet if extended far enough), or 2) multiple straight lines through a given point parallel to a given line in the plane. These become non-Euclidean axioms

 

And they make no sense at all... a mental exercise version of "The Emporer's new Clothes." (Anyone who doesn't "get it" is not too smart.)

 

If by "flat" we mean a plane of straight lines as understood by Euclid, then true non-Euclidean manifolds (i.e. areas, volumes, spacetimes, etc.), in order to really contradict Euclid, who was talking about straight lines, would have to be flat. They could not be curved. Straight lines would be Euclidean straight, but the properties specified by non-Euclidean axioms would be satisfied. Nevertheless, since Bernhard Riemann (1826-1866), non-Euclidean manifolds are said to be "curved," and only Euclidean space itself is called "flat."

 

But, of course, if space is true emptiness, then there is no "flat space" but only the flat geometric plane upon which straight, non-converging parallel lines are nominally "drawn."

 

.... non-Euclidean planes can be modeled as extrinsically curved surfaces within Euclidean space.

 

Curved computer models do not create actual curved space in the real world, but only in the virtual world of computer imaging.

 

 

Damn... I've gotta go. Hope to pick it up where I left off later. Open for commentary meanwhile. It's a long paper. Maybe doing it in smaller bites is better.

Michael

[modest]

However, what I find difficult to understand about spacetime is the way that spatial distances and time intervals combine to form spacetime intervals. The spatial distancess combine according to pythagoras's law, so the square of the spatial distance is equal to the sum of the squares of the distances in the three spatial dimensions. I.e. d2 = x2 + y2 + z2.

Where d2 is the square of the spatial distance, and x2, y2 and z2 mean x squared etc...

 

But the square of the spacetime interval is equal to the difference between the squares of the spatial distance (in light seconds) and time interval (in seconds). I,e, s2 = d2 - t2 (if d is greater than t) or s2 = t2 - d2 (if t is greater than d).

Where s2 is the square of the spacetime interval (in seconds or light seconds), d2 is the square of the spatial distances (in light seconds), and t2 is the square of the time interval (in seconds).

 

Why is this?

You see, as far as I'm aware, because the spacetime interval is invariant, and (we agree) that it is zero for light travelling from a to b, surely it must also be zero for me? If so, and I'm pretty sure that is so, we have what appears to be a logical fallacy that the spacetime interval is zero, but the events are neither co-located nor simultaneous (to me). And the same applies to any other material entities.

 

Jedaisoul, I've spent a fair amount of time in writing this post. I think it will be helpful in illustrating things as I understand them. I appreciate your patience in illustrating your view and feel I should do the same.

 

It contains some math which I've taken crap for in this thread. Nevertheless, your question above explicitly asks about the structure of the metric and any math here follows from that question directly.

 

Ok then—we want to know the distance... the real distance... between two spacetime events. We can first set up some ground rules.

 

1.A clock measures distance in time.

2.A ruler measures distance in space.

3.An event is something that happens at a specific time and place.

 

I intend to give a space-time thought experiment. My purpose in doing this is to show why I don’t share your philosophical objection to the spacetime interval—even when it is zero.

 

Sally is interested in two events. The first event, A, is on earth at zero time. The second event, C, is on a planet 1.6 lightyears distant 2 years later (from earth’s perspective). Sally wants to know the actual spacetime distance between these two events.

 

 

The two events in question are A and C, so Sally is trying to determine the distance of the green line AC. She has a clock that will measure time from A to B. Both these events will be under her feet when they happen, so the clock directly measures the red line AB. We can also imagine she has a measuring tape that spans the entire distance between planets that measures the other red line BC. This is the extent of Sally’s knowledge. She cannot directly measure AC as she will not be at C when it happens (she will be 1.6 lightyears away).

 

If we use the ordinary Pythagorean theorem to find AC we get:

[math]S=\sqrt{AB^2 + BC^2}[/math]

[math]S=\sqrt{2^2 + 1.6^2}[/math]

[math]S=2.56[/math]

The spacetime interval AC would seem to be 2.56. However, this is wrong according to relativity (we will take on faith for a moment). The metric Minkowski proposed is [math]s^2=t^2-x^2[/math], which looks quite-nearly Euclidean with the obvious exception of subtracting the measure of distance and time. Using this metric we get:

[math]S=\sqrt{AB^2 - BC^2}[/math]

[math]S=\sqrt{2^2 - 1.6^2}[/math]

[math]S=1.2[/math]

According to Minkowski, the spacetime interval AC is 1.2. Sally is obviously unconvinced of this. How could the green line above be shorter than either of the red lines? Do time and space really work this way? Yes. They do.

 

Sally decides to test this theory directly. She gives her buddy Tom a clock and sends him from A to C. The reason for doing this may not be immediately apparent, so I will explain. When sally measured AB she was able to use her clock to find the distance. Both events were at her location so the only relevant distance was time. When Tom moves from A to C both events will be at his location. The exact way Sally measured AB, Tom will measure AC.

 

In order for Tom to travel 1.6 of Sally’s lightyears in two of Sally’s years, he will need to go eight-tenths the speed of light from Sally’s perspective. This will place him at events A and C exactly when they happen. Using the equation for time dilation:

[math]T_{tom} = T_{sally} \sqrt{1- \frac{v^2}{c^2}}[/math]

[math]T_{tom} = 2 \sqrt{1- \frac{0.8^2}{1^2}}[/math]

[math]T_{tom} = 2 \times 0.6[/math]

[math]T_{tom} = 1.2[/math]

The time it takes Tom to get from A to C is 1.2 years. Tom directly measures AC at 1.2. This confirms the metric. It has profound philosophical meaning. Consider if Tom returned to Sally via CD. His trip would again take 1.2 years while Sally again ages 2 years along BD. When Sally and Tom meet back up, Tom is 1.6 years younger than Sally. This effect is real. It has been measured. The shortest distance between two points is NOT a straight line. Sally’s path AD was longer than Tom’s path ACD.

 

So then, is a zero interval a counter-example to this?

 

 

No. The example above requires Tom to travel at the speed of light to the 2 lightyear-distant planet. If he could do this, the path length AC would truly be zero. If he traveled ACD he would not age at all while Sally aged 4 years. There is nothing abnormal about a light-like interval. It truly is zero according to relativity, Minkowski’s metric, and reality.

 

Your specific objection is that Sally does not observe A and C to be collocated and simultaneous. This is both true, and to be expected. Your assumption that AC being zero demands AB or BC to be zero is not how relativity works, and it's certainly not how the metric works.

 

The spacetime interval AC in the diagram above is truly zero in every way we humans can measure it.

 

~modest

[Essay]

...clearly makes the assumption that space is not emptiness ...Emptiness has no properties... shape or expansion.

 

...what it contains, .

 

...full two phase cycle must be perpetual.

 

And they make no sense at all... a mental exercise version ...

 

But, of course, if space is true emptiness...

 

Curved computer models do not create actual curved space...

 

Michael

 

Michael, I still think this is mostly a semantic situation.

 

You seem to see (I think) most descriptions for “action at a distance” as implying some sort of mediating aether.

 

It is our language and mathematics that imply the substance or aether.

 

Just because our minds don’t have a category for things (known by their potential or effects) that are composed of nothing, doesn’t mean that we can’t add a new category of thing to our understanding.

 

Politics, for instance, may be an analogy of such a “thing.” It is spoken of as if, at any given instant, there is a certain reality that is true, with a past and a future—a history and a potential, which can be analyzed, parameterized, and on which calculation can be made.

 

You may lean toward the “force-field model” filling space with a network for which, at any given instant, there is a certain reality that is true, with a past and a future—a history and a potential, which can be analyzed, parameterized, and on which calculation can be made.

 

Even this network, “filling” the empty nothingness, leads our language and mathematics to deduce or imply an aether, but it need not be a physical actuality.

 

Similarly, other models that seem to suggest an aether, do so only to make the language and mathematics tenable, IMHO

 

Even assuming the distinction between mattenergy and spacetime is an illusion, we still need some way to talk about it and to make calculations; so we need to develop new categories….

 

…or to recapitulate:

Models may start out positing nothingness, but….

It is just the language and math that push for a term to use when describing, discussing, or manipulating the conclusion.

 

When you see the implication of an aether, just translate that into a ‘nothingness permeated with a history of, and a potential for, interactions,’ or something like that; and then there should be more agreement between these descriptions of models.

 

Models are always metaphors. I never expect one to be right, accurate, or true; but I look for consistency, enough accuracy, and a hint of the “Truth.”

 

p.s. …cycling within atemporal nothingness???

…and get away from that fireworks metaphor--it’s too linear.

…better to think of the nothingness dissipating, as spacetime replaces it everywhere, only then to expand.

…and also remember, there was no nothingness before the bigbang, because it generates spacetime.

...break the preconceptions of middle-world common sense.

 

~ :shrug:

[Michael Mooney]

Hi Essay,

Thanks for your thoughtful reply, but your assumptions are based on exactly that which I (and the title question) are challenging.

 

(Note: I've too much going on in this thread... not to mention my "real life"... most notably a debate with Modest which he presently seems to be avoiding, but for calling my perspective on his focus on math "crap."

 

To illustrate, I will skip down to your "ps":

p.s. …cycling within atemporal nothingness???

…and get away from that fireworks metaphor--it’s too linear.

…better to think of the nothingness dissipating, as spacetime replaces it everywhere, only then to expand.

…and also remember, there was no nothingness before the bigbang, because it generates spacetime.

...break the preconceptions of middle-world common sense.

 

No, not "atemporal nothingness." Space is nothingness but that which occupies it (as I see it) is 'something-ness' (if you will)... matter/energy/plasma of all sorts. Please review my posts in this thread on "time." The perpetual now, the ongoing present... refers to everything everywhere, all of which *is continually happening* always, not a state which the human mind usually considers "frozen in time", if that is what you mean by "atemporal nothingness."

 

I don't take orders, even from self-appointed authorities on any given subject, so you may want to take a different tack than :

".... get away from that fireworks metaphor--it’s too linear."

 

It works well for real cosmic "stuff going bang" as, say the beginning of a perpetual Bang/Crunch oscillating cosmos. (Some folks like the "crunch" "bouncing" off something...? rather than exploding, but I "see" many smaller "bangs" and many smaller "crunches" which might fit an enlarged supernova model... "my cosmic juggling act." It happens in a Euclidean model of the actual cosmic "stuff" we can still see as cosmos *occupying* a small part (as per our cosmic event horizon) of infinite space.

 

…better to think of the nothingness dissipating, as spacetime replaces it everywhere, only then to expand.

 

You really don't "get" "nothingness." Like Modest, you insist that" it" (??) must me something which can expand, "dissipate," etc. And then you posit "spacetime" (as replacing emptiness with some-thing, "spacetime"... yet again as a given, even though this whole thread challenges *it* as any kind of reality (besides a learning aid visual or metaphorical "fabric" to help math equations work. Can you not see that you have again made the assumption that "it" is real... reified "it", even though this whole thread is challenging "it" as a reality?

 

…and also remember, there was no nothingness before the bigbang, because it generates spacetime.

 

"Remember?" What, THE ESTABLISHED COSMOLOGY OF MAINSTREAM SCIENCE? That is what I am here questioning and challenging. (See thread title.)

I see space as infinite emptiness. What happens *in space* is the cosmos, the actual stuff that cosmos is made of. Then cosmology debates where "it all" (the stuff) came from and where it is going... etc.

Before the bang, the way I see cosmology, all the stuff which travels around "in space" was returning from the expansion, via gravity... the implosion half of the cycle.

You are parroting the mainstream *dogma* (as I see it) that spacetime is *something* created by the big bang. This, is nonsense to me, as above.

 

...break the preconceptions of middle-world common sense.

Huh? Is this science or dogmatic belief? Seems the latter to me. See any "preconceptions" in your "scientific" indoctrination, as espoused above.

Doubt if you can even hear me, as your mind is already made up.

 

Maybe I'll get around to your pre-p.s. post later. Maybe not, considering that you think you have corrected my misconceptions without even "grokking" (if you will) the cosmology which makes most sense to me.

 

Michael

[jedaisoul]

Jedaisoul, I've spent a fair amount of time in writing this post. I think it will be helpful in illustrating things as I understand them. I appreciate your patience in illustrating your view and feel I should do the same.

 

It contains some math which I've taken crap for in this thread. Nevertheless, your question above explicitly asks about the structure of the metric and any math here follows from that question directly.

Well, I appreciate the work you have put in, but, to be frank, you have not told me anything I did not already know. I would like you to deal with the simple example I gave in #63, which I repeat below:

I am stationary with respect to another observer who is 600,000 kilometers (two light seconds) away from me. At time zero I clap my hands. Two seconds later the other observer claps his hands. According to special relativity, there is a zero spacetime interval between these two events.

 

It is true to say that for a photon travelling from me to the other observer these events happen at the same place and time. So a zero spacetime interval makes sense for light. That is true.

 

But it is not true from my and the other observer's point of view. The events are neither simultaneous nor co-located from the perspective of either observer, nor indeed for any material object. It's only true for light. Hence the claim that spacetime reflects the universe as experienced by material objects fails.

This example involves observers that are mutually at rest. If spacetime cannot describe that situation, then, so far as I'm concerned, the rest is irrelevant. Spacetime does not reflect reality.

 

So, if you don't agree, please show where this example is wrong.