A Case for the 4-D Space-Space Block Universe

[bobc2]

PeterDonis and DaleSpam, I'll get back to your comments in the recent posts, but first I would like to see if we are on the same page so far as understanding the concepts of time that are often referred to in various articles. Which of the four universe-time descriptions illustrated below best fits your world view? I have added a 4th sketch in order that we can distinguish between a "block time universe" versus a "block spatial universe" with spatial 4th dimension (which also includes the illusion of time as consciousness moves along the spatial 4th dimension at the speed of light).

Throughout all of my posts, I've been trying to present the case for the number 4 concept. And I've been assuming that you two have been advocating the number 1 concept, but I can't be sure, in light of some of your comments. Please describe your world view if none of these four fit with you.

 

[Dale]

I am not advocating any concept. They make no experimental predictions, therefore I use whichever is more convenient for thinking about the problem at hand. However, "eternalism" is my favorite when there is no reason to pick one of the others.

If you will note, there is no distinguishing feature between eternalism and spatial eternalism other than your idiosyncratic and unexplained labelling. It makes it hard to distinguish as a legitimately different concept.

 

[bobc2]

I am not advocating any concept. They make no experimental predictions...

Here is an experimental prediction that could only be made by assuming the concept No. 5 is correct.

So, at the end of this text is a space-time diagram with a sequence of events. The diagram represents a sort of sequence of thought experiments in which three observers in a Lorentz space send messages back and forth as they move through 4-dimensional space. Before the experiments begin, the three observers get together and plan the experiments, documenting the exact sequence of events to be enacted. Predictions about the exact results of data that are to be recorded and transmitted among the observers for each planned event are documented in advance of the experiments. At the end of the sequence of experiments, the three observers get back together and compare notes to see if their experimental results verify existence in any of the Lorentz space planes of simultaneity (volumes) under dispute.

In the sketch below the brown, light brown, and blue observers are initially together in the brown rest frame, synchronizing space-time markers which are available as displays of actual distance traveled in 4-dimensional space, referenced from their starting point. The plan is for each to advance through a sequence of world line events, maintaining a display of distance traveled, photographing data and transmitting data back and forth among the three observers (speed of light transmission).

All three are together at event 1 (events in the space-time diagram are brown, light brown, or blue circles) where they synchronize their distance markers). It is planned that the light brown guy and the blue guy will move to a new position that puts them in brown’s instantaneous plane (3-D volume) of simultaneity at event 8. Light brown and blue have used Lorentz transformations to assure that their distance markers display the same values at event 8 as the brown guy’s markers display at event 2. Light brown and blue both transmit pictures of their displayed values so that brown can validate their numbers when he (brown) arrives at event 3 in the space-time diagram (brown calculates how far he has traveled along the 4th dimension since leaving event 2.

At event 9 the light brown guy transmits a photo of his distance display, which is received by blue at event 14 and received by brown at event 4. The blue and brown guys do calculations that demonstrate that events are still occurring in agreement with theoretical physics and agree with their pre-test predictions for that event. At this point the brown guy is able to confirm that the light brown guy existed in his plane of simultaneity back when he (the brown guy) was at event 3). From the data received from the blue guy at event 4 he is also able to determine that the blue guy was also in his (brown’s) plane of simultaneity back at event 3. Thus, the pre-test predictions for the experiment hold up.

Just one experiment doesn’t seem enough, so they continue acquiring data.
The blue guy arrives at the brown guy’s position at event 5. So, here the blue guy and the brown guy simultaneously occupy the same position at the intersection of their X4 axes. Special relativity tells them that if the light brown guy really still exists, then the light brown guy must exist at event 11 in blue’s instantaneous 3-D space volume, while simultaneously existing at event 12 in brown’s simultaneous space. However, as PeterDonis points out, they can’t really be sure, because they have no way of getting information from those events instantly while they are at event 5. They must wait until later for confirmation from the light brown guy.

Brown gets his confirmation when he arrives at event 6, receiving the picture of light brown’s event 12 photo of his distance traveled along the 4th dimension, which is exactly the same distance that the brown guy recorded for his own trip when at event 5. Thus, brown concludes that the light brown guy must have been in his simultaneous space which included both event 5 and event 12 simultaneously.

The blue guy has to wait until his event 16 for confirmation that light brown was at event 12 simultaneously with event 5 (when both blue and brown guys were simultaneously at event 5). Of course the blue guy saved a copy of brown’s distance position along brown’s X4 dimension when they were together at event 5. So, now he had confirmation that light brown was in brown’s simultaneous space, i.e., both brown and light brown were in the simultaneous space of events 5 and 12. These observations agree with those predicted before the start of the experiment.

But, now, blue asks whether the light brown guy was in his (blue’s) simultaneous space when blue was at event 5. Fortunately, light brown included a photo of his X4 position corresponding to event 11. Light brown and blue both used Lorentz transformations to figure out what each other’s positions should be along their respective X4 axes when blue arrived at brown’s position, event 5. Light brown transmitted his computations that he had made about what blue’s X4 position should be when light brown was at event 11. And blue computed the X4 reading that light brown should have when he (blue) was at event 5.

Light brown and blue wanted to be sure science was working right, so they took photos of their respective X4 distances corresponding to blue’s simultaneous space at blue’s event 16. Light brown did calculations (by prearranged agreements) at event 13. At event 17 blue found that light brown was in his (blue’s) simultaneous space when blue was at event 16 and light brown was at event 13.

All three observers get together at the end of the experiments and review all of their data. They conclude that sure enough, when the brown guy and blue guy were at event 5, the light brown guy simultaneously existed at event 12 (in brown’s simultaneous space) and event 11 (in blue’s simultaneous space). They then conclude that the light brown guy is actually a 4-dimensional object, and-- by extension--they all are. Thus, we have a model in which objects are 4-dimensional extending into a 4th spatial dimension.

However, "eternalism" is my favorite when there is no reason to pick one of the others.

The only problem is that it does not make the predictions that were made using concept number 5 as described above.

If you will note, there is no distinguishing feature between eternalism and spatial eternalism other than your idiosyncratic and unexplained labelling. It makes it hard to distinguish as a legitimately different concept.

The “eternalism” includes just pure time as the character of the 4th dimension. It is clear that having just pure time as your concept for the 4th dimension (without any spatial essence in that direction), you do not have the 4-dimensional space within which 4-dimensional objects can occupy. The thought experiment diagrammed in the sketch below and discussed in the above text emphasizes the agreement with the experimental predictions that 4-dimensional objects exist. "Eternalism" does not imply the existence of 4-dimensional objects.

 

[Dale]

Why don't you stop speculating and:
A) provide a reference for what exactly makes a dimension "spatial"
B) show how your referenced definition applies to time

 

[PeterDonis]

Special relativity tells them that if the light brown guy really still exists, then the light brown guy must exist at event 11 in blue’s instantaneous 3-D space volume, while simultaneously existing at event 12 in brown’s simultaneous space.

No, SR does *not* tell them that. See below.

They conclude that sure enough, when the brown guy and blue guy were at event 5, the light brown guy simultaneously existed at event 12 (in brown’s simultaneous space) and event 11 (in blue’s simultaneous space).

No, they can't conclude this; this statement as you state it doesn't even make sense, because it asserts three incompatible definitions of simultaneity in the same statement, one of which is not even a proper usage of the term. First, you state that light brown was simultaneous with brown at event 12--definition #1 of "simultaneity"; then you state that light brown was simultaneous with blue at event 11--definition #2 of "simultaneity", incompatible with definition #1 if you are trying to assert that both are true "at the same time"--see definition #3 in just a sec; then you state that both #1 and #2 are somehow true "simultaneously"--definition #3, which isn't even a proper relativistic definition of the term "simultaneity" since it doesn't use any single observer's surfaces of simultaneity, it tries to assert that the same object is somehow at two distinct events "at the same time", which has no consistent meaning that I can see. Certainly light brown's clock reading, his proper time, is different at events 11 and 12; certainly neither blue nor brown will calculate that his clock reading is the same at those two different events; and certainly neither blue nor brown receive light signals from those two events at the same time by their own clocks.

They then conclude that the light brown guy is actually a 4-dimensional object, and-- by extension--they all are. Thus, we have a model in which objects are 4-dimensional extending into a 4th spatial dimension.

If they are going to draw any such conclusion, it certainly won't be because of anything you said above, since that doesn't even make sense.

But after all that, what conclusion do you say they should draw? That light brown "has extension" in the 4th dimension. Which, as I've said multiple times now, *NOBODY IS DISAGREEING WITH*. Sorry for shouting, but you have spent a good portion of some very long posts repeating things that we've already told you we agree with. We *agree* that objects "have extension" in the 4th dimension. What we do NOT agree with is calling that 4th dimension "spatial". NOTHING you have said so far justifies the usage of that term; just "having extension" is not enough.

Can you succinctly state some other reasons for using the term "spatial" for X4? Not long-winded thought experiments, but a few short sentences? If not, then I think the question you originally posed in the OP, why your concept of a "space-space block universe" has not gotten much traction here at PF, is answered.

 

[PeterDonis]

It is clear that having just pure time as your concept for the 4th dimension (without any spatial essence in that direction), you do not have the 4-dimensional space within which 4-dimensional objects can occupy.

Again, here your "spatial essence" is just extension in the 4th dimension. We all agree that objects have extension in the 4th dimension. Extension does not necessarily equal "spatial" extension.

 

[bobc2]

Again, here your "spatial essence" is just extension in the 4th dimension. We all agree that objects have extension in the 4th dimension. Extension does not necessarily equal "spatial" extension.

 

[PeterDonis]

So you are basically *defining* "extension" and "spatial" to mean the same thing; i.e., a dimension is "spatial" if an object can extend along it. By this definition, every dimension is spatial, because to be a dimension at all there must be extension along it, so your definition of "spatial" makes it a useless concept. That would explain why it hasn't gotten any traction.

 

[Dale]

A N-dimensional object must have extent in N dimensions (by definition), but that certainly does not imply that all of those dimensions must be spatial. The distinction between spatial and temporal is based on the signature of the metric, as shown in my references above.

Please refer back to my post 74 and answer the challenge there. Asking for mainstream scientific references is always fair game on this forum and you should always be able to back up your claims with them. The fact that you cannot indicates more clearly than anything else that your idea does not belong here on PF.

 

[bobc2]

A N-dimensional object must have extent in N dimensions (by definition), but that certainly does not imply that all of those dimensions must be spatial.

It certainly does if we are talking about a physical object. When you assign a time dimension to a physical object, you are doing it only in the context of an abstract mathematical space. A real 4-dimensional object has 4 spatial dimensions.

The distinction between spatial and temporal is based on the signature of the metric, as shown in my references above.

Those references present no proof that the 4th dimension is time. You can replace the time dimension with X4 = ct (a physical spatial dimension) without affecting the sign of the metric at all. I have pointed out over and over again that the metric is indefinite due to the uniquely slanted coordinates and orentation of world lines in a spatial 4-D universe.

 

[PeterDonis]

A real 4-dimensional object has 4 spatial dimensions.

As I said in post #78, this definition of "spatial" makes it a useless concept, since every dimension is spatial by this definition. This is why this is *not* the definition of "spatial" used in physics.

Those references present no proof that the 4th dimension is time.

We are not arguing that the 4th dimension "is time". We are saying that it is not "spatial" according to the standard definition of that term in physics. You are arguing for a *different* definition of the term "spatial", which, as I have pointed out, would make the term useless since all dimensions would be spatial.

You can replace the time dimension with X4 = ct (a physical spatial dimension) without affecting the sign of the metric at all. I have pointed out over and over again that the metric is indefinite due to the uniquely slanted coordinates and orentation of world lines in a spatial 4-D universe.

None of this supports your usage of the term "spatial".

 

[bobc2]

So you are basically *defining* "extension" and "spatial" to mean the same thing; i.e., a dimension is "spatial" if an object can extend along it.

No, I did not imply that at all. But, an extension is spatial when a real physical object is extended into the 4th dimension, resulting in a real 4-dimensional object. It is not a physically real 4-dimensional object if it does not have spatial extent in the 4th dimension.

There is no problem with doing mathematical calculations using the scale factor, t = X4/c, for time calculations.

 

[PeterDonis]

an extension is spatial when a real physical object is extended into the 4th dimension, resulting in a real 4-dimensional object. It is not a physically real 4-dimensional object if it does not have spatial extent in the 4th dimension.

The phrase bolded in the quote above seems to me to require that *any* dimension into which an object can extend must be spatial. If you disagree, please give an example of a dimension into which an object can extend which would not be "spatial" by your definition.

And since for something to be a "dimension" at all, an object must be able to extend into it, that means the bolded phrase above requires that all dimensions must be spatial. If you disagree, please give an example of something you would call a "dimension" that an object cannot extend into.

 

[Dale]

Those references present no proof that the 4th dimension is time.

On the contrary, it is not a matter of proof but rather a matter of definition. Those references all use the definition that a time dimension is any dimension with the opposite signature of a space dimension. That is clearly the standard definition. Since you recognize that the 4th dimension has the opposite signature you must admit that by the standard definition the 4th dimension is time.

Since you reject that conclusion it means that you are using a non-standard definition. For some reason, you refuse to provide a reference for that definition despite being asked repeatedly by multiple people to do so. Even worse, you are not clear about what the defining characteristics of a "spatial" dimension are in your non-standard definition, most likely because you have not thought through your own terminology carefully either.

I again re-issue my challenge of post 74. Provide a reference for your non-standard definition.

 

[bobc2]

Originally Posted by bobc2 : an extension is spatial when a real physical object is extended into the 4th dimension, resulting in a real 4-dimensional object. It is not a physically real 4-dimensional object if it does not have spatial extent in the 4th dimension.

The phrase bolded in the quote above seems to me to require that *any* dimension into which an object can extend must be spatial.

We must be having semantics problems. I thought the context of my usage of "spatial" was clear, but evidently not. The term space can be used abstractly in association with mathematical objects. We have linear vector spaces, tensors, etc. I assume we can all understand the concept of physical space in relation to our normal X1, X2, X3 physical space we live in populated by 3-dimensional objects. I've been referring to a spatial X4 to imply the same physical nature we associate with X1, X2, and X3 should apply to X4. Perhaps I should always qualify the term, "spatial" as "physically spatial" when referring to X4 in this way. When we observe a real physical object, like a table, in our 3-D world, we associate physical spatial extent with the table and the physical space occupied by the table. In that same way, a 4-dimensional real physical object like a table, must have physical spatial extent in four dimensions, otherwise it is not a real 4-dimensional physical object.

So, I've been maintaing that if you were to associate a purely "time" character with the 4th dimension, you would not have "physically spatial" objects, but merely mathematical objects. Many authors on this subject have a view contrary to mine. They agree (as you and DaleSpam agree) that the universe is 4-dimensional, occupied by 4-dimensional objects, but disagree about the nature (or essence) of the 4th dimension, believing that the 4th dimension is pure time (pure time meaning there is no physically spatial character to it). Here is an excerpt from a note in Petkov's paper that illustrates this, using the term, "spatial" in exactly the same sense that I've been using it:

http://philsci-archive.pitt.edu/2408/1/Petkov-BlockUniverse.pdf

Foot note: It might appear tempting to regard the temporal dimension as not entirely given, but if this were the case spacetime would not be four-dimensional { one cannot talk about a four-dimensional entity if all dimensions are not equally existent. Spacetime is not like space since the nature of the temporal dimension is different from the nature of the spatial dimensions, but this has nothing to do with the equal existence of all dimensions of spacetime (like the different nature of physical objects and phenomena has nothing to do with their existence). In this respect I completely share the position of Taylor and Wheeler regarding the temporal and spatial dimensions of spacetime: "Equal footing, yes; same nature, no." .

Notice that he has referenced Taylor Wheeler as embracing the same view that you and DaleSpam have insisted on. And again, I will say that the majority voice in the physics community holds this view, and I would not want to mislead the forum viewers on this. I just feel that the a physically spatial 4-dimensional universe is implied by special relativity and our conscious experience and observations.

If you disagree, please give an example of a dimension into which an object can extend which would not be "spatial" by your definition.

If it is a real 4-dimensional physical object and is physically extended out of X1, X2, X3, (our real 3-D space) then yes, in that case the physcal extension means that the physical object is occupying a real 4-dimensional space.

Now, we can certainly identify mathematical dimensions and think abstractly about obects extending into those mathematical dimensions. We can envision a configuration space, etc. So, you are right, there are certainly other contexts for using the term "space." I just thought everyone would understand the context in which I had applied the term.

You can even use "time" as the 4th dimension in a mathematical sense. 4-dimensional objects (mathematical objects) can occupy that 4-dimensional mathematical space in the context of that mathematical construct. But, in that example, the 4-dimensional object is not a real physically spatial 4-D object if you are explicitly denying physical spatial extent to the 4th dimension (as Petkov did in his footnote--and as you, DaleSpam, Taylor, and Wheeler are doing).

And since for something to be a "dimension" at all, an object must be able to extend into it, that means the bolded phrase above requires that all dimensions must be spatial. If you disagree, please give an example of something you would call a "dimension" that an object cannot extend into.

Again, not all dimensions are spatial (and now I should always make sure I'm communicating by using the term, "physically spatial"). An example would be the frequencies in the spectrum of a discrete Fourier transform. Each frequency index (the numbers corresponding to the sequence of frequencies) could be associated with an N-dimensional orthogonal space of frequencies, i.e., X1, X2, X3, ... XN. We will call it "Frequency Space." We can use the amplitudes, Ai, of the Fourier spectrum and describe the state of a spectrum by an abstract displacement vector, X, whose distance would be square root of $\Sigma$Xi2

 

[George Jones]

I have closed this thread, since this 85-post thread contains little physics.