Block Time vs Q. Indeterminacy [Archive]

bobc2

Nov20-11, 09:15 AM

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

Nov20-11, 09:18 AM

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, spacial 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

Nov20-11, 09:52 AM

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

Nov20-11, 10:05 AM

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. :smile:

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

Nov20-11, 04:36 PM

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

Nov20-11, 04:59 PM

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

Nov20-11, 06:38 PM

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."
http://i209.photobucket.com/albums/bb185/BobC_03/SR_Coordinates_PythagoreanTheorem.jpg

PeterDonis

Nov20-11, 08:22 PM

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

Nov20-11, 08:26 PM

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

Nov21-11, 06:46 AM

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

Nov21-11, 07:09 AM

...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"?:rofl:

bobc2

Nov21-11, 07:19 AM

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

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

Nov21-11, 07:58 AM

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 http://www.youtube.com/watch?v=WKsNraFxPwk '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

Nov21-11, 09:11 AM

Just for fun looked at a YouTube video by Barbour http://www.youtube.com/watch?v=WKsNraFxPwk '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

Nov21-11, 09:23 AM

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

Nov21-11, 10:32 AM

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

Nov21-11, 11:00 AM

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

Nov21-11, 11:43 AM

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

Nov21-11, 11:47 AM

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

Nov21-11, 12:15 PM

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 spacial cordinates are + and time is -?

PeterDonis

Nov21-11, 12:44 PM

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

And what is -+++? is that spacial 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

Nov21-11, 02:39 PM

(-+++) 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

Nov21-11, 03:20 PM

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

Nov21-11, 03:36 PM

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

Nov21-11, 05:32 PM

(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:

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

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

nitsuj

Nov21-11, 08:24 PM

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:

http://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

Nov21-11, 08:44 PM

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

Nov21-11, 09:00 PM

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

Nov23-11, 02:33 AM

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

Nov23-11, 07:34 AM

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

Nov23-11, 09:14 AM

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

Nov23-11, 09:24 AM

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

Nov23-11, 06:45 PM

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 http://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

Nov23-11, 07:12 PM

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 http://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

Nov23-11, 07:15 PM

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

Nov24-11, 06:54 PM

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

Nov24-11, 09:43 PM

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

Nov24-11, 09:51 PM

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 spacial 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 :smile:

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

Nov24-11, 09:54 PM

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

Nov25-11, 10:13 AM

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

Nov25-11, 10:22 AM

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?

nitsuj

Nov25-11, 12:08 PM

Why not?

Simply because I can't picture it.

I could from the point of veiw of there being only 2 spacial dimensions and one time. Said differently that the sum of individual "Now Slices" make up 3D (and only because time "plays out" / distance).

Now that I can picture the Spacetime diagram from 1 space dimension through to the 3 there are, I cannot see how the block universe "plays out" in time has three spacial dimensions.

The "present" moment surrounds me as a sphere. There is no "this direction future" that "direction past". Perhaps from a concious perspective it could be thought of as future is out there (outside what ever one would define as the present moment sphere) and the past is merely the memory. Ah, the future "comes in" / "falls onto" the observer from all directions, there's no "room" for the past lol.

I may be wrong with my understanding of block universe, among a number of other things :)

EDIT: I guess I'm not buying the block universe concept moslty because of the spacial dimensions. I don't see three spacial ones in the block universe. Im going to read some more about it to try and see how it is 3 spacial dimensions and a time one, but I don't think it's there. Just can't see how.

PeterDonis

Nov25-11, 12:57 PM

Simply because I can't picture it.

Obviously you can't picture a 4-dimensional thing with a mind that's only able to visualize 3 dimensions. What does that have to do with the physics?

EDIT: I guess I'm not buying the block universe concept moslty because of the spacial dimensions. I don't see three spacial ones in the block universe. Im going to read some more about it to try and see how it is 3 spacial dimensions and a time one, but I don't think it's there. Just can't see how.

One of the reasons we invented mathematics was to be able to reason in areas where we can't trust our intuitive capacities, such as "visualizing" things. Mathematically, 4-D spacetime is just 3-D spacetime (2 spatial plus 1 time), which you have said is perfectly OK, with one more spatial dimension added. Adding the one more spatial dimension creates no problems at all, mathematically; the model is still perfectly consistent and the tools for dealing with it still work perfectly well.

To make things as simple as possible, try starting with plain flat Minkowski spacetime, the full 4-D ("3+1") version. The metric is:

d\tau^{2} = dt^{2} - dx^{2} - dy^{2} - dz^{2}

The corresponding "2+1" version is:

d\tau^{2} = dt^{2} - dx^{2} - dy^{2}

What's the problem with adding the - dz^{2}?

nitsuj

Nov25-11, 01:28 PM

Obviously you can't picture a 4-dimensional thing with a mind that's only able to visualize 3 dimensions. What does that have to do with the physics?

Nice tone peter. In that sense, what does physics have to do with reality then?

When you say we can't visualize a 4 dimensional thing 'cause we're only able to visualize 3 dimensions, leads to the point of confusion over time as a dimension. I don't think a dimension (specifically time) is necessarily spacial. So with that being said...

I can easily visualize the 3 spacial dimensions and another for the interval between me and whatever else I see. Or that whatever I see, it will always be cause first, then effect no matter how fast I move to try and exceed my present moment.

My comments are regarding intupreting the block universe visualy as being a 4D spacetime continuum. I can't see it. I dislike the concept more then before. But I still wanna read more about it. But not from PF threads, too heated/biased.

PeterDonis

Nov25-11, 01:33 PM

My comments are regarding intupreting the block universe visualy as being a 4D spacetime continuum. I can't.

Yes, I can't visualize all four dimensions at once either. If that's all you are saying then I'm confused about why you said the block universe concept "doesn't pass the smell test", since that implies that you think it's not valid physics, not just that you can't visualize it.

I can easily visualize the 3 spacial dimensions and an other for the interval between me and whatever else I see.

If by "interval between me and whatever else I see" you mean "interval between the 3 dimensional slice I call 'now' and some other 3 dimensional slice from which the light I am seeing 'now' was emitted", then I don't think this is any different from the 4-D "block universe", except insofar as some people who talk about the "block universe" talk about it as though any concept of 4-D spacetime required complete determinism, which it doesn't.

nitsuj

Nov25-11, 04:10 PM

Yes, I can't visualize all four dimensions at once either. If that's all you are saying then I'm confused about why you said the block universe concept "doesn't pass the smell test", since that implies that you think it's not valid physics, not just that you can't visualize it.

If by "interval between me and whatever else I see" you mean "interval between the 3 dimensional slice I call 'now' and some other 3 dimensional slice from which the light I am seeing 'now' was emitted", then I don't think this is any different from the 4-D "block universe", except insofar as some people who talk about the "block universe" talk about it as though any concept of 4-D spacetime required complete determinism, which it doesn't.

Oh I see now, my comment about it not passing the smell test is far from an interpretation of the block universe from the perspective of a seasoned physicist. Is it valid physics? In this sense I haven't the slightest clue how to determine what is valid physics and what isn't.

Seems too strange to be able to say litteraly, the start of the universe is on one side of me, the future of it, on the other side of me. Any hoo, ima read more about block universe, since I don't doubt your belief in the block universe.

stglyde

Nov25-11, 05:12 PM

Nice tone peter. In that sense, what does physics have to do with reality then?

When you say we can't visualize a 4 dimensional thing 'cause we're only able to visualize 3 dimensions, leads to the point of confusion over time as a dimension. I don't think a dimension (specifically time) is necessarily spacial. So with that being said...

I can easily visualize the 3 spacial dimensions and another for the interval between me and whatever else I see. Or that whatever I see, it will always be cause first, then effect no matter how fast I move to try and exceed my present moment.

My comments are regarding intupreting the block universe visualy as being a 4D spacetime continuum. I can't see it. I dislike the concept more then before. But I still wanna read more about it. But not from PF threads, too heated/biased.

Just imagine 4 dimensional space and time as absolute. Only time and space are relative. If you are stationary in space, all energy is allocated for time so your time moves fast. If you now move in space, some of the enegy for time is allocated for space so time slows down. Now block time is simply cutting the absolute 4D spacetime in different angles. This is one good quick way to visualize spacetime.

nitsuj

Nov25-11, 06:22 PM

Just imagine 4 dimensional space and time as absolute. Only time and space are relative. If you are stationary in space, all energy is allocated for time so your time moves fast. If you now move in space, some of the enegy for time is allocated for space so time slows down. Now block time is simply cutting the absolute 4D spacetime in different angles. This is one good quick way to visualize spacetime.

Is that all that's meant by block universe? I completely agree with that description. Seems to be the way it is. (leaving out things like "energy is allocated for time..." idk what that means, but am aware of the term 4 velocity, and leaving out 4D space, i think it's only 3D and spacetime 4D)

I thought block universe also implied that the future and past are equally as "real" as the present. And from there things like traveling to the past come up, and that's why I [had] disliked the concept.

When I pictured a light cone as a sphere, it really made it clear only the future is out "there" lol, so that's why i said block universe doesn't pass the smell test.

Out of future, past, present & time, the past seems to be the only thing that's an "illusion". I guess for me that's what really muddied the water trying to understand what time is. There's future and present / cause and effect, but no "past". (the past spacetime is still there of course)

Oh lol, that's why it's called a continuum right? cause-effect-cause-effect....

PeterDonis

Nov25-11, 08:08 PM

I thought block universe also implied that the future and past are equally as "real" as the present. And from there things like traveling to the past come up, and that's why I [had] disliked the concept.

That's what I was trying to clarify, what you thought didn't pass the "smell test".

I think of it this way: a "block universe" is a mathematical model that describes a *possible* 4-D spacetime. But to correlate this model with the real world, we have to divide it, conceptually, into three portions.

(1) A portion of this 4-D spacetime is already known to correspond with the real world; that's the part we call the "past". This is the portion that's in the past light cone of the point in the model that corresponds to where we are here and now. This portion of the model cannot change, in the sense that it specifies a single set of conditions that must be fulfilled by *any* possible 4-D model of the complete spacetime. But what's in our past light cone is not sufficient to pick out a single unique 4-D model for the entire spacetime, so we have to consider a number of "possible" models.

(2) Another portion of this 4-D spacetime is the part that we can affect, causally, from here and now. This is the part we call the "future", and decisions we make here and now can "change" it, so we think of it as not being fixed. But in order to "change" it, we have to change the conditions here and now, and that means the model changes; we have to re-compute what the future will be from the changed conditions, and that gives us a *different* 4-D spacetime, which is now our "best estimate" of what block universe is the "real" one (out of all the "possible" ones that are consistent with our knowledge up to now).

(3) The third portion of this 4-D spacetime is not known by us, here and now, to correspond with the actual world, because it's outside of our past light cone; but we also can't affect it causally, because it's outside of our future light cone. The only thing we can do is to compute, based on what we know of our past light cone, what this portion "should" look like; but at any time, we might have new information come to us, as more of this region comes within our past light cone, that forces us to re-compute. And again, every time we re-compute, that yields a *new* 4-D spacetime that becomes our new best estimate of what block universe is the real one.

So each block universe, considered as a single 4-D model of a possible spacetime, is fixed; but we don't know exactly which possible 4-D model corresponds to reality; the best we can do is to estimate it based on the information we have and the decisions we make. A portion of each model we compute is fixed--the part that corresponds to our past light cone. But the rest of it can vary based on our decisions and on information coming in from regions that were spacelike separated from us until just now.

bobc2

Nov26-11, 09:38 AM

As I asked earlier:

I wish. I would really like to see a 4-dimensional spatial universe dispelled. Then, we would be left with just deep mystery--something I could handle. It would be more comfortable to have just the mystery as compared to the spectre of implications that come along with the 4-dimensional space-space and still have mystery lingering.

No, I can't yet shake the 4-D space-space. But, PeterDonis did a credible job of flagging my blunder of identifying the Affine Space as a metric space.

Now, I just need PeterDonis to build the mathematical machinery properly, beginning with a R4 manifold and positive definite metric that allows me to freely choose coordinates (without resorting to Minkowski's imaginary ict). We then establish a 4-D orthonomal vector space consistent with defining Pythagorean Theorem distances in the coordinate system.

I would then try to visualize a simple example universe having two straight line 4-D objects that each begin at the orgin of the orthonormal coordinate system, tracing out world lines angled symmetrically about the 4th dimension of the orthonormal vector space. One object is rotated counter-clockwise 22.5 degrees, and the other object is rotated clockwise by 22.5degrees. PeterDonis would have to give us the field theory that allows a correct mathematical accounting of the 4-D objects.

At this point we are saying nothing about time and nothing about observers. There are no affine X1 coordinates established--and no charts--unless PeterDonis insists that we cannot have two 4-D objects in our universe without a chart. In that case we would have to let the two objects define the chart.

Now, I would want to choose another set of orthonormal coordinates, X1' and X4', rotated counter-clockwise by 22.5 degrees relative to the original orthonormal coordinates (X4' is rotated 22.5 degrees counter-clockwise to X4, and X1' is rotated 22.5 degrees counter-clockwise to X1).

We now pick a point on the clockwise rotated 4-D object and note that the distance from the orgin to the point is invariant--it can be determined equally well with either X1 and X4 or X1' and X4'.

If PeterDonis O.K.'s things so far, we can continue the pursuit of the affine space mapped onto the orthonormal cartesian space. (we still don't have any observers in our universe)

PeterDonis

Nov26-11, 02:46 PM

Now, I just need PeterDonis to build the mathematical machinery properly, beginning with a R4 manifold and positive definite metric

Why do you keep insisting on a positive definite metric? The whole point of Minkowski spacetime is that the metric is *not* positive definite. That's what you need to describe a *spacetime* as opposed to a *space*.

nitsuj

Nov26-11, 03:45 PM

stglyde

Nov26-11, 04:20 PM

With bob2c's last post I noticed another difference between block universe and the way I interpret spacetime diagrams. I think space is only 3 spacial dimensions which all share the quality of the same limited speed.

Don't ever forget that spacetime doesn't really exist like a particle or field do. When asked by reporters to summarize his theory, Einstein said: "People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that
space and time would disappear along with matter."

So it's just matter relationship with one another that we artifically called spacetime and model it as a 4th dimensional differential manifold which is not really there.

bobc2

Nov26-11, 05:42 PM

Why do you keep insisting on a positive definite metric? The whole point of Minkowski spacetime is that the metric is *not* positive definite. That's what you need to describe a *spacetime* as opposed to a *space*.

It seems necessary for a 4-dimensional space-space (not space-time). Time should be nothing more than a parameter, playing exactly the same role as passage of time in the 3-D world. It seems elemental, given the different special relativity 3-D cross-sections that four spatial dimensions must be available for those views.

The Minkowski ict takes away the spatial equivalence of the 4th dimension in special relativity.

nitsuj

Nov26-11, 06:43 PM

Don't ever forget that spacetime doesn't really exist like a particle or field do. When asked by reporters to summarize his theory, Einstein said: "People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that
space and time would disappear along with matter."

So it's just matter relationship with one another that we artifically called spacetime and model it as a 4th dimensional differential manifold which is not really there.

I never learned that spacetime doesn't exist?

It does exist, so I'm not sure in what sense you mean.

Who cares what Einstein told a reporter. (it seems like his point is regarding the role of calculating in defining, without objects to measure you can't determine spacetime's properties, from a physics perspective it's as if it doesn't exist. You need two to tango in other words :smile:). I read that his theory implies spacetime is real and exists. It's properties effect everything.

stglyde

Nov26-11, 07:01 PM

I never learned that spacetime doesn't exist?

It does exist, so I'm not sure in what sense you mean.

Who cares what Einstein told a reporter. I read that his theory implies spacetime is real and exists. It's properties effect everything.

Have you forgotten the thread "Spacetime doesn't really exist does it?"
http://www.physicsforums.com/showthread.php?t=487794&highlight=spacetime+doesn%27t+exist where you also participated? Someone there said:

"GR doesn't really describe gravity in terms of a field. GR deals with tensors, and the gravitational field is not a tensor. GR describes a gravitational wave as an oscillating curvature of spacetime."

Look spacetime is in same company as wavefunction, they are just mathematical abstraction.

Spacetime is just a 4 dimensional differential manifold.. curvature and other geometrical aspects are what producing "gravity". This means things like gravitational field as just PUN some love to say.

Now about Matter. Wave function is just a mathematical abstraction. It is all math. Large scale "things" are just results of decoherence of the mathematical wave functions.

Also Particles are just energy and momentum of the fields... or as Rovelli suggested.. "QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local
operators."

Even virtual particles are just multi variate integrals, just purely mathematical artifacts as Neumaier emphasized.

btw... "don't exist" means no spacetime substrate.. for example... no "aether" substrate or "pilot wave" substrate... spacetime "aether" concept has problems with event horizons and pilot wave has problems with lorentz symmetry.. but if they can solve it.. then aether and pilot wave can be the substrate and make spacetime/matter "exist" in the sense there is a "material substrate".. but for now.. they are less likely....

In short, if you believe spacetime exist. Then you believe in spacetime aether? But it doesn't tally with the observations in event horizons in black holes.. so it's not likely.

PeterDonis

Nov26-11, 07:14 PM

It seems necessary for a 4-dimensional space-space (not space-time).

I think you're missing the point. The 4-dimensional manifold we live in is a space-time, *not* a space-space. It has one timelike dimension and three spacelike dimensions. It has a metric that is not positive definite. These statements are invariant statements of physics; they do not depend on describing the timelike dimension using a "time" parameter. (For example, we can describe spacetime using null coordinates, which replace the timelike coordinate and one spacelike coordinate with a pair of null coordinates. But physically spacetime is still the same, just described differently.) So the 4-D manifold we live in is different, *physically*, than a 4-D space-space with a 4-D positive definite metric. You can't model the former with the latter.

Time should be nothing more than a parameter, playing exactly the same role as passage of time in the 3-D world.

I'm not sure I understand what you mean by this.

It seems elemental, given the different special relativity 3-D cross-sections that four spatial dimensions must be available for those views.

No, this is wrong. What the different SR cross-sections show us is that four *spacetime* dimensions must be available--three spacelike and one timelike (or, alternatively, as I said above, two spacelike and two null, which is physically the same thing). The different SR cross sections are *inconsistent* with there being four *spatial* dimensions, because the SR cross sections require a Minkowski metric, i.e., not positive definite. This is a genuine physical difference; you can't handwave it away.

PeterDonis

Nov26-11, 07:23 PM

Have you forgotten the thread "Spacetime doesn't really exist does it?"
http://www.physicsforums.com/showthread.php?t=487794&highlight=spacetime+doesn%27t+exist where you also participated? Someone there said:

"GR doesn't really describe gravity in terms of a field. GR deals with tensors, and the gravitational field is not a tensor. GR describes a gravitational wave as an oscillating curvature of spacetime."

You should be careful interpreting this statement. If I'm wrong, bcrowell can jump in here and correct me, but I strongly suspect that by "gravitational field" in that statement he meant something like the "acceleration due to gravity", which is not a tensor. However, the "curvature of spacetime" *is* a tensor, the Riemann curvature tensor, and it's oscillations in that tensor that describe gravitational waves. I seriously doubt that bcrowell meant to imply that gravity, in the sense of spacetime curvature, and spacetime itself were not "real".

In short, if you believe spacetime exist. Then you believe in spacetime aether?

This is a non sequitur. Believing that spacetime "exists" does not require believing that there is some non-dynamical "background" portion of spacetime that does not interact with matter.

stglyde

Nov26-11, 07:37 PM

You should be careful interpreting this statement. If I'm wrong, bcrowell can jump in here and correct me, but I strongly suspect that by "gravitational field" in that statement he meant something like the "acceleration due to gravity", which is not a tensor. However, the "curvature of spacetime" *is* a tensor, the Riemann curvature tensor, and it's oscillations in that tensor that describe gravitational waves. I seriously doubt that bcrowell meant to imply that gravity, in the sense of spacetime curvature, and spacetime itself were not "real".

This is a non sequitur. Believing that spacetime "exists" does not require believing that there is some non-dynamical "background" portion of spacetime that does not interact with matter.

but spacetime aether is dynamical.. see:
http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.1547v2.pdf

My understanding is that if spacetime exist.. it should be a "thing".. but if it doesn't.. meaning it is just mathematical abstraction like wave function.. then it isn't a thing.. unless you meant spacetime is like a particle that has independent existence? but if spacetime points are real... then diffeomorphism invariance (general covariance) is wrong.. so how can spacetime be anything other than mathematical abstraction?

PeterDonis

Nov26-11, 08:13 PM

but spacetime aether is dynamical.. see:
http://arxiv.org/PS_cache/arxiv/pdf/0801/0801.1547v2.pdf

Ah, ok, that clarifies what you meant by "ether" (the term has a lot of meanings). Then my response is, believing that spacetime exists does not require believing that there is a preferred "rest frame" at the quantum gravity level.

if spacetime points are real... then diffeomorphism invariance (general covariance) is wrong..

I don't see how this follows. General covariance just means that we can describe the spacetime manifold using any coordinate chart we like; in other words, that the physics of spacetime is independent of how we label the points in the spacetime with coordinates. It says nothing at all about whether the manifold itself, or the points in it, are "real". The latter question depends on what you mean by "real", but since we can measure the curvature of the spacetime manifold (as tidal gravity), it seems unproblematic to me to say that the manifold is real.

bobc2

Nov26-11, 08:14 PM

...This is a non sequitur. Believing that spacetime "exists" does not require believing that there is some non-dynamical "background" portion of spacetime that does not interact with matter.

The post evoking this response was not mine. I'm not sure how it came out as my post.

stglyde

Nov26-11, 08:21 PM

Ah, ok, that clarifies what you meant by "ether" (the term has a lot of meanings). Then my response is, believing that spacetime exists does not require believing that there is a preferred "rest frame" at the quantum gravity level.

I don't see how this follows. General covariance just means that we can describe the spacetime manifold using any coordinate chart we like; in other words, that the physics of spacetime is independent of how we label the points in the spacetime with coordinates. It says nothing at all about whether the manifold itself, or the points in it, are "real". The latter question depends on what you mean by "real", but since we can measure the curvature of the spacetime manifold (as tidal gravity), it seems unproblematic to me to say that the manifold is real.

Are you familiar with the Hole Argument?

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

"Einstein believed that the hole argument implies that the only meaningful definition of location and time is through matter. A point in spacetime is meaningless in itself, because the label which one gives to such a point is undetermined. Spacetime points only acquire their physical significance because matter is moving through them."

In other words. Spacetime points shouldn't be made of substance or General Invariance won't work. Now if Spacetime points are not substantive but just merely mathematical abstraction, then it may not have any independent existence. Without any matter/energy/stress.. do you think there would be spacetime?

PeterDonis

Nov26-11, 08:38 PM

Are you familiar with the Hole Argument?

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

Did you read this in the introduction to that same Wikipedia article:

It [the hole argument] is incorrectly interpreted by some philosophers as an argument against manifold substantialism, a doctrine that the manifold of events in spacetime are a "substance" which exists independently of the matter within it. Physicists disagree with this interpretation, and view the argument as a confusion about gauge invariance and gauge fixing instead.

In other words, the hole argument does not show that general covariance is inconsistent with spacetime being a "real thing". All it shows is that GR is a gauge theory.

Without any matter/energy/stress.. do you think there would be spacetime?

Minkowski spacetime, with zero stress-energy tensor everywhere, is a solution of the Einstein Field Equation, so yes, there is at least one possible "spacetime" without any matter/energy/stress. Einstein, when he made that statement to reporters that you quoted, either didn't think of that or conveniently ignored it because he didn't want to try to go into subtleties in that context (for which I can't blame him).

In other writings, IIRC, Einstein argued that Minkowski spacetime was not a counterexample to claims of the sort he made in your quote, because it required asymptotic flatness as a boundary condition, which was an extra physical assumption over and above the EFE, since the EFE doesn't explain how the boundary condition "at infinity" comes into being. In essence, he argued that the only way to truly satisfy the conditions he described in what you quoted was for the universe as a whole to be closed, so the question of boundary conditions "at infinity" would not arise. Hawking seems to believe something similar with his "no boundary" proposal for quantum cosmology.

Bottom line, I think the question you posed in what I quoted above is a physical question on which the jury is still out. GR, as it stands, is compatible with either alternative, since it has both closed solutions and solutions with boundary conditions at infinity. (More precisely, whichever solution we end up adopting at the quantum gravity level, there will be a GR model that will work as the classical limit of that solution.)

stglyde

Nov26-11, 08:41 PM

Did you read this in the introduction to that same Wikipedia article:

In other words, the hole argument does not show that general covariance is inconsistent with spacetime being a "real thing". All it shows is that GR is a gauge theory.

Minkowski spacetime, with zero stress-energy tensor everywhere, is a solution of the Einstein Field Equation, so yes, there is at least one possible "spacetime" without any matter/energy/stress. Einstein, when he made that statement to reporters that you quoted, either didn't think of that or conveniently ignored it because he didn't want to try to go into subtleties in that context (for which I can't blame him).

In other writings, IIRC, Einstein argued that Minkowski spacetime was not a counterexample to claims of the sort he made in your quote, because it required asymptotic flatness as a boundary condition, which was an extra physical assumption over and above the EFE, since the EFE doesn't explain how the boundary condition "at infinity" comes into being. In essence, he argued that the only way to truly satisfy the conditions he described in what you quoted was for the universe as a whole to be closed, so the question of boundary conditions "at infinity" would not arise. Hawking seems to believe something similar with his "no boundary" proposal for quantum cosmology.

Bottom line, I think the question you posed in what I quoted above is a physical question on which the jury is still out. GR, as it stands, is compatible with either alternative, since it has both closed solutions and solutions with boundary conditions at infinity. (More precisely, whichever solution we end up adopting at the quantum gravity level, there will be a GR model that will work as the classical limit of that solution.)

To clarify my point. Is the wave function real in the sense that there are really physical (or whatever) waves that interfere before say the double slit electron reach the detector? There isn't. So is Spacetime. Nothing is curving there in space or time. It is just a math model like wave function. Spacetime is not the territory but just a map.. and they say not to mistake map for territory.

We don't know how such complex mathematical abstraction like wave function and spacetime connect to our world and physicists don't care. Physics is just studying the math models with a a huge disconnect in correponding to our reality. Agree?

PeterDonis

Nov26-11, 09:00 PM

To clarify my point. Is the wave function real in the sense that there are really physical (or whatever) waves that interfere before say the double slit electron reach the detector? There isn't.

That's another physical question on which the jury is still out. There is certainly a large school of thought in quantum physics that believes this, but it is not established the way, say, the Earth going around the Sun is.

So is Spacetime. Nothing is curving there in space or time. It is just a math model like wave function.

Tidal gravity is not "just a math model". It's a physical observable. It is true that one is not *forced* to model tidal gravity using a curved spacetime; one could use another model. But in the context of that model, "spacetime curvature" is simply another name for "tidal gravity", so if tidal gravity is real (which it is), then spacetime curvature is real.

Spacetime is not the territory but just a map.. and they say not to mistake map for territory.

Yes, but that does not mean that nothing named on the map is real. The United States of America is also part of a map; there is nothing in the territory that carries intrisic labels saying "this belongs to the USA". Does that mean the USA is not real?

This kind of discussion can degenerate very quickly into philosophy instead of physics. The map-territory distinction is supposed to forestall such degeneration, not cause it. The map is not the territory, but the reason for having a map is to guide you through the territory. You can't make use of the map that way if you don't think of the things the map is labeling as real.

We don't know how such complex mathematical abstraction like wave function and spacetime connect to our world...

Certainly we do. We use these complex mathematical abstractions to make predictions that are confirmed to many decimal places. That requires a deep knowledge of how they connect to our world.

...and physicists don't care. Physics is just studying the math models with a a huge disconnect in correponding to our reality. Agree?

No. This kind of statement needs a *huge* amount of support which you have not given, and which I don't see how you could give in view of the predictive accuracy of our models which I have just referred to.

stglyde

Nov26-11, 09:09 PM

That's another physical question on which the jury is still out. There is certainly a large school of thought in quantum physics that believes this, but it is not established the way, say, the Earth going around the Sun is.

Tidal gravity is not "just a math model". It's a physical observable. It is true that one is not *forced* to model tidal gravity using a curved spacetime; one could use another model. But in the context of that model, "spacetime curvature" is simply another name for "tidal gravity", so if tidal gravity is real (which it is), then spacetime curvature is real.

Yes, but that does not mean that nothing named on the map is real. The United States of America is also part of a map; there is nothing in the territory that carries intrisic labels saying "this belongs to the USA". Does that mean the USA is not real?

This kind of discussion can degenerate very quickly into philosophy instead of physics. The map-territory distinction is supposed to forestall such degeneration, not cause it. The map is not the territory, but the reason for having a map is to guide you through the territory. You can't make use of the map that way if you don't think of the things the map is labeling as real.

Certainly we do. We use these complex mathematical abstractions to make predictions that are confirmed to many decimal places. That requires a deep knowledge of how they connect to our world.

No. This kind of statement needs a *huge* amount of support which you have not given, and which I don't see how you could give in view of the predictive accuracy of our models which I have just referred to.

Hmm...

Anyway back to Block Spacetime. Is it a consensus that the past no longer exist or is it only your belief? I just saw Michio Kaku in TV describing how to go back in time.. how come they keep saying this when the past no longer exist? Any idea of how many percentage of physicists share your view, etc.?

PeterDonis

Nov26-11, 09:15 PM

Is it a consensus that the past no longer exist or is it only your belief? I just saw Michio Kaku in TV describing how to go back in time.. how come they keep saying this when the past no longer exist? Any idea of how many percentage of physicists share your view, etc.?

With regard to what physicists believe, as far as I know, all of this talk about going back in time is speculative (certainly the stuff I usually see Michio Kaku saying when he does TV specials is speculative); no physicist claims that we *can* time travel to our past, and no physicist claims to know for certain that it's impossible. It's just speculation.

stglyde

Nov26-11, 09:31 PM

With regard to what physicists believe, as far as I know, all of this talk about going back in time is speculative (certainly the stuff I usually see Michio Kaku saying when he does TV specials is speculative); no physicist claims that we *can* time travel to our past, and no physicist claims to know for certain that it's impossible. It's just speculation.

About general invariance.. it is synonymous to diffeomorphism invariance isn't it.. although other physicists use diffeo morph to mean background independence (no prior geometry). Which do you use?

So far have we actually confirmed general invariance (diffeo morph) in experiments? What experiments actually do that?

I'm interested in local lorentz invariance in quantum gravity studies. General Relativity is not compatible with QM so GR may just be lower limit of a more primary theory. What is your favorite primary theory and Why?

bobc2

Nov26-11, 10:43 PM

I think you're missing the point. The 4-dimensional manifold we live in is a space-time, *not* a space-space. It has one timelike dimension and three spacelike dimensions. It has a metric that is not positive definite.

No. The R4 manifold we live in is space-space and positive definite. I thought you would show us, based on this, the rigorous mathematical procedure for arriving at the coordinate transformations that apply to a special relativity approach to describing our physical experience in the manifold. The physical objects present on the manifold are independent of the manifold and its metric space.

I can lay out a big sheet of paper on the table with a cartesian chart having an X1 horzontal axis and a X2 axis. Then, I arbitrarily place pencils, rulers, sticks, etc. on the paper with random orientations. It would be difficult to find an easy mathematical representation of the object locations, orientations and their relatedness.

On the other hand, I can place objects on the grid in very special thought-out patterns that are ordered in a special way. It may be difficult to describe the positions and orientations of the objects using the cartesian coordinates. However, given the symmetries associated with the object placement, I can perhaps find a special system of coordinates,
X1' and X2', X1'' and X2'', etc., for mathematically expressing the positions and orientations of the objects--along with relatedness among the objects. If the objects are all long, and if they are all generally oriented with their long directions at less than 45 degrees with respect to the cartesian X2 direction, the new X2' and X2'', etc., coordinates would be special as compared to the X1, X1', X1'', etc.

The 4-dimensional positive definite manifold with 4-D objects populating the manifold, lying along 4-D world lines should be viewed the same way.

These statements are invariant statements of physics; they do not depend on describing the timelike dimension using a "time" parameter. (For example, we can describe spacetime using null coordinates, which replace the timelike coordinate and one spacelike coordinate with a pair of null coordinates. But physically spacetime is still the same, just described differently.)

But, they were arbitrarily chosen. And without time as a parameter, along world lines, you are left without a physically understood picture of reality. It's easy to talk about time as the 4th dimension (or some ill-defined mixture of space and time), but in reality no one has the foggiest idea what that means physically. However, a 4-dimensional space with time passing as a parameter as some aspect of the observer moves along the 4th spatial dimension at the speed of light--is a concept that can be envisioned. Without 4 spatial dimensions, you really don't know what you've got for reality--except as an abstract mathematical description.

So, the 4-D manifold we live in is different, *physically*, than a 4-D space-space with a 4-D positive definite metric.

No. I agree that you can model physics with the Minkowski metric. But, that seems arbitrary and contrived. And it gives us a physical picture that is really not comprehensible (on one really knows what it means to have time as a physical dimension). So, in that sense the Minkowski manifold is different from what we live in.

We don't need an R4 manifold other than positive definite with a Euclidean orthonormal basis chart. The coordinate space we live in can be obtained through coordinate transformations.

You can't model the former with the latter.

Why can't you do it with coordinate transformations? We do it with curves on a sheet of paper all of the time. We start with cartesian coordinates and then draw in hyperbolic curves and affine coordinates, etc.

I'm not sure I understand what you mean by this.

We use parametric equations all the time--for example, to describe motion of projectiles in 3-D space, i.e., Y(t) and X(t). Time is just a parameter along the world lines in exactly the same sense.

No, this is wrong. What the different SR cross-sections show us is that four *spacetime* dimensions must be available--three spacelike and one timelike (or, alternatively, as I said above, two spacelike and two null, which is physically the same thing). The different SR cross sections are *inconsistent* with there being four *spatial* dimensions, because the SR cross sections require a Minkowski metric, i.e., not positive definite. This is a genuine physical difference; you can't handwave it away.

Time is not needed at all to describe the 4-dimensional universe populated with 4-dimensional objects. Although, it is useful in computing distances along world lines, since obervers are "moving" along world lines at c. But, from the "birds eye view" you alluded to in an earlier post, you can remove consciousness from the observers (which are, from the "birds" view, after all, just 4-D objects) and the super hyperspace "bird" just sees a static 4-dimensional structure. It would never occur to the "bird" that he would need anything other than an R4 manifold with an orthonormal basis set along with appropriate transformations to describe what he is viewing.

PatrickPowers

Nov26-11, 11:35 PM

We can describe spacetime using null coordinates, which replace the timelike coordinate and one spacelike coordinate with a pair of null coordinates.

I find this most intriguing. Might you offer a reference?

PeterDonis

Nov26-11, 11:38 PM

About general invariance.. it is synonymous to diffeomorphism invariance isn't it.. although other physicists use diffeo morph to mean background independence (no prior geometry). Which do you use?

By "general covariance" I mean, as I said in a previous post, that you can describe spacetime using any coordinates you like. Since transformations between different coordinate systems are diffeomorphisms, this definition of general covariance is equivalent to diffeomorphism invariance of physical laws; i.e., valid physical laws must be expressible in a form that is diffeomorphism invariant. GR meets this requirement since it expresses all physical laws in terms of tensors and other geometric objects, which are diffeomorphism invariant.

I don't know for sure whether the above is equivalent to background independence or not. A physics that included "prior geometry" might still be expressible in diffeomorphism invariant terms. For example, suppose I have a theory that says that the "preferred frame" of the universe is the "comoving" frame in the standard FRW model, so that, for example, the motion of the Earth relative to this frame appears in physical laws. I could still write such laws in terms of tensors and other geometric objects; for example, I could express the motion of the Earth relative to the preferred frame as the contraction of the Earth's 4-momentum at a given event with a 4-vector normal to the spacelike hypersurface of constant comoving time t that contains that event. Such a law would be diffeomorphism invariant but would still express the presence of a preferred frame.

So far have we actually confirmed general invariance (diffeo morph) in experiments? What experiments actually do that?

How would you confirm diffeomorphism invariance in particular by doing experiments? The physical laws of GR are certainly confirmed very well, and those are expressible in diffeomorphism invariant terms. Does that count?

I'm interested in local lorentz invariance in quantum gravity studies. General Relativity is not compatible with QM so GR may just be lower limit of a more primary theory. What is your favorite primary theory and Why?

This is kind of getting off topic, but I agree that we are likely to find that GR is the classical, low energy limit of some quantum gravity theory that may look quite different. I don't have a "favorite" here because we have no experimental data in the regime where such a theory would be expected to show itself (particle energies approaching the Planck energy), so there are no constraints on such a theory other than the need to have GR as a low energy classical limit, which isn't a very tight constraint.

PeterDonis

Nov26-11, 11:39 PM

I find this most intriguing. Might you offer a reference?

Try this page for a start:

http://www.mathpages.com/rr/s1-09/1-09.htm

PeterDonis

Nov26-11, 11:40 PM

The post evoking this response was not mine. I'm not sure how it came out as my post.

That's weird, I'm not sure either. The editing window was still open on my post so I went back and fixed the quote. Sorry for the mixup.

PeterDonis

Nov27-11, 12:07 AM

No. The R4 manifold we live in is space-space and positive definite.

What is your basis for this claim? It seems obviously false to me since spacetime is locally Lorentz invariant, not Euclidean invariant, which is what your statement would imply. (Btw, by "basis" I mean "physical basis"--what physical experiments show you that we live in an R4 manifold with a positive definite metric?)

We use parametric equations all the time--for example, to describe motion of projectiles in 3-D space, i.e., Y(t) and X(t). Time is just a parameter along the world lines in exactly the same sense.

*Proper* time, yes. *Coordinate* time, no. In your terms, all four coordinates, including the "time" coordinate, are functions of the "time parameter" along a timelike curve, which I'll refer to as proper time since that's the standard term. More precisely, a parametrization of a timelike worldline in spacetime is a one-to-one mapping of proper time values to 4-tuples of coordinate values.

I did not mean to say that such a mapping was not possible or that it was not useful for understanding coordinate charts. It certainly is. But proper time should not be confused with coordinate time; they are two different things.

But, they were arbitrarily chosen. And without time as a parameter, along world lines, you are left without a physically understood picture of reality.

I agree with this to an extent. Coordinates, in general, are not physical observables; in some cases you can choose coordinate charts that match up well with certain symmetries of a spacetime and therefore can be more or less equated to certain physical observables, but those are special cases. Proper time, however, is an obvious physical observable: it can be directly read off clocks that follow a given worldline.

But proper time is not left out of the coordinate models I was describing; in fact, it's precisely the physical requirement of making sure the correct proper time is assigned to any given segment of a curve that makes the metric so important. And it's precisely the physical fact that not all curves are timelike that requires a non-positive definite metric; along a non-timelike curve, there is no proper time, and parametrizing such a curve cannot be done using a "time" parameter. You have to use a parameter that corresponds to something else, physically, besides proper time.

Why can't you do it with coordinate transformations? We do it with curves on a sheet of paper all of the time. We start with cartesian coordinates and then draw in hyperbolic curves and affine coordinates, etc.

Yes, and we interpret the lengths along the curves, physically, as lengths--*proper* lengths. But lengths are not times; they are physically different things. You can measure time in the same *units* as length, by using the speed of light as a conversion factor, but that does not make proper times the same, physically, as proper lengths. So if we want to use an R4 manifold to model the actual physical spacetime we live in, we cannot put a metric on it that only allows for one type of measure along a curve; there have to be three (timelike, spacelike, and null), and the measures for nearby curves have to be related in a way that preserves Lorentz invariance. A Euclidean, positive definite metric simply cannot model that.

Note, please, that I am not talking now about "time" or "space" as coordinates; I am talking about them as physical measures along curves. The physical measure along a timelike curve is proper time; the curve can be expressed, as I noted above, as a one-to-one mapping between proper time values and 4-tuples of coordinates, and we can label points on the curve by their proper time values and talk about them without ever using coordinates. But the physical measure along a spacelike curve is proper length, *not* proper time; it is a physically different thing. That is why our model needs to treat time and space differently: because the physical measure along timelike curves is fundamentally different than the physical measure along spacelike curves.

We don't need an R4 manifold other than positive definite with a Euclidean orthonormal basis chart. The coordinate space we live in can be obtained through coordinate transformations.

No, it can't, for the reasons given above.

Time is not needed at all to describe the 4-dimensional universe populated with 4-dimensional objects.

As a coordinate, no. As a measure along timelike curves, which is fundamentally different than the measure along spacelike curves, absolutely yes, it is. Otherwise the correspondence between the model and the real world, which you are so concerned about, is not there.

But, from the "birds eye view" you alluded to in an earlier post, you can remove consciousness from the observers (which are, from the "birds" view, after all, just 4-D objects) and the super hyperspace "bird" just sees a static 4-dimensional structure. It would never occur to the "bird" that he would need anything other than an R4 manifold with an orthonormal basis set along with appropriate transformations to describe what he is viewing.

It sure would, as soon as he tries to capture the physical difference between timelike and spacelike curves. That difference does not require conscious observers following the timelike curves.

stglyde

Nov27-11, 12:58 AM

By "general covariance" I mean, as I said in a previous post, that you can describe spacetime using any coordinates you like. Since transformations between different coordinate systems are diffeomorphisms, this definition of general covariance is equivalent to diffeomorphism invariance of physical laws; i.e., valid physical laws must be expressible in a form that is diffeomorphism invariant. GR meets this requirement since it expresses all physical laws in terms of tensors and other geometric objects, which are diffeomorphism invariant.

I don't know for sure whether the above is equivalent to background independence or not. A physics that included "prior geometry" might still be expressible in diffeomorphism invariant terms. For example, suppose I have a theory that says that the "preferred frame" of the universe is the "comoving" frame in the standard FRW model, so that, for example, the motion of the Earth relative to this frame appears in physical laws. I could still write such laws in terms of tensors and other geometric objects; for example, I could express the motion of the Earth relative to the preferred frame as the contraction of the Earth's 4-momentum at a given event with a 4-vector normal to the spacelike hypersurface of constant comoving time t that contains that event. Such a law would be diffeomorphism invariant but would still express the presence of a preferred frame.

Are you saying "prior geometry" is the same as "preferred frame"? This is getting confusing. Let us define the terms well so we can understand one another. In the Jan 2004 Sci Am cover story "Loop Quantum Gravity". It is defined thus (according to Smolin):

"In particular we kept two key principles of general relativity at the heart of our calculations.

The first is known as background independence. This principle says that the geometry of spacetime is not fixed. Instead the geometry is an evolving, dynamical quantity. To find the geometry, one has to solve certain equations that include all the effects of matter and energy. Incidentally, string theory, as currently formulated, is not background independent; the equations describing the strings are set up in a predetermined classical (that is, nonquantum) spacetime.

The second principle, known by the imposing name of diffeomorphism invariance, is closely related to background independence. This principle implies that, unlike theories prior to general relativity, one is free to choose any set of coordinates to map spacetime and express the equations. A point in spacetime is defined only by what physically happens at it, not by its location according to some special set of coordinates (no coordinates are special). Diffeomorphism Invariance is very powerful and is of fundamental importance in
General Relativity. "

You said diffeomorphism invariant can still be expressed in the presence of a preferred frame. Given Smolin input. You think diffeomorphism invariant can also be expressed in the presence of a background (background dependence or prior geometry)?

PatrickPowers

Nov27-11, 01:38 AM

Try this page for a start:

http://www.mathpages.com/rr/s1-09/1-09.htm

I notice that this the ninth section of a full-sized book. I have read the first four sections and this seems to be exactly what I've been looking for. It will take a while to work through.

atyy

Nov27-11, 08:15 AM

Let us define the terms well so we can understand one another. In the Jan 2004 Sci Am cover story "Loop Quantum Gravity". It is defined thus (according to Smolin):

...

The second principle, known by the imposing name of diffeomorphism invariance, is closely related to background independence. This principle implies that, unlike theories prior to general relativity, one is free to choose any set of coordinates to map spacetime and express the equations. A point in spacetime is defined only by what physically happens at it, not by its location according to some special set of coordinates (no coordinates are special). Diffeomorphism Invariance is very powerful and is of fundamental importance in
General Relativity. "

Smolin is wrong on a detail. Theories prior to general relativity can be expressed in diffeomorphism invariant form. As Andrade, Marolf and Deffayet (http://arxiv.org/abs/1010.2535v3) say, "The point here is that any local theory (e.g., a single free scalar field) can be written in diffeomorphism-invariant form through a process known as parametrization."

PeterDonis

Nov27-11, 11:40 AM

You said diffeomorphism invariant can still be expressed in the presence of a preferred frame.

Not quite. I said that a theory with a preferred frame *might* still be expressible in diffeomorphism invariant form, and I gave an example of how that *might* be possible. Basically, if it turns out that a theory with a preferred frame in it can still be expressed in any coordinates I choose, then it's still diffeomorphism invariant, even though it has a preferred frame.

Given Smolin input. You think diffeomorphism invariant can also be expressed in the presence of a background (background dependence or prior geometry)?

You'll note that Smolin does not say that background independence and diffeomorphism invariance are the same; he only says they're closely related. So it would appear that he would also admit the possibility that there could be a theory that was diffeomorphism invariant but not background independent. This is not to say that anyone actually has such a theory; just that the possibility means we should be careful about making dogmatic statements about what is "required" of a theory.

atyy

Nov27-11, 11:48 AM

Not quite. I said that a theory with a preferred frame *might* still be expressible in diffeomorphism invariant form, and I gave an example of how that *might* be possible. Basically, if it turns out that a theory with a preferred frame in it can still be expressed in any coordinates I choose, then it's still diffeomorphism invariant, even though it has a preferred frame.

You'll note that Smolin does not say that background independence and diffeomorphism invariance are the same; he only says they're closely related. So it would appear that he would also admit the possibility that there could be a theory that was diffeomorphism invariant but not background independent. This is not to say that anyone actually has such a theory; just that the possibility means we should be careful about making dogmatic statements about what is "required" of a theory.

An explicit example of such a theory is given by Laddha and Varadarajan (http://arxiv.org/abs/0805.0208). Andrade et al (http://arxiv.org/abs/1010.2535v3) refer to Torre (http://arxiv.org/abs/hep-th/9204055) who discusses such formulations at length.

Also, Newtonian (http://arxiv.org/abs/gr-qc/0506065) and Nordstrom (http://arxiv.org/abs/gr-qc/0405030) gravity both have formulations as geometric theories, even though they are more conventionally formulated non-geometrically.

bobc2

Nov27-11, 01:56 PM

It sure would, as soon as he tries to capture the physical difference between timelike and spacelike curves. That difference does not require conscious observers following the timelike curves.

As usual you've done a comptetent job of representing the conensus view of special relativity. I understood your points quite well. I was never exposed to anything different throughout my graduate physics curriculum. Usually, whether it was a course in classical field theory, modern physics, special relativity, general relativity, cosmology, etc., we were given the Minkowski metric as a starting point, then went from there.

But I was never satisfied with that, because I don't believe it treats time correctly--and still have not resolved my concerns. My PhD advisor would not discuss the subject--he thought it was a waste of time. And at that stage as a student I knew he was right--that I needed to concentrate on learning physics before challenging established ideas.

At this point on the forum, I'm afraid I've pushed on this to the point of violating the agreed upon rules here. The forum advisors have given me more leeway than was probably justified. Hopefully, others have benefitted from the occasion to consider more carefully the fundamental mathematical machinery upon which special relativity is based (thanks primarily to PeterDonis's contributions).

PeterDonis

Nov27-11, 02:12 PM

Usually, whether it was a course in classical field theory, modern physics, special relativity, general relativity, cosmology, etc., we were given the Minkowski metric as a starting point, then went from there.

But I was never satisfied with that, because I don't believe it treats time correctly--and still have not resolved my concerns.

This is where I get confused; the only "concerns" you have expressed that I can see are: (1) about time being a parameter, which I've agreed with and shown that relativity includes; and (b) that the metric of spacetime is not positive definite, which I've given a good physical reason for: timelike curves are physically different than spacelike curves (and null curves are different from both). So either I'm misunderstanding the point of these concerns, or there are other concerns that I'm not seeing. I don't think expressing them would violate forum rules.

Passionflower

Nov27-11, 02:13 PM

I guess I need some clarification, how can you folks talk about a potential preferred frame in our spacetime which is obviously non-stationary.

ghwellsjr

Nov27-11, 03:22 PM

I guess I need some clarification, how can you folks talk about a potential preferred frame in our spacetime which is obviously non-stationary.
Since Lorentz Ether Theory (LET) is indistinguishable from Special Relativity (SR) save for the claim that there exists a single preferred frame, Einstein designed his concept of spacetime in such a way that every inertial frame satisfies the requirements for a Lorentz ether frame and therefore can be considered a potential preferred frame.

stglyde

Nov27-11, 05:06 PM

PeterDonis

Nov27-11, 06:22 PM

PeterDonis. Can you please go to the thread below as I'd like to inquire more about this Tidal gravity and wave function thing which can become off topic in this thead. Thanks.

http://www.physicsforums.com/showthread.php?t=554273

Sure, going there now.

stglyde

Nov27-11, 08:11 PM

bobc2, what do you make of the following:

http://space.mit.edu/home/tegmark/dimensions.pdf

where Max Tegmark states only 3D space and 1D time is stable. Can you find any flaws in the paper? What is your comment on it?

PeterDonis

Nov27-11, 11:20 PM

Sure, going there now.

Looks like the thread was locked; possibly because you started asking about spacetime again, which would belong back here, or possibly because it was perceived as pursuing your own speculative theory instead of asking about existing theories.

As far as the items you asked that were about modeling tidal gravity some other way than spacetime curvature, there is an alternate model that views gravity as a masless, spin-2 field on a flat background spacetime. I don't know of a good introductory online reference; I learned about it from The Feynman Lectures on Gravitation:

http://books.google.com/books/about/Feynman_lectures_on_gravitation.html?id=jL9reHGIcM gC

This "field on a flat spacetime" model turns out to be equivalent to the standard curved-spacetime model of GR, except for some concerns about whether the starting assumption of a flat background means the model can't deal with, for example, the FRW spacetimes in cosmology. So instead of viewing tidal gravity as a manifestation of spacetime curvature, you could view it as a manifestation of the massless, spin-2 field. But since the models give exactly the same predictions, one could just as well say that "spacetime curvature" and "massless spin-2 field" are different names for the same thing, the whatever-it-is-that-causes-tidal-gravity.

stglyde

Nov28-11, 03:08 AM

Looks like the thread was locked; possibly because you started asking about spacetime again, which would belong back here, or possibly because it was perceived as pursuing your own speculative theory instead of asking about existing theories.

As far as the items you asked that were about modeling tidal gravity some other way than spacetime curvature, there is an alternate model that views gravity as a masless, spin-2 field on a flat background spacetime. I don't know of a good introductory online reference; I learned about it from The Feynman Lectures on Gravitation:

http://books.google.com/books/about/Feynman_lectures_on_gravitation.html?id=jL9reHGIcM gC

This "field on a flat spacetime" model turns out to be equivalent to the standard curved-spacetime model of GR, except for some concerns about whether the starting assumption of a flat background means the model can't deal with, for example, the FRW spacetimes in cosmology. So instead of viewing tidal gravity as a manifestation of spacetime curvature, you could view it as a manifestation of the massless, spin-2 field. But since the models give exactly the same predictions, one could just as well say that "spacetime curvature" and "massless spin-2 field" are different names for the same thing, the whatever-it-is-that-causes-tidal-gravity.

Ok.

Say. Can you think of an experimental setup that we average person can afford that can test for local lorentz invariance? Like some electronics apparatus that can be modified to become sensors for a rough test of orientation and boost lorentz symmetry or CPT symmetry? Think and brainstorm for an hour then please share. Thanks.

stglyde

Nov28-11, 07:16 AM

Looks like the thread was locked; possibly because you started asking about spacetime again, which would belong back here, or possibly because it was perceived as pursuing your own speculative theory instead of asking about existing theories.

As far as the items you asked that were about modeling tidal gravity some other way than spacetime curvature, there is an alternate model that views gravity as a masless, spin-2 field on a flat background spacetime. I don't know of a good introductory online reference; I learned about it from The Feynman Lectures on Gravitation:

http://books.google.com/books/about/Feynman_lectures_on_gravitation.html?id=jL9reHGIcM gC

This "field on a flat spacetime" model turns out to be equivalent to the standard curved-spacetime model of GR, except for some concerns about whether the starting assumption of a flat background means the model can't deal with, for example, the FRW spacetimes in cosmology. So instead of viewing tidal gravity as a manifestation of spacetime curvature, you could view it as a manifestation of the massless, spin-2 field. But since the models give exactly the same predictions, one could just as well say that "spacetime curvature" and "massless spin-2 field" are different names for the same thing, the whatever-it-is-that-causes-tidal-gravity.

Googling "massless, spin-2 field on a flat background spacetime", there are indeed many researches about this.. interesting.. it's about going to flat minkowski space with spin 2 gravitons. Now how about going a step further backward.. like minkowski field on an newtonian spacetime. I mean.. if we can remove the space curvature in GR by going to massless spin 2 field on a flat spacetime.. what is it not possible to move further back... like space+time field on newtonian absolute space and time.. or something akin to it?

nitsuj

Nov28-11, 07:23 AM

Ok.

Say. Can you think of an experimental setup that we average person can afford that can test for local lorentz invariance? Like some electronics apparatus that can be modified to become sensors for a rough test of orientation and boost lorentz symmetry or CPT symmetry? Think and brainstorm for an hour then please share. Thanks.

I think Tom Tom's have come down in price. :smile:

I hope it's okay I did someone else's homework :wink:

stglyde

Nov28-11, 10:22 AM

Googling "massless, spin-2 field on a flat background spacetime", there are indeed many researches about this.. interesting.. it's about going to flat minkowski space with spin 2 gravitons. Now how about going a step further backward.. like minkowski field on an newtonian spacetime. I mean.. if we can remove the space curvature in GR by going to massless spin 2 field on a flat spacetime.. what is it not possible to move further back... like space+time field on newtonian absolute space and time.. or something akin to it?

After writing this. It slowly dawns on me there is indeed such thing. It's Lorentz Ether Theory which occurs in the backdrop of absolute space and time... just like how you can model massless spin-2 field on flat spacetime. You can actually take one step backward... LET field on absolute space and time! Now how do you connect gravity to newtonian. There is one. It's called General Lorentz ether theory applied to newtonian space and time! And all this appears not to be falsifiable! Is this 100% such that no experiment ever will distinguish them??

atyy

Nov28-11, 11:00 AM

After writing this. It slowly dawns on me there is indeed such thing. It's Lorentz Ether Theory which occurs in the backdrop of absolute space and time... just like how you can model massless spin-2 field on flat spacetime. You can actually take one step backward... LET field on absolute space and time! Now how do you connect gravity to newtonian. There is one. It's called General Lorentz ether theory applied to newtonian space and time! And all this appears not to be falsifiable! Is this 100% such that no experiment ever will distinguish them??

LET has absolute space and time in the sense that it is physics in a preferred frame (an inertial frame). LET, however, still has Lorentz invariance, not Galilean invariance. GR/massless spin-2 fields also have Lorentz invariance. Is it possible to find a theory of gravity which is well-approximated as a Lorentz invariant spin-2 field at low energies, but which has Galilean invariance at high energies? At present, no such theory has been discovered. There are, however, non-gravitational theories which have Galilean invariance at high energies and Lorentz invariance at low energies: http://www.nature.com/nature/journal/v438/n7065/abs/nature04233.html.

Ok.

Say. Can you think of an experimental setup that we average person can afford that can test for local lorentz invariance? Like some electronics apparatus that can be modified to become sensors for a rough test of orientation and boost lorentz symmetry or CPT symmetry? Think and brainstorm for an hour then please share. Thanks.

Test Maxwell's equations (which have Lorentz symmetry). In particular test that the speed of light is as predicted by Maxwell's equations: http://www.physics.umd.edu/icpe/newsletters/n34/marshmal.htm (I've never tried this, I'd be interested to know if it really works).

There is also what is commonly advertised as a test of length contraction by measuring the magnetic field due to a current: http://physics.weber.edu/schroeder/mrr/MRRtalk.html.

PeterDonis

Nov28-11, 12:34 PM

Ok.

Say. Can you think of an experimental setup that we average person can afford that can test for local lorentz invariance? Like some electronics apparatus that can be modified to become sensors for a rough test of orientation and boost lorentz symmetry or CPT symmetry? Think and brainstorm for an hour then please share. Thanks.

See here for a good summary of tests of Lorentz invariance:

http://relativity.livingreviews.org/Articles/lrr-2005-5/

PeterDonis

Nov28-11, 12:39 PM

I mean.. if we can remove the space curvature in GR by going to massless spin 2 field on a flat spacetime..

I think you may be misunderstanding what the massless spin-2 field model does. It does not "remove" the spacetime curvature; it shows that the massless spin-2 field is *equivalent* to curvature. (And it's *spacetime* curvature, not just space curvature.)

what is it not possible to move further back... like space+time field on newtonian absolute space and time.. or something akin to it?

If this were possible, it would have been done in the late 19th or early 20th centuries; everybody was looking for a theory like this, in order to try and reconcile Maxwell's Equations with Newtonian physics, and nobody found one.

stglyde

Nov28-11, 04:24 PM

I think you may be misunderstanding what the massless spin-2 field model does. It does not "remove" the spacetime curvature; it shows that the massless spin-2 field is *equivalent* to curvature. (And it's *spacetime* curvature, not just space curvature.)

I know. It's just like the strings in flat spacetime but the gravitons causing effect equivalent to curvature and we can't know.

If this were possible, it would have been done in the late 19th or early 20th centuries; everybody was looking for a theory like this, in order to try and reconcile Maxwell's Equations with Newtonian physics, and nobody found one.

Have you forgotten Lorentz Ether Theory. Here's the analogy.

1. massless spin2 field in flat minkowski is equivalent to General Relativity
2. actual length contraction, etc. in absolute space and time is equivalent to Newtonian Absolute Space and Time

PeterDonis

Nov28-11, 06:45 PM

1. massless spin2 field in flat minkowski is equivalent to General Relativity
2. actual length contraction, etc. in absolute space and time is equivalent to Newtonian Absolute Space and Time

I see the similarity: both examples involve something that's postulated to be part of a physical theory but is "unobservable" (the flat background spacetime and the "absolute rest" frame). But the two examples are not quite the same. In the massless spin-2 field example, there's no need to commit to any particular state of motion as being "at rest". You just have to accept that the flat background is unobservable, because all actual physical measurements are governed by the "curved" metric produced by the massless spin-2 field.

With LET, you have to believe that there is some particular state of motion that corresponds to "absolute rest", we just have no way of ever telling which one it is by experiment. Also, the "absolute rest" frame in LET, corresponding to the "absolute rest" state of motion, is *not* a Newtonian absolute space/time. It's a Lorentz inertial frame; there's just no way of knowing *which* Lorentz inertial frame it is. LET is *not* a theory that adds Lorentz length contraction/time dilation "on top of" Newtonian absolute space and time; there is no such theory, because Newtonian absolute space and time is incompatible with Lorentz invariance (it would require Galilean invariance, corresponding to an infinite speed of light).

stglyde

Nov28-11, 06:57 PM

I see the similarity: both examples involve something that's postulated to be part of a physical theory but is "unobservable" (the flat background spacetime and the "absolute rest" frame). But the two examples are not quite the same. In the massless spin-2 field example, there's no need to commit to any particular state of motion as being "at rest". You just have to accept that the flat background is unobservable, because all actual physical measurements are governed by the "curved" metric produced by the massless spin-2 field.

With LET, you have to believe that there is some particular state of motion that corresponds to "absolute rest", we just have no way of ever telling which one it is by experiment. Also, the "absolute rest" frame in LET, corresponding to the "absolute rest" state of motion, is *not* a Newtonian absolute space/time. It's a Lorentz inertial frame; there's just no way of knowing *which* Lorentz inertial frame it is. LET is *not* a theory that adds Lorentz length contraction/time dilation "on top of" Newtonian absolute space and time; there is no such theory, because Newtonian absolute space and time is incompatible with Lorentz invariance (it would require Galilean invariance, corresponding to an infinite speed of light).

Uhm.. if this is so. How come when Lorentz discovered the Lorentz Transformation. He didn't immediately explore Minkowski Spacetime. He actually thought the physical length contracting was enough to explain it. It took Einstein to discover the Minkowski mechanism. So it could be assume Lorentz Transformation as Lorentz thought it can be an addition to newtonian absolute space and time.

PeterDonis

Nov28-11, 07:04 PM

Uhm.. if this is so. How come when Lorentz discovered the Lorentz Transformation. He didn't immediately explore Minkowski Spacetime. He actually thought the physical length contracting was enough to explain it. It took Einstein to discover the Minkowski mechanism. So it could be assume Lorentz Transformation as Lorentz thought it can be an addition to newtonian absolute space and time.

Actually, Einstein didn't discover Minkowski spacetime; Minkowski did. (Yes, I know things aren't always named after the people who actually discovered them, but in this case it happened that way.) You may be using the term "Minkowski spacetime" more generally than it's normally used; normally it doesn't just refer to SR in general, but to the particular geometric object, a 4-dimensional manifold with a particular metric, that can be used to model SR. As I said, Einstein didn't come up with that; Minkowski did, and Einstein only adopted it when it became clear to him that he needed a geometric model for general relativity, and that Minkowski's flat spacetime was the limiting case of that model when gravity is absent.

I'm not familiar enough with Lorentz's papers to know whether he thought at first that his results could be explained by just adding on length contraction to Newtonian space and time. But I don't think it really matters, because Einstein's 1905 relativity papers did make it clear that that wasn't possible; that to make kinematics consistent with the speed of light being constant for all observers, you *had* to give up Newtonian space and time.

stglyde

Nov28-11, 07:57 PM

Actually, Einstein didn't discover Minkowski spacetime; Minkowski did. (Yes, I know things aren't always named after the people who actually discovered them, but in this case it happened that way.) You may be using the term "Minkowski spacetime" more generally than it's normally used; normally it doesn't just refer to SR in general, but to the particular geometric object, a 4-dimensional manifold with a particular metric, that can be used to model SR. As I said, Einstein didn't come up with that; Minkowski did, and Einstein only adopted it when it became clear to him that he needed a geometric model for general relativity, and that Minkowski's flat spacetime was the limiting case of that model when gravity is absent.

I'm not familiar enough with Lorentz's papers to know whether he thought at first that his results could be explained by just adding on length contraction to Newtonian space and time. But I don't think it really matters, because Einstein's 1905 relativity papers did make it clear that that wasn't possible; that to make kinematics consistent with the speed of light being constant for all observers, you *had* to give up Newtonian space and time.

Thanks for the important distinctions. I'm interested in all this because I'm looking for lorentz violations.

How do you think the quantum vacuum connect with spacetime? Is the quantum vacuum inside spacetime or is spacetime inside the quantum vacuum? They say the quantum vacuum doesn't have a rest frame.. so it's like its connected to spacetime as if part of the manifold.

We still haven't refuted Dirac sea of Electrons where the vacuum is composed of negative sea of electrons. If this were true. Then lorentz violations could be detected at this sector. I wonder if the quantum vacuum can also have spontaneous symmetry breaking where if you can alter it at certain configuration from the default ambient background.. it would no longer follow lorentz symmetry.. and hence lorentz violations detected. What are the arguments that makes it impossible that the quantum vacuum can change default mode to another phase or level?

PeterDonis

Nov28-11, 09:26 PM

Thanks for the important distinctions. I'm interested in all this because I'm looking for lorentz violations.

The living reviews site I linked to earlier gives a good summary of where we stand on this. If there are particular things in there that you have questions about, you should probably start a separate thread.

How do you think the quantum vacuum connect with spacetime? Is the quantum vacuum inside spacetime or is spacetime inside the quantum vacuum? They say the quantum vacuum doesn't have a rest frame.. so it's like its connected to spacetime as if part of the manifold.

Any quantum vacuum state has to respect Lorentz invariance; in this sense it "doesn't have a rest frame". However, a quantum state that looks like the vacuum to inertial observers will *not* look like the vacuum to accelerated observers. See here for an overview:

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

So in this sense there is not a unique "quantum vacuum"; which quantum state is the vacuum can depend on your state of motion (inertial vs. accelerated). In curved spacetime this effect is used to show that black holes emit Hawking radiation:

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

We still haven't refuted Dirac sea of Electrons where the vacuum is composed of negative sea of electrons.

Only in the sense that the predictions of Dirac's "hole theory" are formally equivalent to those of standard quantum field theory (at least, as far as I know they are). But standard QFT makes the same predictions without requiring the existence of the infinite sea of negative energy electrons, so Occam's Razor implies that such a sea does not exist.

I wonder if the quantum vacuum can also have spontaneous symmetry breaking where if you can alter it at certain configuration from the default ambient background.. it would no longer follow lorentz symmetry.. and hence lorentz violations detected. What are the arguments that makes it impossible that the quantum vacuum can change default mode to another phase or level?

The quantum vacuum can certainly undergo spontaneous symmetry breaking: that's the current theory of how the inflationary epoch in cosmology ended (by the vacuum undergoing a phase transition from the symmetric "false vacuum" to the symmetry-broken "true vacuum"):

http://en.wikipedia.org/wiki/Inflation_%28cosmology%29

But as far as I know, this did not involve any violation of Lorentz invariance. I don't know that anyone has proposed spontaneous symmetry breaking as a mechanism for Lorentz violation. If anyone has, I would expect the living reviews site I linked to to talk about it.

stglyde

Nov30-11, 04:00 AM

Actually, Einstein didn't discover Minkowski spacetime; Minkowski did. (Yes, I know things aren't always named after the people who actually discovered them, but in this case it happened that way.) You may be using the term "Minkowski spacetime" more generally than it's normally used; normally it doesn't just refer to SR in general, but to the particular geometric object, a 4-dimensional manifold with a particular metric, that can be used to model SR. As I said, Einstein didn't come up with that; Minkowski did, and Einstein only adopted it when it became clear to him that he needed a geometric model for general relativity, and that Minkowski's flat spacetime was the limiting case of that model when gravity is absent.

I'm not familiar enough with Lorentz's papers to know whether he thought at first that his results could be explained by just adding on length contraction to Newtonian space and time. But I don't think it really matters, because Einstein's 1905 relativity papers did make it clear that that wasn't possible; that to make kinematics consistent with the speed of light being constant for all observers, you *had* to give up Newtonian space and time.

Hi PeterDonis, please go to this related thread where I mentioned about LET, FTL and SR (in order not to make it off topic here) and mentioned about the above where one of them commented:

"I would drop the first assumption immediately and say that the second is also questionable. Dropping the first assumption is sufficient to reject PeterDonis' argument.

Pls address message #19 in:

http://www.physicsforums.com/showthread.php?t=554741&page=2