Block Time vs Q. Indeterminacy

[stglyde]

Block Time in relativity where past, present and future exist all the time seems to be in conflict with quantum indeterminism where the latter states the future is uncertain. So why do physicists still competely believe in Block Time? What is the consensus about this in the physics community at the present time?

 

[pervect]

I don't believe that special relativity necessarily implies block time. Furthermore, I don't think that quantum mechanics implies non-determinism.

For instance, you can find some discussion of quantum determinism on wiki,

http://en.wikipedia.org/w/index.php...60792599#Other_matters_of_quantum_determinism

I wouldn't go so far as to say that the wave function is reality (as the wiki article on quantum determinism discusses), I take the position that it could be and it wouldn't matter. In short, I don't think determinism is a testable theory, it's a non-testable philosohpical issue.

It's really hard to say if this is a "consensus" position or not, but it's mine, and I don'tthink it's terribly uncommon.

 

[ghwellsjr]

Block Time in relativity where past, present and future exist all the time seems to be in conflict with quantum indeterminism where the latter states the future is uncertain. So why do physicists still competely believe in Block Time? What is the consensus about this in the physics community at the present time?

Isn't there an oxymoron going on here?

 

[stglyde]

I don't believe that special relativity necessarily implies block time.

But the lorentz frames and the way they are boosted and lorentz transformation automatically create block time. Block time is the heart and meat of special relativity. How can you create SR without implying block time?

 

[ghwellsjr]

But the lorentz frames and the way they are boosted and lorentz transformation automatically create block time. Block time is the heart and meat of special relativity. How can you create SR without implying block time?

That's a new one on me. That's like saying that since my cell phone has a calendar in it the goes up to the year 2069, then the next 58 years already exist. Maybe you could explain how you arrived at this conclusion because I don't see anything that would suggest block time. Also, maybe you should expand on what you mean by block time, just to make sure we're all on the same page.

 

[stglyde]

That's a new one on me. That's like saying that since my cell phone has a calendar in it the goes up to the year 2069, then the next 58 years already exist. Maybe you could explain how you arrived at this conclusion because I don't see anything that would suggest block time. Also, maybe you should expand on what you mean by block time, just to make sure we're all on the same page.

Block time means the past, present and future are just worldlines which don't flow but already exist. This is how physicists can contemplate how making spacetime loop (like rotating black holes or universe) can entail time travel because you can visit the past.

This is in contrast to old views of space and time where the present exist, the past has happened, and the future is still to come.

 

[stglyde]

That's a new one on me. That's like saying that since my cell phone has a calendar in it the goes up to the year 2069, then the next 58 years already exist. Maybe you could explain how you arrived at this conclusion because I don't see anything that would suggest block time. Also, maybe you should expand on what you mean by block time, just to make sure we're all on the same page.

In addition to the above. Look at the illustration of Block Time by Paul Davies here:

http://www.nikhef.nl/pub/services/biblio/bib_KR/sciam14327034.pdf

 

[PatrickPowers]

Block Time in relativity where past, present and future exist all the time seems to be in conflict with quantum indeterminism where the latter states the future is uncertain. So why do physicists still competely believe in Block Time? What is the consensus about this in the physics community at the present time?

I find block time a useful concept but I don't believe the world is actually like that.

 

[ghwellsjr]

In addition to the above. Look at the illustration of Block Time by Paul Davies here:

http://www.nikhef.nl/pub/services/biblio/bib_KR/sciam14327034.pdf

Thanks for that link. At least now I can see why they call it Block Time.

 

[bobc2]

But the lorentz frames and the way they are boosted and lorentz transformation automatically create block time. Block time is the heart and meat of special relativity. How can you create SR without implying block time?

Well said, stglyde. I think many physicists recoil at the thought of a block universe because some of the implications are quite unwelcome to our thinking. Subjectively, I don't like the implications, but at the same time I have never found a way to objectively discount what you have just stated.

On determinism, one should consider that the 4-dimensional filaments making up the fabric of the 4-dimensional universe do not necesarily have to obey laws of physics at the sub-microscale. In the block universe, filaments are woven into the fabric of the universe (to borrow Brian Greene's language) in a way that manifest physical laws to us observers. The filaments are not positioned along the world lines in response to forces, etc., rather the illusion of forces, masses, etc., are a result of the filament configurations. For whatever reason these filaments are layed out along the 4th dimension in a very special and precise way.

Then there is conscousness and time, about which physics has little to say.

And by the way, ghwellsjr was quite incorrect in implying there was an oxymoron in your earlier statement. A more natural characterization of time than what he probably had in mind is correctly implied in your comments.

 

[nitsuj]

I find block time a useful concept but I don't believe the world is actually like that.

I agree with you.

Doesn't block time come up because we can convert time into the same unit of measure as the other 3Ds? And graphically it's typically represented as time in meters to distance in meters. So graphically how long is a meter?; Very little time.

But in 4D, spatial xyz coordinates already account for position, I don't think time can still be considered a forth distance measurement with 4D space time.

Is the block universe concept considered 2D + 1 time dimension? Otherwise in what sense is a "right now" slice of space 3D?

 

[nitsuj]

And by the way, ghwellsjr was quite incorrect in implying there was an oxymoron in your earlier statement. A more natural characterization of time than what he probably had in mind is correctly implied in your comments.

Yea that was funny.

 

[PeterDonis]

In addition to the above. Look at the illustration of Block Time by Paul Davies here:

http://www.nikhef.nl/pub/services/biblio/bib_KR/sciam14327034.pdf

I see Davies uses the term "block time", but I'm not sure it means what he seems to think it means.

Consider this quote:

For example, during a future manned expedition to Mars, mission controllers back on Earth might say, "I wonder what Commander Jones is doing at Alpha Base now." Looking at their clock and seeing that it was 12:00 P.M. on Mars, their answer might be “Eating lunch.” But an astronaut zooming past Earth at near the speed of light at the same moment could, on looking at his clock, say that the time on Mars was earlier or later than 12:00, depending on his direction of motion. That astronaut’s answer to the question about Commander Jones’s activities would be "Cooking lunch" or "Washing dishes" [see illustration on page 46]. Such mismatches make a mockery of any attempt to confer special status on the present moment, for whose "now" does that moment refer to? If you and I were in relative motion, an event that I might judge to be in the as yet undecided future might for you already exist in the fixed past.

To me, this does not suggest that my "future" already exists; all it suggests is that the question "I wonder what Commander Jones is doing at Alpha Base now" is not well-defined, even though our intuitions suggest that it should be. I can change which event on Commander Jones' worldline corresponds to my "now" by changing my state of motion, but no matter how I change it, I can't bring what Commander Jones is doing "now" into my *causal* future, which is what would be required to say that my future must already exist. No matter how I change my state of motion, whatever Commander Jones is doing "now" will be outside my future light cone. So what he is doing "now" can have no causal effect on what *I* am doing "now", and vice versa. So the question "what is Commander Jones doing now?" is physically meaningless; I can label any event on Jones' worldline that is spacelike separated from me as "what Jones is doing now" and it will make no difference at all to the results of any observation I make or any experiment I run.

However, Davies does bring up a different issue that strikes deeper:

Although we find it convenient to refer to time’s passage in everyday affairs, the notion imparts no new information that cannot be conveyed without it. Consider the following scenario: Alice was hoping for a white Christmas, but when the day came she was disappointed that it only rained; however, she was happy that it snowed the following day. Although this description is replete with tenses and references to time's passage, exactly the same information is conveyed by simply correlating Alice's mental states with dates, in a manner that omits all reference to time passing or the world changing. Thus, the following cumbersome and rather dry catalogue of facts suffices:

December 24: Alice hopes for a white Christmas.
December 25: There is rain. Alice is disappointed.
December 26: There is snow. Alice is happy.

In this description, nothing happens or changes. There are simply states of the world at different dates and associated mental states for Alice.

Julian Barbour has written a number of papers expanding on this kind of thinking:

http://platonia.com/papers.html

However, even this view does not imply that my future "already exists" in the sense of being fixed. All it implies is that time is not something that "flows"; it's just a dimension along which we can assign coordinates to events. It does not require that events with coordinates that we, at this particular point on Earth's worldline, would label as "future" must be "determined" from our viewpoint "now". There can still be quantum indeterminacy; it just shows up as a statistical variation in relationships between types of events, looked at over the entire 4-dimensional continuum.

For example, there might be lots of events, at various different coordinate "locations", that can be described as "spin-up electron going into spin-measuring device oriented left-right", and lots of events at coordinate "locations" very close to the first set that can be described as "electron coming out of the spin-left side of the spin-measuring device" or "electron coming out of the spin-right side of the spin-measuring device". Quantum indeterminacy just means that the two types of "electron coming out" events are randomly associated with the single type of "electron going in" event, with 50-50 odds, if we look at the entire collection of such event pairs over the entire spacetime.

 

[bobc2]

The block universe requires the 4th dimension actually be a spatial dimension. You could not have various 3-D cross-sections required by special relativity without that. The 4th dimension is identified with time because time seems to flow as the observer's consciousness appears to move along his world line (along his rest 4th dimension) at the speed of light.

Let's say everyone is required to move along the interstate from point A to point B at exactly 60 mph. Then, at every mile from point A there is a time marker on the side of the road, i.e., a clock, that reads out the time lapsed from point A. And instead of looking at an odometer, you look at your watch to keep track of time lapsed from point A (no distances are displayed). Now, you've turned the highway (your 3D world line, so to speak) into a time dimension in exactly the same sense that the 4th dimension is regarded as a time dimension.

So, the 4th dimension is a time dimension only in that sense. But, more fundamentally, the 4th dimension is a spatial dimension.

All of the 4-dimensional filaments strung along the 4th dimension that make up objects are just all there. On a macroscale the pattern posses unique forms that allow a description in terms of laws of physics. And from these laws you can predict the future 3-D cross-section organization of the objects. However, you cannot rely on these overall patterns to predict the future 3-D cross-section organization of objects down to the level of individual quark filaments, electron filaments, and photon filaments.

So, the 4-dimensional filaments are all there. You could say that the future is determined, but the rules we physicists have only work for predicting the future on a macro scale. We do not have rules capable of predicting the future of individual elementary particles. We can only predict statistically what to expect of a sizeable group of 4-D elementary particle filaments. And that's not because the filaments have not extended far enough along the 4th dimension; it's just because the filaments down at the sub-micro scale are not layed out with a fixed pattern reflecting the rules recognized at the macro level.

We have the wave functions, but a wave function is not, in this view, an actual object--it is a mathematical description which, when complex conjugate squared, allows you to make statistical predictions about the configuration of some 3-D cross-section of 4-D filaments at some point in the future.

One of the mysteries of the sub-micro patterns is that, even though we don't recognize a specific pattern conforming to specific laws of physicis, the wave functions have a very detailed and specific phase in it's description of the individual 4-D filament shape in 4-dimensional space.

Thus, we have two major mysteries of physics: 1) The many different cross-section views of 4-dimensional space (attended by the constant speed of light) and 2) The double-slit experiment of QM.

 

[PeterDonis]

The block universe requires the 4th dimension actually be a spatial dimension. You could not have various 3-D cross-sections required by special relativity without that.

The fact that the time dimension has the opposite sign in the metric to the three space dimensions indicates that it is not quite the same as a spatial dimension. It is *like* a spatial dimension in some respects (for example, it can be measured in the same units as spatial dimensions by using the speed of light as a conversion factor), but it is not a spatial dimension. It is a dimension of the overall 4-D manifold of spacetime, topologically speaking, which is sufficient to allow 3-D cross-sections to be cut as you describe; cutting those cross sections does not require that the time dimension be exactly like the space dimensions.

 

[bobc2]

The fact that the time dimension has the opposite sign in the metric to the three space dimensions indicates that it is not quite the same as a spatial dimension. It is *like* a spatial dimension in some respects (for example, it can be measured in the same units as spatial dimensions by using the speed of light as a conversion factor), but it is not a spatial dimension. It is a dimension of the overall 4-D manifold of spacetime, topologically speaking, which is sufficient to allow 3-D cross-sections to be cut as you describe; cutting those cross sections does not require that the time dimension be exactly like the space dimensions.

Hi, Peter. I think you've made very good points with that analysis. The other way to look at it may be seen with the sketches below. First, the left sketch symbolizes red and blue rockets moving away from each other with the same speeds relative to the black "rest" system. We have the usual time dilation. Red, when at his world line station 9, "sees" blue in red's simultaneous space at blue's world line station 8. But, blue, when at his station 9, "sees" red in blue's simultaneous space at red's world line station 8.

The 4-D metric, from which the Lorentz transformation time dilation equation follows is derived directly from 4 spatial dimensions. The selection of coordinates in the 4-space is simply selected based on orientations of 4-D world lines in the space. So, we have a right triangle with the blue X4 axis as the hypotenuse. The negative sign in the metric does not arise as a result of some mysterious role of time. It is just related to the orientation of world lines. It just results from the red X4 and blue X1 axes in the position of legs of the triangle. So, when we solve for the red X4 we're just solving for a leg of a right triangle instead of a hypotenuse. Some physicists refer to the red leg of the triangle as "Einstein's Hypotenuse."

 

[PeterDonis]

The 4-D metric, from which the Lorentz transformation time dilation equation follows is derived directly from 4 spatial dimensions.

No, it isn't, because the sign of the "time" term is opposite from the sign of the "space" term. In 4 spatial dimensions, the sign of all the terms would be the same and the metric would be positive definite. In 4-D spacetime, the metric is not positive definite. That makes a big difference.

The selection of coordinates in the 4-space is simply selected based on orientations of 4-D world lines in the space. So, we have a right triangle with the blue X4 axis as the hypotenuse.

Yes, the labeling of events by coordinates respects a standard R4 topology; coordinate 4-tuples that are almost the same represent points that are "close together" topologically, meaning they lie in small open neighborhoods of each other.

The negative sign in the metric does not arise as a result of some mysterious role of time. It is just related to the orientation of world lines. It just results from the red X4 and blue X1 axes in the position of legs of the triangle.

And look at how the axes are tilted relative to the black axes. If both dimensions were "spatial", so the metric was Euclidean, the red and blue sets of axes would each be perpendicular to each other, as the black axes are. But they're not. Minkowski spacetime is not Euclidean space. It's a different geometric object.

 

[PeterDonis]

So, when we solve for the red X4 we're just solving for a leg of a right triangle instead of a hypotenuse.

Also, I can play the same trick with Euclidean space, to make it look like the "metric" has a minus sign for one dimension. But that requires me to mix coordinates from two different frames on one side of the equation, which means it isn't a metric any more; it's just an equation that's been rearranged. A valid metric expression involves coordinates that are all from the same frame. For example, write the equation for the blue X4 in terms of the black X4 and X1; it will have a minus sign. *That* is the metric. I can rearrange that equation to move the negative term to the other side, but all that shows is that I can do algebra; it doesn't change the intrinsic geometry of the manifold.

 

[bobc2]

Also, I can play the same trick with Euclidean space, to make it look like the "metric" has a minus sign for one dimension. But that requires me to mix coordinates from two different frames on one side of the equation, which means it isn't a metric any more; it's just an equation that's been rearranged. A valid metric expression involves coordinates that are all from the same frame. For example, write the equation for the blue X4 in terms of the black X4 and X1; it will have a minus sign. *That* is the metric. I can rearrange that equation to move the negative term to the other side, but all that shows is that I can do algebra; it doesn't change the intrinsic geometry of the manifold.

That's not the way the block universe works. We begin with a Euclidean R4 manifold and freely select an initial set of coordinates using blue X1 and red X4 (blue and red X2 and X3 are the same). Do not regard the blue and red as belonging to two different coordinate systems at this stage.

Using these coordinates we have a distance along the blue X4 direction using Pythagorean theorem. Having these relationships we can now freely select a new set of coordinates, i.e., the blue coordinates X1, X2, X3 and X4. The Minkowski metric follows.

We have had no need to make any reference to time. It is all spatial. Now, if you wish to introduce a concept of time as an observer's consciousness moving along his X4 world line at the speed of light, you are free to postulate that and then investigate the implications and the consistency with special relativity theory.

Again, I don't like the concept at a subjective level. I'm just trying to do the best job I can at explaining the 4-D spatial universe concept. There are probably others on the forum who can make it more clear (and perhaps present it more accurately) than I. The link to Paul Davies's article given in the earlier post is good. I visited Davies's place at Arizona State University and hoped to meet him, but he was out of town on that day.

 

[Q-reeus]

...I visited Davies's place at Arizona State University and hoped to meet him, but he was out of town on that day.

Surely you meant "our eternally static worldtubes had such and such a 4D spatial separation at that region of eternally existent Platonia"?

 

[bobc2]

Surely you meant "our eternally static worldtubes had such and such a 4D spatial separation at that region of eternally existent Platonia"?

Hey, that's a good one, Q-reeus. I'm definitely not into Julian Barbour's platonia stuff. He should have stopped once he built the case for the 4-D spatial universe. However, there's something to be said for investigating the configuration space of 4-D objects. Penrose takes a better approach.

 

[Q-reeus]

Hey, that's a good one, Q-reeus. I'm definitely not into Julian Barbour's platonia stuff. He should have stopped once he built the case for the 4-D spatial universe. However, there's something to be said for investigating the configuration space of 4-D objects. Penrose takes a better approach.

Just for fun looked at a YouTube video by Barbour 'Killing Time'. He starts off with 'time and motion don't really exist'. Oh well, at least he said it, plain and clear. But not 5 minutes in and there is a distinct shifting of ground going on. Now we are being told time is a relational thing - the comparison between a huge number of fundamental clocks. Time is suddenly real after all - just redefined. Sort of weasely to me. Set up and then knock down a straw man - 'everyone believes wrongly that time flows'. About as much as folks these days believe 'the sun rises and sets'. Never read any of his books but actually like his Machian relational ideas in general (sans 'Platonia'), but definitely not the shifty approach demonstrated imo in that video. From the sidelines have looked at various arguments for 'presentism' vs 'eternalism' and conclude it best to spend my time on other topics. So much gets down to subtle definitions.

 

[bobc2]

Just for fun looked at a YouTube video by Barbour 'Killing Time'. He starts off with 'time and motion don't really exist'. Oh well, at least he said it, plain and clear. But not 5 minutes in and there is a distinct shifting of ground going on. Now we are being told time is a relational thing - the comparison between a huge number of fundamental clocks. Time is suddenly real after all - just redefined. Sort of weasely to me. Set up and then knock down a straw man - 'everyone believes wrongly that time flows'. About as much as folks these days believe 'the sun rises and sets'. Never read any of his books but actually like his Machian relational ideas in general (sans 'Platonia'), but definitely not the shifty approach demonstrated imo in that video. From the sidelines have looked at various arguments for 'presentism' vs 'eternalism' and conclude it best to spend my time on other topics. So much gets down to subtle definitions.

I can certainly appreciate where you are coming from, Q-reeus. And thanks for the link. I've read Barbour's book a couple of times (and Davies's and a couple of others). I don't know why, since youth, I've been dogged by this compulsion to comprehend some kind of external reality. It must be genetic. I just can't shake it. I don't talk physics around family and friends--they would think I'm nuts (or rather, discover that I'm nuts). At least I'm a kind of recovering physicist--not anywhere near the condition of poor Kurt Godel.

 

[PeterDonis]

That's not the way the block universe works. We begin with a Euclidean R4 manifold

R4, yes. Euclidean, no, not if the metric ends up being Minkowski. "Euclidean" refers to a metric, not just a topology. Or at least, it does the way I am used to seeing the term used. If "Eucldiean" is just supposed to refer to the topology, then I have no problem with what's quoted above, but I would still object to the term "spatial" since it, too, implies a Euclidean, positive definite metric, at least as I am used to seeing the term used. The key is that there is a fundamental geometric difference between a Euclidean metric and a Minkowski metric, which is there no matter how you rearrange terms in equations. See below.

We have had no need to make any reference to time. It is all spatial. Now, if you wish to introduce a concept of time as an observer's consciousness moving along his X4 world line at the speed of light, you are free to postulate that and then investigate the implications and the consistency with special relativity theory.

I don't need to introduce that to introduce a concept of "time". As soon as I have the Minkowski metric, I have one "direction" which is singled out from the others as being fundamentally different, because of the opposite sign in the metric.

I understand how the "block universe" concept *derives* temporal relationships instead of treating them as fundamental. Basically, some portions of the universe contain "records" of other portions, and you can use the "records" to create a temporal ordering on the entire block universe. That still doesn't change the fact that once you've created the temporal ordering, it is not a Euclidean ordering; the metric on the "block universe" is Minkowski and is not positive definite, so there is a fundamental physical difference between "temporal" relationships (a portion of the universe containing a "record" of another portion must be in the future light cone of the portion it contains a record of) and "spatial" relationships (between portions of the block universe that are spacelike separated, so neither portion can contain a "record" of the other).

 

[bobc2]

R4, yes. Euclidean, no, not if the metric ends up being Minkowski. "Euclidean" refers to a metric, not just a topology. Or at least, it does the way I am used to seeing the term used. If "Eucldiean" is just supposed to refer to the topology, then I have no problem with what's quoted above, but I would still object to the term "spatial" since it, too, implies a Euclidean, positive definite metric, at least as I am used to seeing the term used. The key is that there is a fundamental geometric difference between a Euclidean metric and a Minkowski metric, which is there no matter how you rearrange terms in equations.

But, I'm just establishing the Euclidean R4 with the blue X1 and red X4, then using the one-to-one correspondence between the Affine space (a generalization of Euclidean) and the orthonormal Euclidean space, S. So, we have the fundamental space, S, associated with the positive definite metric, then any point in the Affine space, A, can be reached with 4-tuples of a S vector using the basis vectors defining A.

I can understand your preference for not referring to a metric for the A space. You may wish to restrict the language to Affine coordinates associated with the S space (the S space having the positive definite metric). The 4-dimensional description of special relativity remains intact in this context.

 

[PeterDonis]

But, I'm just establishing the Euclidean R4 with the blue X1 and red X4, then using the one-to-one correspondence between the Affine space (a generalization of Euclidean) and the orthonormal Euclidean space, S. So, we have the fundamental space, S, associated with the positive definite metric, then any point in the Affine space, A, can be reached with 4-tuples of a S vector using the basis vectors defining A.

No, what you're doing is mixing together coordinates from different coordinate charts on the same manifold. Your blue and red X1, X4 values are coordinates from different charts, so mixing them together the way you mix them does not count as a Euclidean metric. I agree that you have an affine space R4, where each point of the space can be labeled by a 4-tuple of values (X1, X2, X3, X4), but all the values have to be of the same "color" to evaluate whether the metric is positive definite or not.

 

[PeterDonis]

Your blue and red X1, X4 values are coordinates from different charts, so mixing them together the way you mix them does not count as a Euclidean metric.

Another way to see this is to ask what would happen if we tried to express red X1 in terms of blue X1 and X4, instead of red X4. The Minkowski metric formula gives:

(red X1)^2 = (blue X1)^2 - (blue X4)^2

We can rearrange this into your "Pythagorean" form:

(blue X1)^2 = (red X1)^2 + (blue X4)^2

There's only one problem: in this case, (red X1) is the *hypotenuse* of the triangle, not a leg! So clearly the actual metric of this manifold is not Euclidean and is not positive definite.

 

[bobc2]

No, what you're doing is mixing together coordinates from different coordinate charts on the same manifold. Your blue and red X1, X4 values are coordinates from different charts, so mixing them together the way you mix them does not count as a Euclidean metric.

I'm selecting blue X1 and red X4 as coordinates on the same chart. The blue and red coordinates were initially described to make it easy to visualize what is going on with observers. But the manifold is independent of the observers, and we can freely choose our orthonormal coordinates on the manifold to define our metric space.

However, I agree that this becomes a convoluted way of getting there, because we then have to haggle over nitty gritty details of how did I know how to choose those same-chart coordinates without resorting to other spaces, etc. Physically, you look at a universe with a bunch of world lines running off in different directions and lay a coordinate down on one of them, then use some procedure to put down the remaining orthogonal coordinates. But, mathematically we have to argue over what the world lines are doing there and what the metric of the space was that defined their configurations in space, etc.

For this purpose it might have been simpler to just start with the black rest frame positive definite metric and then define the affine space using the appropriate Lorentz related basis. But then, the fundamental spatial character of the affine space seems more difficult for some to grasp, due to the negative sign. The method I was trying to show makes it quite clear how a negative sign arises in the 4-dimensional space.

But, in any case the negative sign should be no more of a problem than the negative sign showing up when solving for the leg of a right triangle. The triangle leg, Y, represented in the equation below is no more less spatial because of the negative sign.

R^2 = X^2 + Y^2

Y^2 = R^2 - X^2

 

[nitsuj]

There's only one problem: in this case, (red X1) is the *hypotenuse* of the triangle, not a leg! So clearly the actual metric of this manifold is not Euclidean and is not positive definite.

What does positive definite mean? is that from the -+++ thing I see on here sometimes?

And what is -+++? is that spatial cordinates are + and time is -?

 

[PeterDonis]

What does positive definite mean? is that from the -+++ thing I see on here sometimes?

And what is -+++? is that spatial cordinates are + and time is -?

(-+++) is called a metric "signature"; it means the sign of timelike squared intervals is negative and the sign of spacelike squared intervals is positive. For a diagonal metric, this means the "t-t" metric coefficient is negative and the "x-x", "y-y", and "z-z" metric coefficients are positive. (A null squared interval is always zero.)

The fact that it is possible to have negative, zero, and positive squared intervals means that the metric is *not* positive definite; a positive definite metric only has positive squared intervals (except in the limiting case where we are evaluating the "interval" from a point to itself, which is zero).

I'm answering this question before responding to bobc2's post because it gives me a chance to clarify why I keep objecting to what he's saying.

I'm selecting blue X1 and red X4 as coordinates on the same chart.

The way you have written your equations, it seems like X1, X4 (regardless of color) are numbers, i.e., lengths along the lines along which they're marked. That means they can't be coordinates on the same chart; blue X1, X4 are coordinates on the blue chart, and red X1, X4 are coordinates on the red chart. Are you saying that you do not intend your X1, X4 of various colors to be numbers, but that each of them are 4-tuples giving the coordinates of the points you have labeled (presumably in the black coordinate chart)?

If you are thinking of them as 4-tuples, then I see why you are saying they are "coordinates on the same chart"; but you should recognize that you are squaring these 4-tuples, so they function in your equations exactly the same as if they are numbers taken from the chart of the appropriate color, because the "square" of a 4-tuple can only be its squared length, which is equivalent to a single number giving the corresponding coordinate from the chart of the given color--i.e., the squared length of the 4-tuple "blue X1" is the *coordinate* "blue X1", i.e., the X1-component of the 4-tuple from the blue coordinate chart that describes the indicated point. So both ways of talking about your X1, X4 of various colors are equivalent in this sense.

Also, none of this is relevant to the objections I've been making, which center around the fact that the metric of spacetime is not positive definite. See further comments below.

The blue and red coordinates were initially described to make it easy to visualize what is going on with observers. But the manifold is independent of the observers, and we can freely choose our orthonormal coordinates on the manifold to define our metric space.

You can freely choose the coordinates, yes. But once you choose the coordinates, you can't freely choose the metric. The metric is determined by the actual, physical intervals between points, so the metric coefficients in your chosen coordinate system are fully determined once you have chosen your coordinates.

For this purpose it might have been simpler to just start with the black rest frame positive definite metric

This is where you keep missing my point. The metric of the black "rest frame" is *NOT* positive definite. Squared intervals on the underlying spacetime can be positive, negative, or zero, and the metric has to capture that. The underlying spacetime, as a *metric space*, is *not* Euclidean.

and then define the affine space using the appropriate Lorentz related basis.

An affine space doesn't have a metric; it doesn't "know" anything about lengths. You can define basis vectors, but since there is no metric, there is no way to assign squared lengths to the basis vectors, so you can't even express the concept of a "spatial" vector as opposed to some other kind, because you can't express the concept of a "squared length", let alone its sign.

As an *affine space*, yes, you can call R4 "Euclidean", as long as you remember that that *only* refers to the *affine* properties of Euclidean space, *not* its metrical properties.

 

[nitsuj]

(-+++) is called a metric "signature"; it means the sign of timelike squared intervals is negative and the sign of spacelike squared intervals is positive. For a diagonal metric, this means the "t-t" metric coefficient is negative and the "x-x", "y-y", and "z-z" metric coefficients are positive. (A null squared interval is always zero.)

The fact that it is possible to have negative, zero, and positive squared intervals means that the metric is *not* positive definite; a positive definite metric only has positive squared intervals (except in the limiting case where we are evaluating the "interval" from a point to itself, which is zero).

Thanks for the reply.

One more thing, can an interval be the distance between two mirrors of a light clock?

Where an observer traveling very fast with the clock sees it as say one second, and an at rest observer sees it as taking more time? Is the spacetime? between the mirrors (events) of the same interval for the two observers? is that right?

 

[PeterDonis]

can an interval be the distance between two mirrors of a light clock?

Yes, it would be a spacelike interval (assuming the mirrors themselves were moving on timelike worldlines, as they would have to be to be part of a light clock). However, this interval is not the same as the interval between the events of light striking one mirror and then the other; the latter is a null interval. See below.

Where an observer traveling very fast with the clock sees it as say one second, and an at rest observer sees it as taking more time? Is the spacetime? between the mirrors (events) of the same interval for the two observers? is that right?

The spacetime interval between two given events is always the same for all observers. That's the basic foundation of SR. (Strictly speaking, this is only true when spacetime is flat, so SR is valid globally. We'll ignore the complications introduced by GR here.) However, how that interval is split up into "space" and "time" parts is observer-dependent. A pair of events that occur at the same point in space as seen by an observer at rest relative to the mirrors (say, successive bounces of the light beam off one of the mirrors) will *not* occur at the same point in space as seen by an observer to whom the mirrors are moving. So the latter observer will see a *larger* time separation between the two events, but will also see a space separation, and the interval, t^{2} - x^{2}, will be the same for both observers.

 

[nitsuj]

Yes, it would be a spacelike interval (assuming the mirrors themselves were moving on timelike worldlines, as they would have to be to be part of a light clock). However, this interval is not the same as the interval between the events of light striking one mirror and then the other; the latter is a null interval. See below.



The spacetime interval between two given events is always the same for all observers. That's the basic foundation of SR. (Strictly speaking, this is only true when spacetime is flat, so SR is valid globally. We'll ignore the complications introduced by GR here.) However, how that interval is split up into "space" and "time" parts is observer-dependent. A pair of events that occur at the same point in space as seen by an observer at rest relative to the mirrors (say, successive bounces of the light beam off one of the mirrors) will *not* occur at the same point in space as seen by an observer to whom the mirrors are moving. So the latter observer will see a *larger* time separation between the two events, but will also see a space separation, and the interval, t^{2} - x^{2}, will be the same for both observers.

Awesome, thanks Peter! I'm gunna re-read that when I get home (null interval specificaly, cause t=0? for things at c?). It looks like it's gunna help me understand spacetime diagrams / terminology better.

 

[PeterDonis]

(null interval specificaly, cause t=0? for things at c?)

Careful; a null interval is an interval whose squared length is zero, but that does *not* mean that "t = 0". It means that t^2 - x^2 = 0, where t, x are coordinates in some inertial frame, i.e., as assigned by some observer moving on a timelike worldline; which means that t = +/- x, i.e., null intervals are intervals along lines that are sloped at 45 degrees on a standard spacetime diagram. Such lines are not timelike; they are not possible worldlines for any timelike observer. So it's not a good idea to use the word "time" or anything that could be interpreted as "time" (such as "t") to refer to intervals along such lines. Null lines *are* worldlines of massless objects, such as light rays; but again, since those worldlines are not timelike, saying that "time stops" or "t = 0" for objects moving on such worldlines is not a good idea because it invites a lot of erroneous inferences.

There's a whole other thread that is largely about this issue, in which I've posted a number of times:

https://www.physicsforums.com/showthread.php?t=552175

(There are other threads running that touch on this too.)

 

[nitsuj]

Careful; a null interval is an interval whose squared length is zero, but that does *not* mean that "t = 0". It means that t^2 - x^2 = 0, where t, x are coordinates in some inertial frame, i.e., as assigned by some observer moving on a timelike worldline; which means that t = +/- x, i.e., null intervals are intervals along lines that are sloped at 45 degrees on a standard spacetime diagram. Such lines are not timelike; they are not possible worldlines for any timelike observer. So it's not a good idea to use the word "time" or anything that could be interpreted as "time" (such as "t") to refer to intervals along such lines. Null lines *are* worldlines of massless objects, such as light rays; but again, since those worldlines are not timelike, saying that "time stops" or "t = 0" for objects moving on such worldlines is not a good idea because it invites a lot of erroneous inferences.

There's a whole other thread that is largely about this issue, in which I've posted a number of times:

https://www.physicsforums.com/showthread.php?t=552175

(There are other threads running that touch on this too.)

I think that clarifies space time diagrams for me.

Simply put, st diagrams are done where ct= x and 1ct= 1x slope is the 45 degree line that represents c. This is a null line. Two events along this path ( like light passing something) one second apart is a null interval. One side of the 45 is time like(2ct = 1x), the other space like (1ct = 2x), the line itself null (1ct = 1x).

Am I getting that right?

 

[bobc2]

The way you have written your equations, it seems like X1, X4 (regardless of color) are numbers, i.e., lengths along the lines along which they're marked. That means they can't be coordinates on the same chart; blue X1, X4 are coordinates on the blue chart, and red X1, X4 are coordinates on the red chart. Are you saying that you do not intend your X1, X4 of various colors to be numbers, but that each of them are 4-tuples giving the coordinates of the points you have labeled (presumably in the black coordinate chart)?

If you are thinking of them as 4-tuples, then I see why you are saying they are "coordinates on the same chart"; but you should recognize that you are squaring these 4-tuples, so they function in your equations exactly the same as if they are numbers taken from the chart of the appropriate color, because the "square" of a 4-tuple can only be its squared length, which is equivalent to a single number giving the corresponding coordinate from the chart of the given color--i.e., the squared length of the 4-tuple "blue X1" is the *coordinate* "blue X1", i.e., the X1-component of the 4-tuple from the blue coordinate chart that describes the indicated point. So both ways of talking about your X1, X4 of various colors are equivalent in this sense.

Also, none of this is relevant to the objections I've been making, which center around the fact that the metric of spacetime is not positive definite. See further comments below.

You can freely choose the coordinates, yes. But once you choose the coordinates, you can't freely choose the metric. The metric is determined by the actual, physical intervals between points, so the metric coefficients in your chosen coordinate system are fully determined once you have chosen your coordinates.

This is where you keep missing my point. The metric of the black "rest frame" is *NOT* positive definite. Squared intervals on the underlying spacetime can be positive, negative, or zero, and the metric has to capture that. The underlying spacetime, as a *metric space*, is *not* Euclidean.

An affine space doesn't have a metric; it doesn't "know" anything about lengths. You can define basis vectors, but since there is no metric, there is no way to assign squared lengths to the basis vectors, so you can't even express the concept of a "spatial" vector as opposed to some other kind, because you can't express the concept of a "squared length", let alone its sign.

As an *affine space*, yes, you can call R4 "Euclidean", as long as you remember that that *only* refers to the *affine* properties of Euclidean space, *not* its metrical properties.

Good job, Peter. Yes, you caught me red handed trying to pass the Affine space off as a metric. I'm too use to looking at a distance and calling it a metric (or not considering the mixed use of the term, "distance"). The usual treatment to get the metric is to use Minkowski's ict for X4, then get the ++++ signature. Einstein referred to that as a Euclidean space. But, I've never liked the ict treatment. I guess it works for mathematicians (and obviously for many physicists).

Anyway, you are a great asset for this physics forum. Thanks.

 

[PeterDonis]

The usual treatment to get the metric is to use Minkowski's ict for X4, then get the ++++ signature.

Yes, this treatment appears in many textbooks and many physicists seem to like it. Hawking, for example, uses it in his "no-boundary" proposal for quantum cosmology. (I'll see if I can dig up a reference.) And it's used a lot in quantum field theory in general, where it goes by the name "Wick rotation" to confuse lay people. But not all; IIRC, Misner, Thorne & Wheeler spend a page or so explaining why they *don't* use it. I'm not a great fan of it either, since it seems to me to obscure the physical distinction between time and space.

Anyway, you are a great asset for this physics forum. Thanks.

You're welcome. Thanks for the kudos!

 

[ghwellsjr]

Good job, Peter. Yes, you caught me red handed trying to pass the Affine space off as a metric. I'm too use to looking at a distance and calling it a metric (or not considering the mixed use of the term, "distance"). The usual treatment to get the metric is to use Minkowski's ict for X4, then get the ++++ signature. Einstein referred to that as a Euclidean space. But, I've never liked the ict treatment. I guess it works for mathematicians (and obviously for many physicists).

Anyway, you are a great asset for this physics forum. Thanks.

Does this mean you are persuaded that the 4th dimension is not spatial but temporal?

 

[stglyde]

So bobc2 and PeterDonis and others,

Do you deny or accept the possibility the future already exist but contained domain of high probability and low probability... like Barbour's mist of Platonia in Hilbert Space. Watch this interview with Max Tegmark:

http://discovermagazine.com/2008/jul/16-is-the-universe-actually-made-of-math/article_view?b_start:int=3&-C=

"So the mathematical structure that is the theory of relativity has a piece that explicitly describes time or, better yet, is time. But the integers don’t have anything similar.

Yes, and the important thing to remember is that Einstein’s theory taken as a whole represents the bird’s perspective. In relativity all of time already exists. All events, including your entire life, already exist as the mathematical structure called space-time. In space-time, nothing happens or changes because it contains all time at once. From the frog’s perspective it appears that time is flowing, but that is just an illusion. The frog looks out and sees the moon in space, orbiting around Earth. But from the bird’s perspective, the moon’s orbit is a static spiral in space-time.

The frog feels time pass, but from the bird’s perspective it’s all just one eternal, unalterable mathematical structure.

That is it. If the history of our universe were a movie, the mathematical structure would correspond not to a single frame but to the entire DVD. That explains how change can be an illusion.

Of course, quantum mechanics with its notorious uncertainty principle and its Schrödinger equation will have to be part of the theory of everything.

Right. Things are more complicated than just relativity. If Einstein’s theory described all of physics, then all events would be predetermined. But thanks to quantum mechanics, it’s more interesting.

Plausible conclusion: Although the future may already exist. They are not definite. There are Hilbert Platonia mist where Obama would be reelected. Another probability mist where Arnold Schwarzenegger would become president. And everything is not yet set in stone.. but the probabilities are not unlimited but set within certain boundaries or limits of possibilities.

No problem about this aspect of the future. But the more question now. Does the past still exist? If not, why do many physicists explore time travel to a past that still exist? I'm partly interested in this because I'd like to go 5 years prior to do some things right.

 

[PeterDonis]

Simply put, st diagrams are done where ct= x and 1ct= 1x slope is the 45 degree line that represents c. This is a null line.

Yes.

Two events along this path ( like light passing something) one second apart is a null interval.

Yes; to clarify a bit, two events along the worldline of a light ray which are separated by one second in time will also be separated by one second in space--i.e., one light-second, or 3 x 10^8 meters. The same for any other time separation.

One side of the 45 is time like(2ct = 1x), the other space like (1ct = 2x), the line itself null (1ct = 1x).

Yes; again, to clarify a bit, the timelike "side" of the 45-degree line (which is usually called the "light cone" because it looks like a cone if we put back in one more spatial dimension) contains worldlines where t > x, i.e., the "slope" dt/dx is greater than 1 (it doesn't have to be 2, it can be any value > 1). This is more usually stated as the velocity, dx/dt, being less than 1 (i.e., less than the speed of light, which is 1 in the units usually used in SR, where c = 1).

The spacelike "side" of the light cone, OTOH, contains curves (which aren't called "worldlines" because they're not possible paths for any real object) for which t < x, i.e., the "slope" dt/dt is less than 1.

 

[PeterDonis]

Plausible conclusion: Although the future may already exist. They are not definite. There are Hilbert Platonia mist where Obama would be reelected. Another probability mist where Arnold Schwarzenegger would become president. And everything is not yet set in stone.. but the probabilities are not unlimited but set within certain boundaries or limits of possibilities.

This seems like a reasonable summary of what you quoted from the Tegmark interview.

No problem about this aspect of the future. But the more question now. Does the past still exist? If not, why do many physicists explore time travel to a past that still exist? I'm partly interested in this because I'd like to go 5 years prior to do some things right.

From our perspective (the frog's perspective, as it's described in the Tegmark quote), no, the past doesn't "still" exist. "Still" is a concept that's only applicable from the frog's perspective. The frog may *remember* past events, but those memories are not in the past, they're in the present; they are part of the frog's present state. A week from now, the frog may remember events that are happening now, but those events will not "still exist" a week from now; only their traces in the frog's memory (or other records that they leave) will exist then.

However, this does not, in itself, prevent time travel to the past; from the frog's perspective, traveling to a point in time five years ago would be just like traveling to tomorrow; you would experience time "flowing" forward as usual, but your experience would happen to pass through events that it had passed through before. One of the best descriptions of what this could be like that I've read, at least in fiction, is the classic Heinlein story By His Bootstraps:

http://en.wikipedia.org/wiki/By_His_Bootstraps

From the bird's perspective, the word "still" does not apply. The entire 4-dimensional spacetime is a single "thing" that is just there; it does not "flow" or "evolve" or anything like that. If this single "thing" happens to contain closed timelike curves, i.e., timelike curves (possible worldlines that "frogs" could follow) that pass through the same event more than once, then time travel to the past is part of the 4-dimensional thing.

 

[stglyde]

This seems like a reasonable summary of what you quoted from the Tegmark interview.



From our perspective (the frog's perspective, as it's described in the Tegmark quote), no, the past doesn't "still" exist. "Still" is a concept that's only applicable from the frog's perspective. The frog may *remember* past events, but those memories are not in the past, they're in the present; they are part of the frog's present state. A week from now, the frog may remember events that are happening now, but those events will not "still exist" a week from now; only their traces in the frog's memory (or other records that they leave) will exist then.

However, this does not, in itself, prevent time travel to the past; from the frog's perspective, traveling to a point in time five years ago would be just like traveling to tomorrow; you would experience time "flowing" forward as usual, but your experience would happen to pass through events that it had passed through before. One of the best descriptions of what this could be like that I've read, at least in fiction, is the classic Heinlein story By His Bootstraps:

http://en.wikipedia.org/wiki/By_His_Bootstraps

From the bird's perspective, the word "still" does not apply. The entire 4-dimensional spacetime is a single "thing" that is just there; it does not "flow" or "evolve" or anything like that. If this single "thing" happens to contain closed timelike curves, i.e., timelike curves (possible worldlines that "frogs" could follow) that pass through the same event more than once, then time travel to the past is part of the 4-dimensional thing.

But if Many Worlds were true. Things may not be that simple. If quantum choices can split worlds, so can choices in the future or past be their own worlds. According to David Deutch and Michael Lockwood in their article "The Quantum Physics of Time Travel" (saw complete article link in 2009 archive https://www.physicsforums.com/showthread.php?t=360188 ):

"What, then, does quantum mechanics, by Everett's interpretation, say about time travel paradoxes? Well, the grandfather paradox, for one, simply does not arise. Suppose that Sonia embarks on a paradoxical project that, if completed, would prevent her own conception. What happens? If the classical space-time contains CTCs, then, according to quantum mechanics, the
universes in the multiverse must be linked up in an unusual way. Instead of having many disjoint, parallel universes, each containing CTCs, we have in effect a single, convoluted space-time consisting of many connected universes. The links force Sonia to travel to a universe that is identical, up to the instant of her arrival, with the one she left, but that is thereafter different because of her presence."

Can you refute it or give penetrating arguments why Many Worlds can't be true in the Present, Past or Future Timelines?

 

[atyy]

But if Many Worlds were true. Things may not be that simple. If quantum choices can split worlds, so can choices in the future or past be their own worlds. According to David Deutch and Michael Lockwood in their article "The Quantum Physics of Time Travel" (saw complete article link in 2009 archive https://www.physicsforums.com/showthread.php?t=360188 ):

"What, then, does quantum mechanics, by Everett's interpretation, say about time travel paradoxes? Well, the grandfather paradox, for one, simply does not arise. Suppose that Sonia embarks on a paradoxical project that, if completed, would prevent her own conception. What happens? If the classical space-time contains CTCs, then, according to quantum mechanics, the
universes in the multiverse must be linked up in an unusual way. Instead of having many disjoint, parallel universes, each containing CTCs, we have in effect a single, convoluted space-time consisting of many connected universes. The links force Sonia to travel to a universe that is identical, up to the instant of her arrival, with the one she left, but that is thereafter different because of her presence."

Can you refute it or give penetrating arguments why Many Worlds can't be true in the Present, Past or Future Timelines?

I'm not sure such a theory of quantum gravity is known. We do have a working theory of quantum gravity as a low energy effective theory. It assumes that the topology of spacetime is boring.

 

[PeterDonis]

If the classical space-time contains CTCs, then, according to quantum mechanics, the universes in the multiverse must be linked up in an unusual way. Instead of having many disjoint, parallel universes, each containing CTCs, we have in effect a single, convoluted space-time consisting of many connected universes. The links force Sonia to travel to a universe that is identical, up to the instant of her arrival, with the one she left, but that is thereafter different because of her presence."

Can you refute it or give penetrating arguments why Many Worlds can't be true in the Present, Past or Future Timelines?

I don't see that I would have to refute it. What you say looks OK to me, and I don't see any inconsistency with what I said. Considering Sonia as a "frog", she still experiences "flowing" along her worldline normally; when she arrives at the event that, classically, would complete a CTC, she simply experiences the alternate version in which she is present at that event (where, supposing she passed through the same event before, she would remember experiencing the "original" version where she was not present). So the frog's eye view still works for Sonia.

From the bird's-eye perspective, as the quoted passage says, spacetime is now a convoluted, multiply-connected thing, instead of a simply-connected thing that happens to contain CTCs. But it's still a single thing that is just "there", and the statement "the past still exists" is still not applicable from this point of view. From Sonia's point of view, the event at which she arrives back in her own past can be considered a "splitting point", where a decision she makes causes the past to "change"; but from the bird's-eye perspective, her "decision" is simply an event on her convoluted worldline in the convoluted multiply connected spacetime, which does not change; it is all there "at once" as part of the whole spacetime.

 

[stglyde]

I don't see that I would have to refute it. What you say looks OK to me, and I don't see any inconsistency with what I said. Considering Sonia as a "frog", she still experiences "flowing" along her worldline normally; when she arrives at the event that, classically, would complete a CTC, she simply experiences the alternate version in which she is present at that event (where, supposing she passed through the same event before, she would remember experiencing the "original" version where she was not present). So the frog's eye view still works for Sonia.

From the bird's-eye perspective, as the quoted passage says, spacetime is now a convoluted, multiply-connected thing, instead of a simply-connected thing that happens to contain CTCs. But it's still a single thing that is just "there", and the statement "the past still exists" is still not applicable from this point of view. From Sonia's point of view, the event at which she arrives back in her own past can be considered a "splitting point", where a decision she makes causes the past to "change"; but from the bird's-eye perspective, her "decision" is simply an event on her convoluted worldline in the convoluted multiply connected spacetime, which does not change; it is all there "at once" as part of the whole spacetime.

Do you agree that there are two kinds of time. Real time experienced and Pime (Parameter Time) in Spacetime equations? And distinguising them can illuminate many areas in physics? It's according to Demystifier who wrote:

http://fqxi.org/data/essay-contest-files/Nikolic_FQXi_time.pdf

Do you or do you not agree with it and why?

 

[PeterDonis]

Do you agree that there are two kinds of time. Real time experienced and Pime (Parameter Time) in Spacetime equations? And distinguising them can illuminate many areas in physics? It's according to Demystifier who wrote:

http://fqxi.org/data/essay-contest-files/Nikolic_FQXi_time.pdf

Do you or do you not agree with it and why?

I'll have to read the paper you linked to before I can really respond to your questions, since I'm not sure what specifically the issue is that you're concerned about. From a quick skim of the abstract, it looks like the distinction between "Real time" and "Pime" is more an issue of theories of consciousness than theories of physics.

 

[nitsuj]

Yes.
Yes; to clarify a bit, two events along the worldline of a light ray which are separated by one second in time will also be separated by one second in space--i.e., one light-second, or 3 x 10^8 meters. The same for any other time separation.
Yes; again, to clarify a bit, the timelike "side" of the 45-degree line (which is usually called the "light cone" because it looks like a cone if we put back in one more spatial dimension) contains worldlines where t > x, i.e., the "slope" dt/dx is greater than 1 (it doesn't have to be 2, it can be any value > 1). This is more usually stated as the velocity, dx/dt, being less than 1 (i.e., less than the speed of light, which is 1 in the units usually used in SR, where c = 1).

The spacelike "side" of the light cone, OTOH, contains curves (which aren't called "worldlines" because they're not possible paths for any real object) for which t < x, i.e., the "slope" dt/dt is less than 1.

Yea a cone is 2 spatial dimensions, a sphere for 3 i guess. The diagram helps me ignore time as being the period between events and more on it being simply a "cause effect" thing. Said differently the null line illustrates causality (I can't picture where it goes with a sphere). Oh cool, the moon is 3d, the distance between it and me is the 4th lol (i pictured causality as a sphere, neat-o)

I wonder if it's a shared point; having to measure the two way speed of light to calculate c and causality. So in a big stretch, "reality" falls onto an observer at c from all around. ANY direction you move in changes things accordingly, via the Lorentz transformations and the constancy of c, or causality in this example. I just got all Greene there

Time is easily identified as a dimension from this perspective; time and distance in meters. However, block universe really doesn't pass the smell test now.

 

[bobc2]

From the bird's-eye perspective, as the quoted passage says, spacetime is now a convoluted, multiply-connected thing, instead of a simply-connected thing that happens to contain CTCs. But it's still a single thing that is just "there", and the statement "the past still exists" is still not applicable from this point of view. From Sonia's point of view, the event at which she arrives back in her own past can be considered a "splitting point", where a decision she makes causes the past to "change"; but from the bird's-eye perspective, her "decision" is simply an event on her convoluted worldline in the convoluted multiply connected spacetime, which does not change; it is all there "at once" as part of the whole spacetime.

Good way to size it up. Peter gets it right and puts things in the proper perspective, as usual.

 

[ghwellsjr]

Good way to size it up. Peter gets it right and puts things in the proper perspective, as usual.

As I asked earlier:

Does this mean you are persuaded that the 4th dimension is not spatial but temporal?

 

[PeterDonis]

Time is easily identified as a dimension from this perspective; time and distance in meters. However, block universe really doesn't pass the smell test now.

Why not?