VikingF

Senior Members

92

Posts posted by VikingF

Simultaneity in general relativity

Here is a simple analogy.

But beware analogs are never exact, but they can offer enough correspondence to promote understanding.

Right so SR is 'flat or euclidian' GR is not.

Going down to 2 dimensions for the analog consider a plane and a sphere, both of which have two dimensions, X and Y for the plane, Latitude and Longitude for the sphere. Remember a sphere is mathematically a surface, not a solid.

The plane is flat like SR.

The sphere corresponds to GR.

The plane only approximates a small portion of the surface of the sphere with any pretention to accuracy.

The smaller the curvature ( ie the larger the sphere) the greater is this 'patch'.

A function or transformation that maps points on the plane to points on the sphere is called a chart.

Clearly a chart good at the equator is not good for mapping the polar regions.

This is what is meant by local.

In fact no single transformation will put every point of any given sphere into one-to one correspondence with a point on the plane.

There will always be at least one sphere point left out, when every available point on the plane has been used up.

Proving this is the subject of topology.

So the planar grid can never be a global coordinate system for the surface of a sphere.

You have to 'cover' the sphere with reference to at least two different planes.

Of course the sphere is the simplest most regular 2 D surface in 3D.

The real universe is quite irregular so the only global grid is the universe itself, which is effectively saying there is no global grid.

That is enough for now, but does it help?

I think I got the point.

It is easy to draw a straight line (e.g. the x-axis of a specific frame of reference) if you have a flat surface (and SR talks about flat spacetime), however, GR talks about a curved spacetime, hence you cannot describe a straight x-axis in the same way due to the curvation of spacetime. So simultaneity (e.g. the x-axis of a specific frame of reference) is relative in SR but not clearly described in GR.

Is this correct?

Simultaneity in general relativity

In GR , there are no frames of reference covering the whole space, so, the notion of simultaneity can only be discussed locally. For a small enough region, the spacetime is locally Minkowski, so the GR notion of simultaneity reduces to the SR notion of simultaneity. For large® extents of space, nothing can be said about simultaneity. There is not much else that can be said on this subject.

Do I understand it correctly by saying that from Newtonian physics to SR, simultaneity went from being absolute to relative, and from SR to GR, it more or less "disappeared" (since it can only be discussed locally as you say)?

Please correct me if I am wrong. I try to wrap my head around this.

Eternalism vs Presentism?

Surely the only valid definition of existence is whether something is physically "there" in the spacetime. e.g. Nowhere in the spacetime does there exist a flying spaghetti monster therefore the FSM does not physically exist. On the other hand, there does exist, somewhere, in the spacetime Tim Berners-Lee therefore Tim Berners-Lee exists.

Of course, but I meant the difference between being somewhere in spacetime, and at this specific point of time in spacetime. Shakespeare exists in spacetime, but not at this very point of time. According to Presentism, he doesn't exist at all, because they do not believe in a four-dimensional spacetime, hence for something to exist, it has to exist now.

Eternalism vs Presentism?

The problem with this is, yes Shakespeare may not "exist" in your reference frame, but he does in fact exist in a different reference frame. So does this mean that Shakespeare both exists and does not exist...?

You have to choose your definitions first. If to exist is to exist in spacetime, then he exists.

Eternalism vs Presentism?

I think this boils down to how we define the word "exist". If by "exist" we mean "simultaneous in my reference frame" (existing right now for me), then surely, Shakespeare does not exist. However, if by "exist" we mean "simultaneous in any reference frame" (existing in spacetime), then he does indeed exist, since simultaneity is relative based on which reference frame you are in. Shakespeare is certainly existing in the spacetime, whether or not he is existing "right now" in my frame of reference.

The main difference between Presentism and Eternalism is really about whether time is an own dimension or not. Presentism says "no, time is just a measurement of changes in space", while Eternalism says "yes, time is a temporal dimension containing all events that have happened, are happening, and will happen, and "now" is not a privileged point of time".

Does Eternalism imply eternal return?

Interesting. How would an Eternalist respond to the objection: "Why don't we experience all moments in our life at once?"

I cannot speak on behalf of all Eternalists, but I would answer it in the same way as I did in my last post: "Because that is how consciousness works".

The consciousness is a process that exist from about your birth to your death. Every temporal part of you, i.e. the consciousness within your brain, remember its past and have expectations about its future, and this - somehow - creates the illusion that time is "rolling on" in the future direction. Entropy and the arrow of time could be the reason why we feel time is running in that specific direction.

I don't know... I am just throwing out some ideas to think about here.

Eternalism vs Presentism?

To the point:

IMHO the Block Universe is a remain of the belief that something can exist in 3D space only. The Block Universe is the image of a collection of stacked 3Dspaces the one above the other (or the one after the other). I think this is a wrong conception.

IMHO things exist in time first (that means vertically through the stacks) and then, eventually, horizontally (that is in 3d space). Existence means first displacement in time.

I don't see the difference. The block universe/Eternalism is the view that everything is four-dimensional, i.e. consisting of three spatial dimensions and one temporal dimension. Your view sounds like Eternalism.

Does Eternalism imply eternal return?

Two questions naturally follow that then:

1. How are "temporal parts" defined?

2. What would the eternalist's explanation be to why we experience only a present moment?

1. According to Eternalism, everything exist in (and consist of) four dimensions, i.e. three spatial dimensions and one temporal dimension. An object, e.g. a person, is a four-dimensional "tube" between the its beginning and its ending moment, and a temporal part would be the four-dimensional part of the "tube"/object between two moments.

2. Eternalism is just the view that the world consists of four dimensions, i.e. three spatial and one temporal, and nothing more. We probably experience one-by-one moment because that is just how the consciousness works.

Eternalism vs Presentism?

VikingF- rarely have I encountered an answer to one of my questions that so absolutely addresses the issue as the paper you have recommended. I can not thank you enough. I'm going to work in my garden to digest what I've read, and re-read at least a few times, but it seems that my concept of world-line-ism is entirely compatible with eternalism. In fact, on page 5, there exists a diagram that had I taken the time to draw, would nearly exactly match what I had envisioned. My only remaining question, then, is how can there be any support whatsoever for presentism? It seems obviously false to me, and I have learned to be wary of my "obvious" conclusions.

You're welcome. This topic has fascinated me for quite some years now.

The main argument for Presentism that I have seen is that Relativity of Simultaneity is a part of SR that has not been tested directly, and could just be a "theoretical truth", but not a part of the ontological reality. However, it is a central part of SR and can be seen by examining a simple Minkowski diagram (spacetime diagram), and from the same diagram we can extract e.g. the Lorentz transformations, which have actually been tested and verified.

Eternalism vs Presentism?

I plead ignorance again, on more than one front. What is "RoS"?

Perhaps I need to revisit my understanding of eternalism. Do you have a specific source that is better than wikipedia?

Relativity of Simultaneity.

I think this is an interesting paper: http://philsci-archive.pitt.edu/2408/1/Petkov-BlockUniverse.pdf by Vesselin Petkov, who I also mentioned in a previous post.

Eternalism vs Presentism?

Is there such a thing as "world-line-ism"? While none can agree on a universal present, past, or future, events only occur once, and all can agree on the progression of a world line. Simultaneity between events on different world lines is relative to the observer, but events on a world line are universally observed to occur in the same order. Where two world lines cross, all events prior to the crossing are universally recognizable as occurring prior to the crossing event (past in both world lines), and all events after the crossing are universally recognizable as occurring after the crossing event (future in both world lines).

Eternalism seems to me to rely on a false construct, the idea that we can arrange all world lines together in a great big block and meaningfully proclaim that future events on my world line already exist from some other's perspective. Instead, it makes more sense to me to recognize that there's no such thing as an external observer, and the timing of events is always dependent upon the world line from which you are measuring those events. Words like "past", "present", and "future" are only meaningful in the context of a world line.

I don't understand your ontology of time. Either only the present exists (Presentism), the complete spacetime exists (Eternalism), or the past and present exist but not the future (Growing block view). I think the growing block view is somewhat unappealing, because if all temporal parts of me up until now exist, then how can I know that THIS exact moment, i.e. what I call "now", is "the present moment", and not one of the points of time in the future of now? The temporal part of me that exists in e.g. 2001 will also say that he is in "the present" and that it is only his temporal part and his past temporal parts that exist.

Hence, I think Presentism and Eternalism are the views that are easiest to cope with, and as you say yourself, Presentism is incompatible with SR, or more specifically RoS.

Does Eternalism imply eternal return?

The question of course is, as the events still exist, do I - since I would also still exist - experience them?

Yes, that temporal part of you does (did). Since you did experience it (unless you were unconscious at that moment), and spacetime is static (according to Eternalism, that is), then you did (does).

At least that is how I think about it. Other people may disagree.

Does Eternalism imply eternal return?

This question occurred to me thanks to my other thread

Since Eternalism says that every point in time still exists, which means that there's another me - in my past - a few keystrokes behind, doesn't that suggest eternal return.

According to Eternalists, when a person dies it is trivial because they are still alive and well in the relative past. If this was correct, would this mean we all have to go through our lives, as we would perceive, ad infinitum?

I think your thoughts are heading in the right direction, however, I don't think "eternal return" is the correct term to use, because you don't come back so to say. I think it is more correct to call it "atemporal existence", i.e. when you die you "still" exist - in the past, between your birth and death, and each 3D slice of you will "still" remember what is in it's past and have expectations about it's future. (And yes, "still" was not a correct term either, just to highlight that before I get a philosopher of language on my neck. )

Eternalism vs Presentism?

Lol. Thanks!

Is there anything Petkov has written that you can recommend reading?

I recommend "Relativity and the Nature of Spacetime". You can find it on Amazon. It is a book which gives a good overview of Relativity, and how it is more or less given that our universe must be four-dimensional, i.e. containing three spatial dimensions and one temporal dimension. At least that is Petkov's conclusion.

Eternalism vs Presentism?

I think Eternalism is a more correct model of the universe than Presentism because of SR and Relativity of Simultaneity, and I agree with the rest of your post. (This is probably the most boring answer of this century )

According to Vesselin Petkov, the experiments confirming SR have also disproved Presentism.

Relativity, spacetime, and determinism

I don't see it that way. It wouldn't be simply unknown, because the information would not exist. There would be nothing about the present - not even unknowable hidden variables - that determine the future. Is that not the very definition of non-deterministic?

He was probably thinking tenselessly about time, i.e. that all points of time exist on par. In that case, there must be either true or false whether a sea battle happens tomorrow, whether or not we have the ability to predict it using the information within the present point of time. I think the right term for this is logical determinism, and this should be compatible with causal indeterminism in the way you explain in your post above.

How can the universe be infinite and finite at the same time?

So it actually seems like the universe might be closed, instead of being flat. If this turns out to be the case, then is it possible that the universe is heading towards a Big Crunch in the far future?

How can the universe be infinite and finite at the same time?

If Omega were exactly 1.012 that would say a finite positive curved universe with a radius of curvature of about 130 billion LY.

Yeah, I see your point. However, from what I have understood of cosmology, the measures of this value have always given results very close to 1, and the universe seems to be accelerating. I am no cosmologist, so I really have no clue other than referring to what I have read.

I would recommend you go directly to working observational cosmologists, who analyse the data directly. Also Guth is somewhat the "elder statesman". My guess is that Guth is just quoting some result from David Spergel, or Ned Wright, Joanna Dunkley----one of those younger people currently leading the field.

His data is described in the article "Cosmological parameters from SDSS and WMAP" by Tegmark, et al.

http://arxiv.org/abs/astro-ph/0310723 (in the table on page 9).

I don't trust him because he has his inflation ax to grind (his claim to fame). So I would go direct to the working cosmologists and see what size error bar you find.

I thought the inflationary cosmology was rather strong, compared to many of the other models that exist? It has a great explanatory power, doesn't it?

How can the universe be infinite and finite at the same time?

The best estimates by physicists of the value of omega, the variable that tells us whether we're in an infinite open universe (omega value equal to 1) or a finite closed universe (omega value greater than or less than 1) suggests we're in a finite closed universe.

Really? According to Alan Guth's article "Eternal inflation and its implications" (http://arxiv.org/pdf/hep-th/0702178), the omega constant is found to be approximately 1.012 (+0.018/-0.022), hence the universe seems to be rather flat.

Are YOU in the 98% or the 2%

Are you thinking of a Kangaroo in Denmark eating an Orange?

Wow! I was actually thinking of a kangaroo in Denmark, eating an orange!

Big Bang

Anyway Ashtekar's two main papers last year have been about two main cases, which he called the k=0 and k=1 case, and which I can roughly characterize this way:

1. in the whole history of the universe there is only one bounce. the expanding phase we are now in extends indefinitely into the future and the prior contracting phase (figuratively mirroring this) could extend indefinitely into the past.

2. there is a series of bounces going back indefinitely into the past and indefinitely into the future

I am not sure I understand whether or not you see a problem with this, or what problem there could be.

What I don't get is this: If the "single bounce" scenario is correct, then the universe is (more or less) the same on each side of the Big Bang/Bounce, and hence the universe we have now is almost the same as the universe 13.7 billion years before the bounce. But if this is the case, then the universe must have started exactly like it will end in the future, that is with a "inverse Big Rip". How can a (inverse) Big Rip be the begining of the universe?

Or have I misunderstood completely?

Infinity

∞ is a stubborn constant.

∞ is not a constant at all, it's more like a direction. A constant, let's say n, can move towards ∞ (n->∞), or towards -∞ (n->-∞), but it can never BE ∞.

The .999... = 1 "debate"

You aren't wrong' date=' but you did miss a summation sign out in the opening line:

[math'] 0.9\ldots = 0.9+0.09+\cdots = \sum_{n=1}^{\infty} \frac{9}{10^n}[/math]

Yes, you're right... I forgot that.

(It's fixed now. Thanks for noticing!)

The .999... = 1 "debate"

0.999... = 0.9+0.09+0.009+0.0009+... = $\sum_{n=1}^{\infty} \frac{9}{10^n}$,

which is an infinite row.

The sum of an infinite row is defined as

S=a_0/(1-k), where a_0 is the first number of the row, and k=a_n/a_(n-1).

Here: k=0.09/0.9=0.1 and a_0=0.9

=> S=0.9/(1-0.1)=0.9/0.9=1

(Q.E.D.)

Those who disagree should say where in my calculations I am wrong.

The .999... = 1 "debate"

Why?

Because some people don't understand what a limit is, and that "..." means the limit where the number of 9s goes towards infinite. I talk from my own experience actually. I was one of those stupid lads who disagreed that 0.99...=1, saying that "no matter how many 9s you place behind the '.', the result will never be exact 1!".

I am less ignorant today.

×
×
• Create New...