What is "spacetime" really?

[modest]

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:

 

The second diagram above follows that example exactly.

 

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.

 

The two planets above (on which the two events happen) are mutually at rest.

 

If you're having trouble interpreting the diagram this site might help.

 

~modest

[jedaisoul]

The second diagram above follows that example exactly. The two planets above (on which the two events happen) are mutually at rest. If you're having trouble interpreting the diagram this site might help.

Modest, I'm not having any problem understanding the metric. Your first example is of a spacetime interval of 1.2, not zero. Your second example requires Tom to travel at the velocity of light. Therefore your argument fails because the first is irrelevant, and the second impossible.

 

I want you to deal philosophically with the zero interval and describe how it reflects how any material object experiences reality. It doesn't. You even said:

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.

That's all I'm claiming. The zero interval does not describe how material objects experience reality.

[modest]

Measuring a light-like interval requires traveling at the speed of light. Material objects can't go the speed of light. Your objection—that it requires photons to actually measure a zero interval while massive objects cannot is not a problem for the metric.

 

It is a rule the universe imposes on massive particles!

 

The metric works for both massive and massless particles. It gives the exact answer we expect. How could that possibly be a problem?

 

You'll have to be more specific, because noting that the metric also works for light isn't really an objection.

 

~modest

[Michael Mooney]

jedaisoul,

I thought I understood and agreed with you, but after reading the example which you reiterated above, I have a question. It could be the key to my understanding how a "spacetime interval" differers from "real" space and elapsed time between two events.

 

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.

 

If there are 600,000 kilometers (two light seconds of distance) between the observers and two seconds of elapsed time between their claps, how can your latter paragraph be true? It still takes two seconds for a photon to travel the distance *between the two* (not in the same place), and, if two seconds elapse between claps, they still don't happen at the same time.

So what can a " zero spacetime interval between these two events" possibly mean in the real world?

If you can make sense of this for me I would greatly appreciate it. Thanks.

(Modest's math is Greek to me.)

Michael

[Michael Mooney]

Continuing with quotes and my commentaries on The Ontology and Cosmology of Non-Euclidean Geometry as above.

 

...Thus the surface of a sphere is the classic model of a two-dimensional, positively curved Riemannian space; but while great circles are the straight lines (geodesics) according to the intrinsic properties of that surface, we see the surface as itself curved into the third dimension of Euclidean space.

 

So the mind-game afoot in the transition from Euclidean to Riemannian spherically curved space is that we train our minds to call the curved lines on a given arc of a hypothetical sphere "straight lines"..."according to the intrinsic properties of that surface." Neat trick! Re-define "straight" by creating a virtual reality of space itself as curved, so that there are no longer, in this new virtual reality, any such things as straight lines as we once knew them in the *actual* reality of the real world/cosmos. (This is the error of reification, plain and simple, and modern cosmology, based on non-Euclidean "space" has fallen victim to the error with hardly anyone of respected scientific stature noticing. (Seems the mystique of the genius of Einstein has created a dogma in science where free thinking used to belong.)

 

Accepting positively curved spaces means that those [Euclidean] axioms must be rejected.

No, thanks.

...The biggest problem is with Lobachevskian space. A saddle shaped surface is a Lobachevskian space at the center of the saddle, but a true Lobachevskian space does not have a center. Other Lobachevskian models distort shapes and sizes.

Same deal but more complex with "space" taking on a parabolic shape. I'll skip the critique as the same basic objection applies... space becoming some-thing with "shape" rather than the stuff *in space* "taking shape."

 

This raises two questions: 1) what can we spatially visualize? (a question of psychology) And 2) what can exist in reality? (a question of ontology). We cannot visualize any true Lobachevskian spaces or any non-Euclidean spaces at all with more than two dimensions--or any spaces at all with more than three dimensions. Also we can only visualize a positively curved surface if this is embedded in a Euclidean volume with an explicit extrinsic curvature. "Curvature" was thus a natural term for intrinsic properties because there always was extrinsic curvature for any model that could be visualized. Why are there these limits on what we can visualize? Why is our visual imagination confined to three Euclidean dimensions? It is now common to say that computer graphics are breaking through these limitations, but such references are always to projections of non-Euclidean or multi-dimensional spaces onto two dimensional computer screens. Such projections could be done, laboriously, long before computers; but they never produced more, and can produce no more, than flat Euclidean drawings of curves. If such graphics are expected to alter our minds so that we can see things differently, this is no more than a prediction, or a hope, not a fact. And considering that non-Euclidean geometries have been conceived for almost two centuries, the transformation of our imagination seems a bit tardy, however much help computers can now give to it. Mathematicians don't have to worry about these questions of visualization because visualization is not necessary for the analytic formulas that describe the spaces. The formulas gave meaningfulness to non-Euclidean geometry as common sense never could.

 

The above is fundamental to the argument I've been making in this thread. If the "virtual reality" of computer imaging and the mathematical esoterica has taken the place of observation of actual phenomena/objects in the real world/cosmos and made common sense obsolete, then science is the poorer, not the richer for it.

 

This takes us through about a third of the paper, but I see no need to belabor the critique any further. Yet the rest of the paper continues in the same rich vein, and like Modest (thanks again) I highly recommend it for the further edification of the forum on the subject of this thread.

 

Well, just another gem or two:

Just because the math works doesn't mean that we understand what is happening in nature. Every physical theory has a mathematical component and a conceptual component, but these two are often confused. Many speak as though the mathematical component confers understanding,

 

Now we actually have two competing ways of understanding gravity, either through Einstein's geometrical method or through the interaction of virtual particles in quantum mechanics.

 

I've mentioned the latter a few times in this thread... but no comment. Beyond the above, I've also affirmed that Einstein's equations, which certainly fine-tuned gravitational predictions, do not require and actual "fabric, spacetime" to work, yet the latter has been thoroughly reified and codified into the scientific equivalent of a religious dogma.

 

Finally and in summary:

Nevertheless, there is often still a kind of deliberate know-nothing-ism that the mathematics is the explanation. It isn't. Instead, each theory contains a conceptual interpretation that assigns meaning to its mathematical expressions. In non-Euclidean geometry and its application by Einstein, the most important conceptual question is over the meaning of "curvature" and the ontological status of the dimensions of space, time, or whatever. The most important point is that the ontological status of the dimensions involved with the distinction between intrinsic and extrinsic curvature is a question entirely separate from the mathematics.

 

Whew! This should be food for thought and further dialogue here.

 

Michael

[Erasmus00]

Michael, I can only recommend to you (and anyone else in this thread) that if you REALLY want to understand the theory well enough to discuss the ontological implications, it helps very much to pursue some study of the mathematics involved. Its challenging, but very much worth pursuing if you are seriously interested in understanding something of the reality involved.

 

And, to respond to the comments about visualizing curved geometries, etc: why should reality be visualizable? We evolved to handle very specific situations, and very specific length scales. Neither quantum theory nor relativity are visualizable, but these theories apply to extremes largely not found in the environment that produced humans.

-Will

[Michael Mooney]

Michael, I can only recommend to you (and anyone else in this thread) that if you REALLY want to understand the theory well enough to discuss the ontological implications, it helps very much to pursue some study of the mathematics involved. Its challenging, but very much worth pursuing if you are seriously interested in understanding something of the reality involved.

 

And, to respond to the comments about visualizing curved geometries, etc: why should reality be visualizable? We evolved to handle very specific situations, and very specific length scales. Neither quantum theory nor relativity are visualizable, but these theories apply to extremes largely not found in the environment that produced humans.

-Will

Will,

I really do understand the theory well enough to discuss the ontological implications of the "reality" or lack of it in the "spacetime" concept of curved space and distorted time. Epistemology, with which I am very familiar, is *the most serious study* of the "reality involved" not only in the concepts which are the subject of this thread and the paper reviewed above but of how we know what we know in all fields of study. In this context, math is a very specific tool of knowledge and it *must* have referents in the "real world" to have scientific relevance. Epistemology is not just about "visualizable reality" but how we know what is *actually real.*

Again:

This raises two questions: 1) what can we spatially visualize? (a question of psychology) And 2) what can exist in reality? (a question of ontology).

You have addresses none of the the very astute comments on the limits of math as expressed in the quotes above. One must wonder if you even read them.

Here again is are two samples:

Just because the math works doesn't mean that we understand what is happening in nature. Every physical theory has a mathematical component and a conceptual component, but these two are often confused. Many speak as though the mathematical component confers understanding,

Nevertheless, there is often still a kind of deliberate know-nothing-ism that the mathematics is the explanation. It isn't. Instead, each theory contains a conceptual interpretation that assigns meaning to its mathematical expressions. In non-Euclidean geometry and its application by Einstein, the most important conceptual question is over the meaning of "curvature" and the ontological status of the dimensions of space, time, or whatever. The most important point is that the ontological status of the dimensions involved with the distinction between intrinsic and extrinsic curvature is a question entirely separate from the mathematics.

 

I am not a matematician, nor do I aspire to become one. Yet you say:

"

Its [the math]] challenging, but very much worth pursuing if you are seriously interested in understanding something of the reality involved."

It is as if you equate the matematics with the reality... see qoutes above.

 

You dismiss how serious I am about this subject quite off-hand with the above statement and seem the disregard the whole paper, "The Ontology and Cosmology of Non-Euclidean Geometry" and my commentaries on it above in an equally glib and off-hand manner.

 

Your post seems defensive of mathematics while totally ignoring the more "modest" place of math in the overall ontology and epistemoplogy of the subject at hand.

Michael

[modest]

Whew! This should be food for thought and further dialogue here.

 

Michael

 

I thought you'd like it ;)

 

~modest

[jedaisoul]

The metric works for both massive and massless particles. It gives the exact answer we expect. How could that possibly be a problem?

The problem is that your argument rests on only interpreting zero intervals for light, and only interpreting spacelike and timelike intervals for material objects. That is what the metric does. Timelike and spacelike intervals do not exist for light, because space and time do not exist for light. So the question "how does light experience a timelike or spacelike interval?" is meaningless. But zero intervals exist for material objects. So the question "how do material objects experience zero intervals?" is quite legitimate.

 

I have asked "what does Sally experience when an event happens in her vicinity, then a second event happens two light-seconds away from her and two seconds afterwards"? In reply, you have said that the zero interval should not mean that the events are co-located and simultaneous for material objects, but you have not said what it should mean. Please address this point.

 

Sally does not experience the events at the same place and time (which you agree with). From that I deduce that, to Sally, a zero spacetime interval merely means that the spatial interval and time interval have the same magnitude (which you do not agree with). Further, if spatial and time intervals do not cancel for material objects when they are the same, why should they when they are not the same , i.e. for time-like and space-like spacetime intervals? This assumption is based on the fact that timelike and spacelike intervals do cancel for light (which I agree with). But it ignores the evidence that spatial and time intervals do not cancel for material objects, (as is evidenced by what Sally experiences).

 

The fundamental assumption I'm addressing is whether:

• Space and time do not exist for light because the spatial and time intervals cancel, or...
  
• Spatial and time intervals are zero for light because space and time do not exist for light.

If the former is true, then I would suggest that spatial and time intervals should also cancel for material objects, which clearly they do not (at least in the case of a zero interval). Therefore I suggest that the latter is a more reasonable explanation.

[jedaisoul]

If there are 600,000 kilometers (two light seconds of distance) between the observers and two seconds of elapsed time between their claps, how can your latter paragraph be true? It still takes two seconds for a photon to travel the distance *between the two* (not in the same place), and, if two seconds elapse between claps, they still don't happen at the same time.

This is where I have to (partially) agree with modest. Traveling at the veloity of light, time stops and all spatial distances are zero. So the two seconds delay and the two light-seconds distance simply do not exist to light. You need to get your head round that. The universe is a very different place to a photon. Light is emitted by one object and absorbed by another instantaneously and the distance between the objects does not exist (from the photon's perspective). That's part of what modest's maths means, and I have no argument with that.

 

So what can a "zero spacetime interval between these two events" possibly mean in the real world?

That's what I've been trying to describe. Try reading #94 above, and let me know if you have any specific questions with what I've put there...

[jedaisoul]

Michael, I can only recommend to you (and anyone else in this thread) that if you REALLY want to understand the theory well enough to discuss the ontological implications, it helps very much to pursue some study of the mathematics involved. Its challenging, but very much worth pursuing if you are seriously interested in understanding something of the reality involved.

I agree that it is necessary to be able to understand Pythagorean relationships, and the way that spacelike and timelike intervals are combined in the spacetime interval. However, I question whether that enables you to understand the reality involved. It only enables you to understand the theory.

[Michael Mooney]

jediasoul,

Thanks for the specifics in your reply. They give me a clear focus for my inquiry.

 

From post 94:

Timelike and spacelike intervals do not exist for light, because space and time do not exist for light.

 

And from your last post to me:

Traveling at the veloity of light, time stops and all spatial distances are zero. So the two seconds delay and the two light-seconds distance simply do not exist to light. You need to get your head round that. The universe is a very different place to a photon. Light is emitted by one object and absorbed by another instantaneously and the distance between the objects does not exist...

 

Since elapsed time describes actual duration of specifically designated events or "travel time" and space is actual distance between actual things (albeit possibly "empty space"), what is the ontological meaning of a special "reality" for photons/light such that time and space "do not exist *for light*"

 

In direct contradiction of your last statement above, for instance, light emitted from the sun requires 8+ minutes to reach and be absorbed by earth.This is an objective fact. How is the above "instantaneous" "for light?"

 

Any reasonable explanation would help me "get my head around" how space and time don't exist "for light" (as if it creates a special reality of its own.

Thanks.

Micharl

[modest]

The problem is that your argument rests on only interpreting zero intervals for light, and only interpreting spacelike and timelike intervals for material objects.

This is not true. The metric works perfectly well for “interpreting” a zero interval for a massive particle.

That is what the metric does. Timelike and spacelike intervals do not exist for light, because space and time do not exist for light. So the question "how does light experience a timelike or spacelike interval?" is meaningless. But zero intervals exist for material objects. So the question "how do material objects experience zero intervals?" is quite legitimate.

Massive objects can’t ‘experience’ a zero interval. Massless objects can’t ‘experience’ space-like or time-like intervals. Neither is more or less meaningless from the standpoint of the other. From our standpoint a zero interval seems a bit odd. From light’s perspective, a positive or negative interval would seem a bit odd.

I have asked "what does Sally experience when an event happens in her vicinity, then a second event happens two light-seconds away from her and two seconds afterwards"?

She experiences one event followed by two seconds of proper time.

In reply, you have said that the zero interval should not mean that the events are co-located and simultaneous for material objects, but you have not said what it should mean. Please address this point.

It means there’s zero spacetime distance between an event near Sally 2 seconds in her past and an event 2 light-seconds from Sally in her present. Anything (e.g. light or other gauge bosons) that travel this path will find its distance to be zero.

 

Sally cannot directly measure this distance nor should she be able to according to the metric. Sally’s clock is measuring time on earth. The second event is not on earth. Her measuring tape can determine the distance between earth (in her now) and the other planet (in her now). But, at least one of those events are not in her now. In other words, those two events are neither parallel with her t or her x axis.

 

For two events to be simultaneous to Sally they would need to be parallel with her x axis. For them to be collocated they would be parallel with her t axis. This is not the case in this example. We shouldn’t then expect the change in x or change in t to be equal to the value of the interval. Minkowski’s geometry is no different from Euclid’s in this respect.

Sally does not experience the events at the same place and time (which you agree with). From that I deduce that, to Sally, a zero spacetime interval merely means that the spatial interval and time interval have the same magnitude (which you do not agree with).

From Sally’s perspective the time component and space component of a light-like interval are equal. I’ve agreed with that many times. It is a postulate of SR. All inertial frames measure the speed of light at c.

Further, if spatial and time intervals do not cancel for material objects when they are the same, why should they when they are not the same , i.e. for time-like and space-like spacetime intervals?

We know the method works for time-like and space-like intervals because it has been tested via time dilation and length contraction.

This assumption is based on the fact that timelike and spacelike intervals do cancel for light (which I agree with).

Yes, Sally determines that the distance of the path is zero. If light travels the path then it should experience it that way. Her measure of space and her measure of time "cancel" giving the distance between events as zero. This is exactly how the metric should work. She is using the geometry at hand to describe some path that is not her own. The answer she gets describes nature very well.

But it ignores the evidence that spatial and time intervals do not cancel for material objects, (as is evidenced by what Sally experiences).

What you say here is wrong. We keep going in circles to get back to it, but this here is your problem. Nothing Sally measures, experiences, or observes demonstrates that the path length is not zero, or, as you say: they “do not cancel”. You assume incorrectly that when space and time “cancel” for a light-like interval then massive objects should measure zero time and/or zero space between them.

 

Sally is measuring (or experiencing) two sides of a triangle (her dimension of space and her dimension of time). She can only solve the third side (which is some other interval—light-like or not) with some form of geometry. That geometry being Minkowskian means the path length can easily be shorter than either of her two “experiences”.

 

This is true of all intervals. The only time we would expect her experience to equal the interval is when her proper time equals the interval because she’s intersecting both events or when her proper length equals the interval because the events are simultaneous to her. Neither of those apply for this example. So, we cannot and should not expect what you assume.

The fundamental assumption I'm addressing is whether:

• Space and time do not exist for light because the spatial and time intervals cancel, or...
  
• Spatial and time intervals are zero for light because space and time do not exist for light.

If the former is true, then I would suggest that spatial and time intervals should also cancel for material objects,

I can safely assume you mean massive objects should measure zero space and/or time of a light-like interval, that they should judge collocation and simultaneity for an interval 45 degrees to either of their axes. The metric doesn't want that. If that were true, the metric would be broken. Sally measures/experiences exactly what she's supposed to and light experiences just what it's supposed to according to their two spacetime paths. In no way is anything unusual happening in this example.

 

~modest

[modest]

In direct contradiction of your last statement above, for instance, light emitted from the sun requires 8+ minutes to reach and be absorbed by earth.This is an objective fact. How is the above "instantaneous" "for light?"

 

If you went to the sun in a spaceship going 3/4 the speed of light, it would take you 5.3 minutes (from your perspective). If you traveled at 9/10 the speed of light, it would take you 3.5 minutes. If you went .999 times the speed of light, it would take you a third of a minute.

 

The closer you get to the speed of light, the closer your time gets to zero for you to travel the distance. A person could (overcoming seemingly insurmountable practical problems) visit the center of the galaxy and return to earth only aging a second. This is time dilation.

 

Photons actually do get to go the speed of light, their time dilation is infinite, they do not experience the passage of time. Check out:

 

6191

 

~modest

[jedaisoul]

Since elapsed time describes actual duration of specifically designated events or "travel time" and space is actual distance between actual things (albeit possibly "empty space"), what is the ontological meaning of a special "reality" for photons/light such that time and space "do not exist *for light*"

 

In direct contradiction of your last statement above, for instance, light emitted from the sun requires 8+ minutes to reach and be absorbed by earth.This is an objective fact. How is the above "instantaneous" "for light?"

 

Any reasonable explanation would help me "get my head around" how space and time don't exist "for light" (as if it creates a special reality of its own.

The idea in relativity is not that light "creates a special reality of it's own", but that the effect is proportional to relative velocity. If we were travelling at a significant proportion of the velocity of light, say more than one tenth (i.e. 30,000 kilometers per second), then the time dilation and spatial contraction would be apparent to us. It's just light is at one extreme of the scale (very fast), and we are at the other extreme (very slow).

 

So there is no contradiction in stating that light takes 8+ minutes to travel from the sun to the Earth (from our perspective), but travels instantaneously (from the light's perpsective). There is no absolute time in relativity. Everything, including time, is relative. Hence the nature of spacetime. It's non-Euclidean.

[jedaisoul]

This is not true. The metric works perfectly well for “interpreting” a zero interval for a massive particle.

 

Massive objects can’t ‘experience’ a zero interval. Massless objects can’t ‘experience’ space-like or time-like intervals. Neither is more or less meaningless from the standpoint of the other. From our standpoint a zero interval seems a bit odd. From light’s perspective, a positive or negative interval would seem a bit odd.

I have to admire your persistence, but you are not correct in this. I agree that massless objects cannot experience space-like and time-like intervals, because space and time do not exist to massless objects. But we experience space and time, so we can experience zero intervals. So what does Sally experience?

 

She experiences one event followed by two seconds of proper time.

True, as far as it goes, but incomplete. What Sally experiences is event A then after 2 seconds event C happens. She does not directly experience that, but we know that it is true because, if the event C was a flash of light, after a further 2 seconds she would see it. Knowing that the planet is 2 light-seconds distant, she deduces that event C happened 2 seconds after event A. That is what she experiences. And it illustrates that the 2 second delay between events A and C is not cancelled by the 2 light-seconds distance. It is real. And the effects of the intervals add in the overall 4 second delay that Sally experiences.

 

So if the time-like and space-like components of the zero interval do not cancel for Sally in this example (where they are the same), why should they cancel when they are not the same?

 

P.S. Just quoting the accepted interpretation to me will not answer this. I know the accepted interpretation that zero intervals cancel. That is an assumption based on the fact that they do cancel for light (or rather are both zero). You have to deal conceptually with my argument and (if you can) show where it is wrong. We are discussing "what is spacetime really?". I suggest that this is an important aspect of the nature of spacetime. Zero intervals do not cancel for massive objects.

 

So are zero intervals zero for light because the light-like and space-like intervals cancel, or because both are zero anyway (hence there is no need for them to cancel)?

[modest]

What Sally experiences is event A then after 2 seconds event C happens. She does not directly experience that, but we know that it is true because, if the event C was a flash of light, after a further 2 seconds she would see it. Knowing that the planet is 2 light-seconds distant, she deduces that event C happened 2 seconds after event A. That is what she experiences.

 

As I’ve repeatedly shown, this is exactly what the metric demands Sally experience.

 

And it illustrates that the 2 second delay between events A and C is not cancelled by the 2 light-seconds distance.

 

Sally doesn’t (and can't) measure AC. Why do her measurements of AB and BC invalidate AC? You skipped a few steps there—please explain.

 

Zero intervals do not cancel for massive objects.

 

Massive objects don't measure the length of a zero interval.

 

~modest