What is "spacetime" really?

[watcher]

MM,

 

as a thought experiment. what do you think is the shortest distance between a point in 3d space and a point in 5d space? if i could plot it for demonstration, i will, but i can't. just a gut feeling that it aint a straight line.

 

Can you imagine a cosmos with no intelligent life forms "observing?" Does the distance between objects then disappear sans "observation?" Ans: No.

 

regardless of anything. the conservation of energy as an expression of the varying proportionality between the wavelength and frequency stands. i think here lies our basic difference in philosophy . i imagine a cosmos of undulating energy . and space and time are the same thing that is simply out of phase with itself. iow , the ontological "what is" is not space. space is only an aspect of it.

 

a good philosophical rule about the nature of "what is" is ... if you can perceive it, it ain't it. so most of the time it is just referred to as a potential. this explains why it is called a "no thing". but this "no thing" manifests itself as things. thoughts are things and so is space because you can perceived them. so again, i don't deny the existence of "what is", only it is not space neither.

 

i know its simpler to think space as an absolute emptiness. but this postulate is limited to a 3 dimensional space only. and i happened to believed that space has more than three dimensions.

[Pyrotex]

...regardless of anything. the conservation of energy as an expression of the varying proportionality between the wavelength and frequency stands. i think here lies our basic difference in philosophy . i imagine a cosmos of undulating energy . and space and time are the same thing that is simply out of phase with itself. iow , the ontological "what is" is not space. space is only an aspect of it. ...

Clever words. But what do they mean?

What value added do they bring to the conversation, "What is Spacetime?".

Any philosophy is worthless, until you can "ground it" in some aspect of observable Reality.

 

P.S.: the shortest distance between ANY two points in a Space of ANY number of dimensions is defined as a "geodesic". If the Space is Cartesian, then ALL geodesics are straight lines.

 

Stop listening to your gut. You're just hungry. Eat a cookie. :)

[Michael Mooney]

MM:

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

Modest:

"If nothing in the universe existed relative to anything else then the cosmos would cease to exist in any meaningful way. Beyond that, your use of the word objective continues to confuse me."

 

I can't say it any more plainly than, "in and of itself independent of relative observational perspectives?" What part of that do you not understand?

 

So you either can not or will not engage in my "thought experiment" in which cosmos exists, " in and of itself independent of relative observational perspectives?"

 

So every part of the cosmos *and cosmos as a whole* exists whether or not one aspect is being compared to another in a relativistic way. Of course if your "ground zero" absolute "frame of references" is that nothing can exist "in and of itself" without considering local frames of reference and how things look from one *frame of reference * to another... then you are incapable of understanding the existential reality of any and all things *as they are* regardless of relative relationships. Not only do all things exist "on their own" but the space or distance between them also exists independent of observation/measurement, varying only with relative movement between them... objectively speaking! Relative perspectives do not change the actual distances between things.

 

Until you understand this you must continue to believe "It's all relative" and simply ignore the existential reality of cosmos and things which constitute cosmos and their spacial relationships in the real cosmos regardless of observational point of view.

 

In fact you are the one here insisting that relativity is the *absolute reality* describing the cosmos. I hope you can see the irony in this!

 

To my direct answers to your persistent "clock" line of questioning, rather than tell me how you think I am wrong, you go back to me being stuck in earth-frame-of-reference, saying:

Do you see what you did? You've chosen clocks on earth (and rulers on earth) to describe you cosmic reference frame. You've given priority to our human perspective here on earth.

 

What I did was tell the truth about the inability of clocks to travel faster than light, give the actual elapsed time of light traveling the actual (objective) sun-to-earth distance , and admit that I don't know how fast a clock can be made to travel or how slowly it can be made to "tick." ... Whereas *if* it can go fast enough and tick slowly enough, then "yes" it would register less than a minute for the journey. OK?

 

I believe that all the sophisticated measures of earth to sun distance (and to other planets) are accurate descriptions of the actual distance, as given in light minutes or whatever units of distance regardless of the "frame of reference", tho of course the equations of relativity must be used to correct for measurement error from different frames of reference. You have never yet understood what I just said, tho I've said it many different ways and in many different contexts.

 

I am, therefore, ready to give it up... "it" being communication with you on "relativity."

 

Seems to me that you are the one with a myopic "frame of reference" here, but obviously our communication has utterly failed. Sorry.

 

Michael

[freeztar]

Seems to me that you are the one with a myopic "frame of reference" here, but obviously our communication has utterly failed. Sorry.

And you wonder why people are reluctant to discuss this subject with you? :)

[Michael Mooney]

Pyrotex:

Michael,

I'm sorry, but it is so damned hard to understand what you are really getting at. I seriously wonder if you really know what "ontological" really means, or if you've just been to a lot of Forum Seminars lately.

 

Actually I have a dual masters in both philosophy and psychology. I have no argument with the Wiki definition and exposition:

"In philosophy, ontology (from the Greek , genitive : of being (part. of : to be) and -λογία: science, study, theory) is the most fundamental branch of metaphysics. Ontology is the study of being or existence and its basic categories and relationships."

Wiki encyclopedia:

"... ontology deals with questions concerning what entities exist or can be said to exist."

 

You continue (my reply in italics context proximity):

But here is my best try at rephrasing what you may be asking:

 

Can we say that between two points in the Universe, A and B, ignoring all frames of reference, there "exists" a unique minimum distance between them that can be said to be the "actual" distance between them, irrespective of any observers, or even in the total absence of observers?

 

To be clear, the distance between any two points varies with their movement relative to each other, but this distance remains unaffected by "observation" or lack therof.

 

There IS an answer to this question, but I'm not sure you're gonna like it.

 

Yes, Michael, if that's what you're trying to say, then you can say that.

And if you're charming and persuasive enough, you can even get us to agree with you.

 

Is there a special rule where moderators can be rude and offensive and other contributors can't.... or did you forget the tongue-in-cheek emoticon? :)... or a wink.

 

But there is NOTHING MORE you can say about points A or B or the distance between them. Nothing. No assumptions, no conclusions. You can't use that distance as evidence for anything else. Without any observations at all, the points themselves and any distance there may be between them lies in the realm of idle speculation. Or philosophy.

 

Actually, I can say quite a lot about the ontology of "spacetime" by arguing with the non-Euclidean assumptions upon which relativity is based while still recognizing the improved sophistication and accuracy of the math. This without reifying space into something which can curve, expand, etc or reifying time into something other than event duration (whether measured or not)... certainly not an event itself which speeds up and slows down.

 

I would be happy if "spacetime" were explicitly explained (in academia) as a metaphor or visual aid for understanding the effects of gravity... without making it into a malleable (curving, bending, wrinkling, expanding) "fabric" ... an actual existential entity, that it has become.

Then there is "Occam's Razor." The "fine fabric" of the "Emporer's New Clothes" is then transparent as noot an actual entity, cut away as in non-existent,... and science is the better, and the more honest for it.

 

But you can say anything you like about their "independent existence".

Thanks. You are too kind. ;)

 

"Points A and B. They're Out There!"

Yup. And in deep contemplation the illusory boundary between "out there" and "in here" is transcended and one can actually see "what it is." I can not only say this, but it is true for me. I realize not for you. And I feel no need to try to convince you of what you have not directly experienced. I am a avid advocate of healthy skepticism, as long as it doesn't become closed minded in certainty of ones "beliefs."

 

Thanks for the conversation.

PS: Give up on the "shortest distance between two points" challenge? If so, non-Euclidean cosmology is make-believe... as in "lets pretend that an arc of a circle/sphere is the shortest distance between two points on the sphere... and build a cosmology out of it."

Michael

[Pyrotex]

...Actually I have a dual masters in both philosophy and psychology. I have no argument with the Wiki definition and exposition...And in deep contemplation the illusory boundary between "out there" and "in here" is transcended and one can actually see "what it is." I can not only say this, but it is true for me. ...Thanks for the conversation....

Michael,

okay, you have an "ontology" and you know how to use it. ;)

 

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? :) WHO is it that says that observing causes distances to change? :hihi:

 

Oh, and what you call "transcending" is just an ordinary act of imagination. I do that all the time. :)

 

But transcending does not change the truth "out there"; it can only change the truth "in here". ;)

[Michael Mooney]

MM:

Seems to me that you (Modest) are the one with a myopic "frame of reference" here, but obviously our communication has utterly failed. Sorry.

Freeztar:

And you wonder why people are reluctant to discuss this subject with you?

 

Psych 101: "It seems to me" owns the perception without claiming "this is how you are." The context supports the perception: Modest is all about local frame of reference (metaphor: "myopic")...clearly not even considering the big picture (metaphor: "far-sighted.) Clearly our communication has failed. As near to factual as these miscommunication gets . I expressed honest regret.

With what part of the above do you have a problem?

 

(Also see Pyrotex's insinuation that I got my understanding of ontology out of a fortune cookie, or the less-than-respectable equivalent thereof. Rude? I dunno. Maybe there is a different standard of license for that among you moderators??

Michael

[Michael Mooney]

Pyrotex:

Michael,

okay, you have an "ontology" and you know how to use it.

Cute!

 

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.

 

OK... Modest is always saying "for (this or that) observer... the distance, as measured from (such and such) is..." How is this *not* making distance relative to observer position/velocity/measurement etc??

 

Nobody is saying that it can.

 

Relativity does not say it can.

 

So, WHO are you arguing against? WHO is it that says that observing causes distances to change?

 

Oh, and what you call "transcending" is just an ordinary act of imagination. I do that all the time.

 

Oh, and you can stick to a scientific materialism worldview 'til hell freezes over (that's a metaphor too :hihi: in denial of the validity of mystic vision... but that don't mean you are right and all mystics are not only wrong but deluded.

Maybe if you spent 40 years, an hour a day sitting in stillness beyond mind chatter and scientific conceptualization .... Nah!... :)

 

But transcending does not change the truth "out there"; it can only change the truth "in here".

Guess you missed how the difference is ultimately an illusion. Again... ;)

 

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?"

(Maybe one question at a time would serve better understanding.)

Michael

[watcher]

Clever words. But what do they mean?

it means i favored wave theory over particle theory.

What value added do they bring to the conversation, "What is Spacetime?".

as you have cited earlier. the title of the thread should not be what is spacetime but the ontology of space and time. because spacetime interval has a very specific meaning in relativity and the OP's constant referral to "what is" suggests that he's interested not in the technical meaning of the word but its origination.

 

Any philosophy is worthless, until you can "ground it" in some aspect of observable Reality.

i agree. the so called "cosmic perspective" is a privileged one. as i have mentioned twice already to the OP, it is outside the scope of science.

but the again, newton was deep in metaphysics, most founding fathers of QM were mystics, i suspect einstein was one although none had attributed their great intuitive insights to mysticism. none the less, they were inspite of being scientists

 

P.S.: the shortest distance between ANY two points in a Space of ANY number of dimensions is defined as a "geodesic". If the Space is Cartesian, then ALL geodesics are straight lines.

or the geodesic of a straight line in hyperspace is a complex number.

a straight line is an artifact of geometry.

it is only an axiomatic postulate in euclidean geometry.

the fact that non-euclid space is as effective as well and with a wider scope of applicability implies that the euclidean postulate of straight lines between points are not absolute .

 

Stop listening to your gut. You're just hungry. Eat a cookie. :)

:)

[Erasmus00]

Michael, maybe modests and my point is best explained as follows- IF light speed is constant for all observers, there exists no method of measuring distance that returns the same answer for all observers. How then do you define distance? You make the claim that Earth is 8 light minutes from the Sun, but how was that measured? As you've indicated this distance can be determined by parallax. Would it surprise you if you tried to use the same technique to find the Earth/Sun distance, but you did the (now two) measurements on Mercury you would get a slightly different answer? If you did the same measurement from Earth but on a moving rocket ship, and get a different answer?

 

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

 

Onward and upward- you have claimed the shortest distance between two points is a straight line, because thats what you can visualize. IF however, we were ants living on a beachball, we'd disagree. So, let me ask- can you prove that the shortest distance between two points is a straight line? i.e. lets differentiate between what we can see and what we know is true.

[modest]

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

If nothing in the universe existed relative to anything else then the cosmos would cease to exist in any meaningful way. Beyond that, your use of the word objective continues to confuse me.

 

I can't say it any more plainly than, "in and of itself independent of relative observational perspectives?" What part of that do you not understand?

 

So you either can not or will not engage in my "thought experiment" in which cosmos exists, " in and of itself independent of relative observational perspectives?"

 

Well, now... I'm just pointing out the problems of implementing what you're describing. The problems are real regardless of my affinity for them... ya know?

 

Oddly enough, there is a way to steer clear of these problems, and, in fact, use them to implement a philosophy of space and time. It's a philosophy that not only avoids all these pesky relative notions of space and time—but explains them. Rather than having to disregard laws of physics in this philosophy, it would actually explain their foundation.

 

I think you know what I'm talking about.... "spacetime" :Alien:

 

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. There are three spatial dimensions and one temporal dimension combined in a single manifold. A point in this setting isn't just a location (in space), it is an event (in spacetime).

 

This system was invented by Hermann Minkowski about a hundred years ago who introduced it with this description:

 

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

 

A point of space at a point of time, that is, a system of values, x, y, x, t, I will call a world-point. The multiplicity of all thinkable x, y, x, t systems of values we will christen the world... Not to leave a yawning void anywhere, we will imagine that everywhere and everywhen there is something perceptible. To avoid saying "matter" or "electricity" I will use for this something the word "substance". We fix our attention on the substantial point which is at the world-point x, y, x, t, and imagine that we are able to recognize this substantial point at any other time. Let the variations dx, dy, dz of the space co-ordinates of this substantial point correspond to a time element dt. Then we obtain, as an image, so to speak, of the everlasting career of the substantial point, a curve in the world, a world-line, the points of which can be referred unequivocally to the parameter t from - oo to + oo. The whole universe is seen to resolve itself into similar world-lines, and I would fain anticipate myself by saying that in my opinion physical laws might find their most perfect expression as reciprocal relations between these world-lines.

 

Spacetime Society - Minkowski

 

And it worked... it worked beautifully. What you are looking for in your transcendent vision of the universe may-well be the very thing you're railing against—spacetime. It's a way to lay the whole universe out in front of you in a single coherent expression.

 

I'm not going to spend pages and pages of posts trying to sell you on the concept, Michael. But, it's something to consider...

 

~modest

[jedaisoul]

So, again I beg the indulgence of all scientists here to engage in a *thought experiment* in which there *is* a transcendental, cosmic perspective independent of all local frames of reference. In this experiment, cosmos exists *as it is* regardless of local observations of it. (The latter *is* the realm of relativity, with which I am not arguing... not have I ever.)

 

Then... all of the "standard measures of distance", as in my list for this solar system above, are actual, objective distances. Regardless of point of view (from earth, sun or other planets.) The "measuring rod" of lightspeed as applied to all above distances (say, by a virtual, transcendental, cosmic observer) will remain exactly as listed above. To clarify... I am not speaking relativistically of the "measuring rod of lightspeed" as objects are observed from various local perspectives.... (Please indulge the experiment)... but the *actual* distance light travels in a given precise time interval between each of the bodies in the list above... independent of who sees what from where and when relative to each observer.

Michael, I'd like to investigate how far you have examined this "transcendental, cosmic perspective independent of all local frames of reference". Firstly, I would assume from your comments above that the answer to both the following questions is "yes", but I just want to be sure:

1. Do you agree that the velocity of light is finite?

2. Do you agree that the velocity of light is fixed?

 

However, a velocity is meaningless if it is not with respect TO something. So we may talk of a car travelling at 50 m.p.h., but that is implicitly with respect to the road (which is taken to be stationary). Similarly, we may talk about an aircraft flying at 500 m.p.h., but in this case it could be 500 m.p.h. with respect to the air around it (the air speed), or with respect to the ground beneath it (the ground speed). Both are legitimate measures of an aircraft's speed, and they can differ by more than 100 m.p.h.

 

So, what, in your "transcendental, cosmic perspective", is the velocity of light fixed with respect to?

 

Note: This is not an idle, nor a trick, question. I genuinely want to know if you have thought this through.

 

P.S. If you have already answered these questions then I apologise, and would be grateful if you could point out where...

[Michael Mooney]

jedaisoul (my replies in bold):

Michael, I'd like to investigate how far you have examined this "transcendental, cosmic perspective independent of all local frames of reference". Firstly, I would assume from your comments above that the answer to both the following questions is "yes", but I just want to be sure:

1. Do you agree that the velocity of light is finite? Yes. Precisely 299,792,458 meters per second.

2. Do you agree that the velocity of light is fixed? Yes. Ditto. I've acknowledged SR dozens of times in this thread.

 

However, a velocity is meaningless if it is not with respect TO something.

 

I disagree. Whether your units are meters per second, miles per hour or "earth diameters per" whatever, light travels at constant velocity anywhere in the universe regardless of "frame of reference."

So we may talk of a car travelling at 50 m.p.h., but that is implicitly with respect to the road (which is taken to be stationary). Similarly, we may talk about an aircraft flying at 500 m.p.h., but in this case it could be 500 m.p.h. with respect to the air around it (the air speed), or with respect to the ground beneath it (the ground speed). Both are legitimate measures of an aircraft's speed, and they can differ by more than 100 m.p.h.

 

I fly an airplane occasionally and am quite familiar with the above. Of course a car or plane has a velocity relative to the center of the galaxy too, but we can take that to be the same as our solar system's velocity rel. to galactic center. But beyond such specific designations of "relative to what", a mile is the same distance whether measured "down the road" as usual or that same distance in the void of space beyond all cosmic content. Of course this would be strictly theoretical, but when you say miles per hour it does in fact designate an exact and unchanging distance traveled during an exact and unchanging period of time, no matter where the car, plane or photon is doing the traveling or relative to what.

 

So, what, in your "transcendental, cosmic perspective", is the velocity of light fixed with respect to?

Again, it travels at a fixed velocity of 299,792,458 meters per second no matter what its source, the direction its heading or what it goes past on the way.... or what any observer sees from whatever perspective.

 

Note: This is not an idle, nor a trick, question. I genuinely want to know if you have thought this through.

Yes. Time does not slow down. Clocks do. Space does not expand or contract, tho all cosmic "stuff" is expanding outward into space, and, I believe, will eventually implode or contract back to whence it came. Distance between objects varies, of course as they move relative to each other. But a mile is a mile no matter what planet you are on... or in deep empty space. Same for a light minute or year... a universal standard for distance... the same everywhere.

 

P.S. If you have already answered these questions then I apologise, and would be grateful if you could point out where...

 

Actually I've answered these questions many times in many contexts, but I don't mind saying it again. Who knows when I will say it just right for mutual understanding in a given context?

 

Michael

[Michael Mooney]

Modest,

Maybe if I just keep repeating the questions you will eventually answer them directly. (Maybe not.)

Do you or do you not believe that cosmos exists objectively in and of itself independent of relative observational perspectives? (I still didn't get what part of "in and of itself... "etc., you don't understand.)

 

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

(See my recent unanswered debate on that, where I poked a rod through a globe to connect two cities on the sphere with the shortest line... which is not the surface arc between them.

 

I've told you quite a few times, from the very beginning of this thread, that I have a thorough understanding of Einstein/Minkowski's non-Euclidean basis of "curved spacetime." Still do.

But this thread challenges anyone and everyone here to show how and why Euclidean space is discarded and what exactly it is that is 'curved' other than a visual graphic for understanding the effects of gravity. Of course the math of relativity works better for predicting gravitational effects than Newtonian physics. (I take it that is your point... yet again! above.)

Yet this doesn't make the metaphor, graphic, (whatever) of "curvature" into an existential entity, an actual medium.

 

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.

 

But then, Ive said this dozens of times already, to no avail. That's why I gave up on communication with you.

 

Will anyone here examine the transition away from Euclidean geometry with me *without the preconceived absolute belief that the math proves non-Euclidean geometry to be true and Euclidean false?*

The argument that ants on a beach ball "think" it's a flat surface is totally bogus. Humans thought the same of the Earth, and look how wrong the "flat earth" concept was!

 

Anyone??

Michael

[Michael Mooney]

Pyrotex,

I would very much appreciate your clarification of this exchange:

You:

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.

Me:

OK... Modest is always saying "for (this or that) observer... the distance, as measured from (such and such) is..." How is this *not* making distance relative to observer position/velocity/measurement etc??

 

Michael

[Michael Mooney]

Erasmus,

See my post on "distance" above. Ditto here.

But you challenged:

So, let me ask- can you prove that the shortest distance between two points is a straight line? i.e. lets differentiate between what we can see and what we know is true.

 

Well, I could put two dots on paper and ask a thousand intelligent people (and maybe a few morons who understand the concept)... What is the shortest distance between the dots? Would a total consensus on the obvious straight line be considered "proof." Maybe not, but....

 

Oh, then I could bend the paper into an arc and ask the same question... with a long needle through both points. How many will choose the arc. None I think.

 

Michael

[Erasmus00]

I've told you quite a few times, from the very beginning of this thread, that I have a thorough understanding of Einstein/Minkowski's non-Euclidean basis of "curved spacetime." Still do.

 

Michael, put try to examine things from another perspective. Imagine someone shows up, claims repeatedly to have studied arithmetic, but then makes the claim 2+2=5. Try to open yourself to the idea that you have misunderstood something in your studies.

 

Will anyone here examine the transition away from Euclidean geometry with me *without the preconceived absolute belief that the math proves non-Euclidean geometry to be true and Euclidean false?*

 

I am attempting. Once again though, you have suggested math "proves non-Euclidean geometry to be true." This is not the case- math shows that non-Euclidean geometry COULD be true. So could Euclidean geometry.

 

The argument that ants on a beach ball "think" it's a flat surface is totally bogus. Humans thought the same of the Earth, and look how wrong the "flat earth" concept was!

 

Lets start from this idea and explore. Imagine you are 2 dimensional geometry geometry, and you use the surface of the Earth for your drawing board, using the area around your house (your local neighborhood) to develop your ideas. You take out a piece of chalk, and you use draw some figures, and you prove that the angles of a triangle always total to exactly 180 degrees.

 

Now, at student comes along and says "lets check this" and they use a very accurate compass and measure that the angles of a triangle are actually slightly greater than 180 degrees. After a many more measurements, the student learns that the bigger the triangle the bigger the deviation from 180.

 

"How can this be?", you say. "I proved quite generally that a triangle always has 180 degrees?" At this point, the clever student says "you assumed you were working on something flat, but it turns out the surface isn't flat. In fact, if we make very accurate measurements of triangles, we can figure out the surface we live on." After taking this very accurate measurements, our student determines we live on a sphere, and even knows its radius.

 

Now, lets extend this parable to three dimensions. We cannot picture a 3 dimensional curved space (though we can picture a 2d one, which is why I used the ants on a beach ball example). We must never make the unfounded assumption that what we can visualize is all that can exist.

 

Like the character above, we make the untested assumption that we live in a euclidean space, because thats what we evolved to deal with. In our local neighborhood (around Earth) everything looks like its Euclidean.

 

Now, imagine what that clever student might say. "How do we really know until we make a really big triangle and measure some angles?" So the question of what kind of geometry (Euclidean, non-Euclidean) is an experimental question. One that can be determined by measuring (for instance) the angles of a very large triangle.

 

Modern science cannot actually do this experiment, but there are equivalent experiments, and they have been done.

 

Erasmus,

See my post on "distance" above. Ditto here.

 

Michael, you defined distance via parallax determination in your posts on the Earth, Sun distance. I can calculate for you (if you like) or you can take my word that parallax gives different answers depending on where you are, and how you are moving.

 

Imagine sending out three groups to measure the distance between the Earth and the Sun using parallax. One group goes to Mercury and does the measurement. One group stays on Earth and does the measurement. One goes and lands on Halley's comet and does the measurement. All three come back with different numbers. Which group gives your correct distance?

 

What is the shortest distance between the dots? Would a total consensus on the obvious straight line be considered "proof." Maybe not, but....

 

Consensus doesn't equal truth. There are probably hundreds of questions both qualitative and quantitative on which the consensus will indicate the wrong answer.