Hyperplanes of Simultaneity and BigBang

[lektroon]

TL;DR Summary

Is it really possible to conclude that eternalism must be true following the implications of special relativity like the relativity of simultaneity?

As a layman in physics, I cannot understand the block universe concept followed by Rietdijk-Putnam-Penrose Argument. Let me clarify my question as follows:

Suppose two objects, one stationary and one moving towards the other one at constant relativistic speed, e.g. 05.c and let's also presume that these two objects are space-like separated by a great distance, e.g. 30 billion light years.

Following the time transformation formula of Lorentz transformations, which is:

t' = gamma * (t - v.x/c^2), where
gamma = 1/sqrt(1-v^2/c^2)

Then the difference between the simultaneities of these two objects becomes around 17.8 billion light years which is far before the BigBang took place! However, we don't know if the time existed before the BigBang.

If that is the case then how can we conclude that the block universe must be true following the implications of special relativity like the relativity of simultaneity as stated in arguments like Rietdijk-Putnam-Penrose?

 

[Ibix]

The block universe is an interpretation. Others are available. None is more right than another, but given the way the maths of relativity works some kind of 4d interpretation is a lot easier to work with than 3d+time+some explanation for why something that's 3d looks 4d.

Yes, if you choose a simultaneity plane that is not a plane of constant cosmological time then there are portions of the universe that never have a time simultaneous with now by that definition of simultaneity. That is a general feature of such coordinate choices, regardless of whether you view it through a block universe interpretation or not. It doesn't matter. No physics depends on your choice of simultaneity criterion.

 

[jbriggs444]

Following the time transformation formula of Lorentz transformations, which is:

t' = gamma * (t - v.x/c^2), where
gamma = 1/sqrt(1-v^2/c^2)

Then the difference between the simultaneities of these two objects becomes around 17.8 billion light years which is far before the BigBang took place! However, we don't know if the time existed before the BigBang.

The Lorentz transformations work globally in the flat spacetime contemplated by the special theory of relativity.

In the curved spacetime contemplated by general relativity, they only hold accurately in the limit of regions that are small in both space and time. They hold approximately over larger regions. But by the time you get to regions that span large fractions of the observable universe (like 30 billion light years) the approximations break down.

In particular, we live in a universe that is curved enough so that over the course of about 13.7 billion years (according to co-moving coordinates) the observable universe now has a radius of around 46.5 billion light years.

As long as you are contemplating small chunks of the universe like the chunk containing ourselves and the Andromeda galaxy then special relativity works well. The available synchronization error due to the relativity of simultaneity is basically one round trip time.

There is a frame of reference where a forward signal would be received nearly instantly and a return signal would take the remainder of the round trip time.

There is a frame of reference where the reverse holds. The forward signal takes essentially the entire round trip time and the return signal is received nearly instantly.

Either way, observers on both Earth and Andromeda would measure about 5 million years round trip time if they were both patient and skilled.

 

[lektroon]

The block universe is an interpretation. Others are available. None is more right than another, but given the way the maths of relativity works some kind of 4d interpretation is a lot easier to work with than 3d+time+some explanation for why something that's 3d looks 4d.

Yes, if you choose a simultaneity plane that is not a plane of constant cosmological time then there are portions of the universe that never have a time simultaneous with now by that definition of simultaneity. That is a general feature of such coordinate choices, regardless of whether you view it through a block universe interpretation or not. It doesn't matter. No physics depends on your choice of simultaneity criterion.

And what others are you talking about? Because the only other alternatives are presentism and possibilism (the growing block). However, is it really possible to reconcile them with special relativity?

 

[lektroon]

The Lorentz transformations work globally in the flat spacetime contemplated by the special theory of relativity.

In the curved spacetime contemplated by general relativity, they only hold accurately in the limit of regions that are small in both space and time. They hold approximately over larger regions. But by the time you get to regions that span large fractions of the observable universe (like 30 billion light years) the approximations break down.

In particular, we live in a universe that is curved enough so that over the course of about 13.7 billion years (according to co-moving coordinates) the observable universe now has a radius of around 46.5 billion light years.

As long as you are contemplating small chunks of the universe like the chunk containing ourselves and the Andromeda galaxy then special relativity works well. The available synchronization error due to the relativity of simultaneity is basically one round trip time.

There is a frame of reference where a forward signal would be received nearly instantly and a return signal would take the remainder of the round trip time.

There is a frame of reference where the reverse holds. The forward signal takes essentially the entire round trip time and the return signal is received nearly instantly.

Either way, observers on both Earth and Andromeda would measure about 5 million years round trip time if they were both patient and skilled.

OK, but this is also what my point is. The size of the observable universe is vast. We know that it has started around 13.77 billion years ago and it has a diameter of around 93 billion light years. I don't think that whether the spacetime has a Riemannian (curved) or Eucledian geometry changes the essence of my question and a very similar example had also been given by Brian Greene which can be seen as follows:



So, my question is: what if the alien in this video who is around 10 billion light years away from the stationary guy at the gas station travels at a relativistic speed (e.g. 0.5c) instead of riding a bike? In this case, it would a make huge difference rather than a couple of centuries and the simultaneity hyperplane of the alien, "the now slice" in Greene's own words, would point at a moment which is far earlier than the BigBang took place!

 

[Ibix]

And what others are you talking about?

Lorentz Ether Theory is what I think you are referring to as "presentism". Its predictions are the same as the usual SR - in fact, it's really just SR with the added claim that one inertial frame's "now" is real and it's all a peculiar coincidence that you can't tell which inertial frame is "the one". So there's nothing to reconcile - it's literally the same theory as SR with some added philosophical baggage.

"the now slice" in Greene's own words, would point at a moment which is far earlier than the BigBang took place!

Yes. (Edit: to the extent that makes sense, anyway. A better way to put it would be that the "now slice" reaches the Big Bang singularity at a finite distance.) So what?

 

[lektroon]

Lotentz Ether Theory is what I think you are referring to as "presentism". Its predictions are the same as the usual SR - in fact, it's really just SR with the added claim that one inertial frame's "now" is real and it's all a peculiar coincidence that you can't tell which inertial frame is "the one". So there's nothing to reconcile - it's literally the same theory as SR with some added philosophical baggage.

Yes (edit: to the extent that makes sense - a better way to put it would be that the "now slice" reaches the Big Bang singularity at a finite distance). So what?

No, presentism doesn't have anything to do with the Aether theory. It is a philosophy of time which is in the group of A series of time defined by McTaggart. Past, present and future do not exist ontologically according to this view and only the present exists. However, we know that it doesn't really comply with the implications of the special relativity.

And for your question "So what?" Well, that is the essence of my question. Because people like Rietdijk and Putnam exactly used these simultaneity differences in order to prove that we are actually living inside a block universe which corresponds to the B series of time in McTaggart's terminology. Therefore, "So what?" is not a pertinent answer because the simultaneity difference is in the very core of my question since it points at a moment in time which we don't even know whether it existed or not. It is pure speculation. That is what my whole point is. Otherwise, prove me wrong.

 

[Ibix]

No, presentism doesn't have anything to do with the Aether theory. It is a philosophy of time which is in the group of A series of time defined by McTaggart. Past, present and future do not exist ontologically according to this view and only the present exists. However, we know that it doesn't really comply with the implications of the special relativity.

You might want to look up Lorentz Ether Theory. It started as a mechanical ether theory but all the actual physical aspects of ether got stripped away by experiment until all that was left was the notion that one frame is "the ether rest frame" and its now slices as "more real" than others. This is presentism. It is also fully equivalent to SR. It is not the kind of ether theory ruled out by experiment - it is all that is left of such an ether theory after you chop out the falsfied bits, which is SR plus a notion of one "now" somehow being real without the choice having any physical consequence.

Because it points at a moment in time which we don't even whether it existed or not.

Not really. It intersects the Big Bang singularity and cannot be extended beyond there (note my edit to my last post).

prove me wrong.

Prove you wrong about what? That the block universe isn't the only possible interpretation of relativity? I've just spent three posts agreeing with you on that.

 

[lektroon]

You might want to look up Lorentz Ether Theory. It started as a mechanical ether theory but all the actual physical aspects of ether got stripped away by experiment until all that was left was the notion that one frame is "the ether rest frame" and its now slices as "more real" than others. This is presentism. It is also fully equivalent to SR. It is not the kind of ether theory ruled out by experiment - it is all that is left of an ether theory after you chop out the falsfied bits.

Not really. It intersects the Big Bang singularity and cannot be extended beyond there (note my edit to my last post).

Prove you wrong about what? That the block universe isn't the only possible interpretation of relativity? I've just spent three posts agreeing with you on that.

I don't believe in the block universe. I think that a "growing block" suits much better with the reality we are experiencing. It requires reconciliation with SR, yes but other than that, it makes much more sense to me. Now, you know about what you need to prove me wrong.

 

[lektroon]

You might want to look up Lorentz Ether Theory. It started as a mechanical ether theory but all the actual physical aspects of ether got stripped away by experiment until all that was left was the notion that one frame is "the ether rest frame" and its now slices as "more real" than others. This is presentism. It is also fully equivalent to SR. It is not the kind of ether theory ruled out by experiment - it is all that is left of such an ether theory after you chop out the falsfied bits, which is SR plus a notion of one "now" somehow being real without the choice having any physical consequence.

Not really. It intersects the Big Bang singularity and cannot be extended beyond there (note my edit to my last post).

Prove you wrong about what? That the block universe isn't the only possible interpretation of relativity? I've just spent three posts agreeing with you on that.

And you're also wrong about your statement "Not really. It intersects the Big Bang singularity and cannot be extended beyond there (note my edit to my last post)." because if you place the numbers that I shared in my original post to the time transformation formula of Lorentz then you will see that you get 17.8 billion years which is almost 4 billion years before BigBang took place (whatever that means...). Do the math and see it yourself...

 

[Ibix]

Now, you know about what you need to prove me wrong.

You mean you want me to prove that a "growing block" interpretation is invalid? Why would I do that? There's nothing wrong with the idea. The ADM formalism in GR is probably the closest mathematical fit to it.

The only question mark is around spacetimes containing things like closed timelike curves, where the past is also the future. Such spacetimes are hard to reconcile with anything except the 4d block interpretation (and can't be modelled in ADM), but are pretty physically implausible anyway.

 

[weirdoguy]

Do the math and see it yourself...

You do realize that formula you used is not applicable in GR context? You've even been told that in post #3.

 

[lektroon]

You do realize that formula you used is not applicable in GR context?

Then why does Penrose use the exact same formula in his famous Andromeda Paradox?

 

[weirdoguy]

Ask Penrose. What GR textbooks have you studied?

 

[lektroon]

Ask Penrose.

Well, is he a member of this forum? I would love to do that...

 

[Ibix]

And you're also wrong about your statement "Not really. It intersects the Big Bang singularity and cannot be extended beyond there (note my edit to my last post)." because if you place the numbers that I have shared in my original post to the time transformation formula of Lorentz then you will see that you get 17.8 billion years which is almost 4 billion years before BigBang took took place (whatever that means...). Do the math and see it yourself...

You might want to study some GR before making such assertions. Your calculation is assuming a Minkowski spacetime which does not have a Big Bang. An FLRW spacetime, which does have a Big Bang singularity, is geodesically incomplete and the "now slices" you are talking about terminate at the singularity. Thus, as I said earlier, there are portions of spacetime that don't exist "now" by that definition.

 

[Ibix]

Then why does Penrose use the exact same formula in his famous Andromeda Paradox?

Because he understands GR well enough to know when he can get away with it. The Andromeda paradox (low speeds, fairly short distances on cosmological scales) is one such. Your variant runs into singularity-induced trouble.

 

[lektroon]

You might want to study some GR before making such assertions. Your calculation is assuming a Minkowski spacetime which does not have a Big Bang. An FLRW spacetime, which does have a Big Bang singularity, is geodesically incomplete and the "now slices" you are talking about terminate at the singularity. Thus, as I said earlier, there are portions of spacetime that don't exist "now" by that definition.

Yes, that makes sense. However, what you don't understand (or maybe I can't explain) is the fact that the exact same logic has been used by scientists, like Penrose, in the past to prove the block universe. Then, why did they do that? If they did that then I definitely have the right to ask this question. I hope that you've got my point now.

 

[lektroon]

Because he understands GR well enough to know when he can get away with it. The Andromeda paradox (low speeds, fairly short distances on cosmological scales) is one such. Your variant runs into singularity-induced trouble.

Alright, fair enough. Then let me rephrase my question: Why did Greene give this example then? In his example, he mentions about a distance of 10 billion light years. I believe that it is far enough...

 

[lektroon]

Because he understands GR well enough to know when he can get away with it. The Andromeda paradox (low speeds, fairly short distances on cosmological scales) is one such. Your variant runs into singularity-induced trouble.

Then people like him were supposed to be more specific but thanks, I think that you have given me the answer that I was looking for. Such simultaneity differences do work differently in GR terms.

 

[Ibix]

like Penrose in the past to prove the block universe.

I would suspect such "proofs" are only in their popsci writings.

It's inevitable that you reach the position that the maths of pseudo-Riemannian manifolds is an accurate predictor of reality. It's therefore very sensible to conclude that such manifolds are an accurate model of reality, but you are not required to do so. As I said, the ADM formalism is a good fit for the notion of a "growing block" if you prefer it, although it's perfectly compatible with a block model too.

I think some popularisations, even by respected scientists, fail to make clear distinctions between the mathematical model (which is a pseudo-Riemann manifold, however you slice it), the reality, and the interpretation, and whether any interpretation goes anywhere near the reality.

I would say that the discovery of a closed timelike curve (or something of the sort) in reality would shoot "growing block" interpretations down in flames. However, they're pretty implausible, so until that day and as long as you are happy to assume all such spacetimes are unphysical on a philosophical rather than scientific basis, go ahead.

Why did Greene give this example then? In his example, he mentions about a distance of 10 bilion light years.

Greene's popularisations are well known hereabouts for the issues they raise. He may be simply picking a big number for the distance and ignoring the complications from an FLRW spacetime because he knows most of his viewers won't follow through the maths. Or maybe he is assuming a low enough speed to not run into problems and not being explicit enough about the caveats. Who knows?

 

[lektroon]

I would suspect such "proofs" are only in their popsci writings.

It's inevitable that you reach the position that the maths of pseudo-Riemannian manifolds is an accurate predictor of reality. It's therefore very sensible to conclude that such manifolds are an accurate model of reality, but you are not required to do so. As I said, the ADM formalism is a good fit for the notion of a "growing block" if you prefer it, although it's perfectly compatible with a block model too.

I think some popularisations, even by respected scientists, fail to make clear distinctions between the mathematical model (which is a pseudo-Riemann manifold, however you slice it), the reality, and the interpretation, and whether any interpretation goes anywhere near the reality.

I would say that the discovery of a closed timelike curve (or something of the sort) in reality would shoot "growing block" interpretations down in flames. However, they're pretty implausible, so until that day and as long as you are happy to assume all such spacetimes are unphysical on a philosophical rather than scientific basis, go ahead.

Greene's popularisations are well known hereabouts for the issues they raise. He may be simply picking a big number for the distance and ignoring the complications from an FLRW spacetime because he knows most of his viewers won't follow through the maths. Or maybe he is assuming a low enough speed to not run into problems and not being explicit enough about the caveats. Who knows?

Alright. Yes, fair and explanatory enough. Thank you for the clarifications.

 

[Dale]

Because the only other alternatives are presentism and possibilism (the growing block). However, is it really possible to reconcile them with special relativity?

Those are all human inventions. They have no bearing on nature.

I don't believe in the block universe. I think that a "growing block" suits much better with the reality we are experiencing. It requires reconciliation with SR, yes but other than that, it makes much more sense to me. Now, you know about what you need to prove me wrong.

Ok, stop the attitude. Nobody is required to prove you wrong. On PF it is incumbent on the person making an argument to support it sufficiently to be convincing. Usually through reference to the established professional scientific literature.

In this case, there is no scientific argument to make. It is purely philosophical. If you don’t like one philosophical perspective then use another.

 

[PeterDonis]

how can we conclude that the block universe must be true following the implications of special relativity like the relativity of simultaneity as stated in arguments like Rietdijk-Putnam-Penrose?

We can't. See this Insights article:

https://www.physicsforums.com/insights/block-universe-refuting-common-argument/

 

[jbriggs444]

I don't think that whether the spacetime has a Riemannian (curved) or Eucledian geometry changes the essence of my question

A pseudo-Riemannian manifold is not necessarily curved. For instance, the flat Minkowski spacetime of special relativity is not curved. It is a flat pseudo-Riemannian manifold.

Our spacetime does not have a Euclidean geometry.
Our spacetime is not flat.

Our spacetime is a curved pseudo-Riemannian manifold. The coordinate transformations of special relativity do not apply to our universe on the large scale that your calculations demand.

 

[lektroon]

Those are all human inventions. They have no bearing on nature.

Ok, stop the attitude. Nobody is required to prove you wrong. On PF it is incumbent on the person making an argument to support it sufficiently to be convincing. Usually through reference to the established professional scientific literature.

In this case, there is no scientific argument to make. It is purely philosophical. If you don’t like one philosophical perspective then use another.

I don't know know if you have checked out my later responses but I have already accepted the counter arguments and I mentioned that I am convinced with the fact that large scale Lorentz transformations are not applicable in the universe. So, there is nothing to stop anymore :)

 

[lektroon]

A pseudo-Riemannian manifold is not necessarily curved. For instance, the flat Minkowski spacetime of special relativity is not curved. It is a flat pseudo-Riemannian manifold.

Our spacetime does not have a Euclidean geometry.
Our spacetime is not flat.

Our spacetime is a curved pseudo-Riemannian manifold. The coordinate transformations of special relativity do not apply to our universe on the large scale that your calculations demand.

Yes, I've got the point and I have already accepted it in my earlier replies. You've made a good wrap-up though.

 

[lektroon]

We can't. See this Insights article:

https://www.physicsforums.com/insights/block-universe-refuting-common-argument/

Thanks. I will check it out.