Exploring the Paradox of Relative Truth in Special Relativity

[PeterDonis]

Are there not experiments where entangled particles are separated and they then subsequently have certain properties tested such as their spin for example, and that even if they are tested within a time frame which wouldn't allow for any causal effect from the testing of one even if traveling at the speed of light to have influenced the testing of the other, the spins for example are always opposite?

Does Bell's Inequality theorem not indicate that there could be no local hidden variables responsible?

Yes, there have been experiments verifying that quantum phenomena violate the Bell inequalities. No, that doesn't mean relativistic causality is violated. As I've already said.

 

[Ebeb]

The usual model is to treat spacetime as a 4d whole. You can select any 3d plane passing through your worldline "now" and call that "the universe now", but there's no significance to any particular choice. All are arbitrary 3d subsets of the 4d whole.

Looks fine to me.

We're not saying that the 3d subsets don't exist. Just that there are infinitely many ways to pick a subset and no good reason to prefer one choice over another.

Great.

No 3D world is physical. The physical world if 4D.

No 3D world is physical?
If the physical world is 4D, then 3D as a part of 4D has to be physical too.

Didn’t we have a really really long conversation about this already?

Yes, and I gave up because we couldn't get on the same wavelength.
Maybe we disagree on the meaning of physical.
As far as I understand Ibix, the events as such are indeed physical entities. If we consider an event 'car hits tree' then there is definitely car and a tree at a spacelike distance. There are physical object(s) at spacelike distance, hence the 3D world of simultameous events is physical.
And because there is no preference for a simultaneous collection, all 3D are physical. Which makes 4D physical too.

None. As @Dale and @Ibix have said, the usual model is to consider 4D spacetime as "real".

None? If the usual model is to consider 4D spacetime as "real", then the 3D collection of events is real too, see above, i.o.w. your -quote-" None" -unquote- cannot be correct.

I think Name123 too is a bit lost with above discrepancies. That's why he struggles with 'post topic Relative truth'.

 

[PeterDonis]

The issue was whether the two events can be interpreted as being causally related.

No, the issue is whether relativistic causality is violated. It isn't.

Asking whether two spacelike separated measurement events themselves are "causally related" is a different question. The strict answer to it if we take the viewpoint of relativistic causality is that the question has no meaning, because relativistic causality does not tell you which events can be "causally related". It just tells you that spacelike separated events have to commute--i.e., what happens at them does not depend on their ordering. The fact that the events commute does not prevent what happens at them from being correlated.

 

[PeterDonis]

If the usual model is to consider 4D spacetime as "real", then the 3D collection of events is real too

No, if the model considers all of 4D spacetime as real, then you cannot pick out any particular 3D collection of events as "real" while the others aren't. But you were implicitly saying that just one 3D collection of events was "real" and the others weren't.

If you're willing to say that "all 3D worlds are real", including 3D worlds that only contain events billions of years in our past here and now, and also 3D worlds that only contain events billions of years in our future here and now, then yes, you can say that. But then you can't draw the conclusions you are trying to draw from "3D worlds are real".

 

[Ebeb]

No, if the model considers all of 4D spacetime as real, then you cannot pick out any particular 3D collection of events as "real" while the others aren't. But you were implicitly saying that just one 3D collection of events was "real" and the others weren't.

I never said that. How can you pretend this after reading what I said about Ibix post? see #142

If you're willing to say that "all 3D worlds are real", including 3D worlds that only contain events billions of years in our past here and now, and also 3D worlds that only contain events billions of years in our future here and now, then yes, you can say that. But then you can't draw the conclusions you are trying to draw from "3D worlds are real".

No. You didn't understand me. I'm talking of 3D worlds or 3D universe 'now' as 3D sections made of simultaeous events.
What's you point of view on Ibix post #127 ?

 

[name123]

Yes, there have been experiments verifying that quantum phenomena violate the Bell inequalities. No, that doesn't mean relativistic causality is violated. As I've already said.

I never said it did mean relativistic causality is violated.

Dale had written:

One key physical constraint is that spacelike separated events cannot be causally related,

I had replied:

Well presumably this is up for debate given "spooky" action at a distance.

And then you wrote:

No, it isn't. Quantum phenomena still obey relativistic causality.

Though presumably you knew that quantum phenomena being interpreted as indicating that spacelike separated events can be causally related didn't imply that they were being interpreted as not obeying relativistic causality. So I found it slightly strange that you made such a switch on what I thought was supposed to be an educational site.

You seem to understand that many do interpret the experiments as indicating that spacelike separated events can be causally related and thus a claim that they cannot be is debatable. As I mentioned.

 

[name123]

No, the issue is whether relativistic causality is violated. It isn't.

No that was not the issue. That was what you tried to change the issue to as explained above in post #146

 

[PeterDonis]

I'm talking of 3D worlds or 3D universe 'now' as 3D sections made of simultaeous events.

Yes, but why pick out "now"? And why pick out your particular "now" (the events simultaneous to "here and now" in your rest frame), as opposed to someone else's "now" (the events simultaneous to "here and now" in someone else's frame)? Unless you want to give "now" some special status, there is no point to even mentioning it. And if all of 4D spacetime is real, then "now" has no special status.

What's you point of view on Ibix post #127 ?

See my post #128.

 

[PeterDonis]

I never said it did mean relativistic causality is violated.

Good. Then what have we spent the last hundred or so posts discussing?

You seem to understand that many do interpret the experiments as indicating that spacelike separated events can be causally related

I understand no such thing. I already explained what I understand in post #143.

 

[PeterDonis]

And if all of 4D spacetime is real, then "now" has no special status.

And similarly, if you take the alternative viewpoint I described in post #128 (that what is in your past light cone is what is "real"), then again "now" has no special status, so again there's no reason to even mention it.

 

[PeterDonis]

because there is no preference for a simultaneous collection, all 3D are physical. Which makes 4D physical too.

As a logical argument for the "block universe" (all 4D spacetime is real) viewpoint, this is flawed. See the Insights article I wrote about this:

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

 

[name123]

Good. Then what have we spent the last hundred or so posts discussing?

I have only been discussing this with you for a few posts, after you jumped in on a conversation I was having with Dale.

I understand no such thing. I already explained what I understand in post #143.

Let me rephrase more in line with Dale's statement. As I have already outlined to you in post #146

Dale wrote:

One key physical constraint is that spacelike separated events cannot be causally related,

I replied:

Well presumably this is up for debate given "spooky" action at a distance.

And you replied:

No, it isn't.

In post #146 you indicated that:

The strict answer to it if we take the viewpoint of relativistic causality is that the question has no meaning, because relativistic causality does not tell you which events can be "causally related". It just tells you that spacelike separated events have to commute--i.e., what happens at them does not depend on their ordering. The fact that the events commute does not prevent what happens at them from being correlated.

As the discussion outline hopefully makes clear it is not an issue of whether relativity prevents commuting events from correlating.

The issue is whether relativity is compatible with spacelike separated events being causally related. As I understand it relativity does not prohibit spacelike separated events from being causally related because it does not prohibit particles of a negative mass from traveling faster than the speed of light.

Is it that in post #143 were you claiming that causality has no meaning in relativity? If you were, might I ask whether that became accepted after the "spooky" action at a distance experiments were performed? Either way, I don't think Dale was claiming that there is no such thing as causality, else he wouldn't have specified the constraint involved spacelike separated events.

Edit: If you were to claim that with relativity there is not such thing as causality, because of spooky action at a distance, I do not understand why causality cannot be relative. Also Everett's model is compatible with relativity is it not, and it has non-relative causality does it not?

 

[PeterDonis]

I have only been discussing this with you for a few posts, after you jumped in on a conversation I was having with Dale.

To clarify, by "we", I meant all of the participants in this thread, not just you and me.

The issue is whether relativity is compatible with spacelike separated events being causally related.

No, it isn't, because "causally related" isn't a well-defined concept. That's the point I'm making, which you continue to miss.

The well-defined concepts are: whether a given pair of events are spacelike, timelike, or null separated; and what the observed correlations are between measurement results at a given pair of events.

If you could define whether a pair of events are "causally related" in terms of those well-defined concepts, then it would also be a well-defined concept. But you can't. That's the point.

Is it that in post #143 were you claiming that causality has no meaning in relativity?

No. Go read what I wrote again.

If you were to claim that with relativity there is not such thing as causality, because of spooky action at a distance

I wasn't. Go read what I wrote again.

 

[PeterDonis]

If you could define whether a pair of events are "causally related" in terms of those well-defined concepts, then it would also be a well-defined concept. But you can't.

More precisely, you can't and still do justice to both the intuition that spacelike separated events can't causally affect each other, and the intuition that correlations that violate the Bell inequalities imply some kind of causal effect. The way to fix that is to give up the idea that "causally related" is a well-defined concept, and focus on the other well-defined concepts I gave. (Plus the well-defined concept of whether measurements at a given pair of events commute.)

 

[PeterDonis]

One key physical constraint is that spacelike separated events cannot be causally related

In view of the confusion it is causing, I would recommend abandoning this language ("causally related"), as I explained in my previous few posts.

 

[name123]

More precisely, you can't and still do justice to both the intuition that spacelike separated events can't causally affect each other, and the intuition that correlations that violate the Bell inequalities imply some kind of causal effect. The way to fix that is to give up the idea that "causally related" is a well-defined concept, and focus on the other well-defined concepts I gave. (Plus the well-defined concept of whether measurements at a given pair of events commute.)

Everett's theory has the intuition that spacelike separated events can't causally affect each other and the intuition that correlations that violate the Bell inequalities imply some kind of causal effect does it not.

There is a difference between stating that you would choose to give up causality, and stating that your decision is not debatable and is compulsory for everyone that wishes to cling to a relativity interpretation. Apart from Everett's theory, relativity also seems to be open to the interpretation that spacelike separated events can causally affect each other, and that causality is relative.

 

[Ibix]

No 3D world is physical?

The point is - how would you describe a 2d slice through 3d space? It exists. I can pick an infinite number of different ones that pass through a given point. But so what? It's not particularly interesting in any physical sense. It's just some random choice of slice. It may be tactically useful to consider such a slice (the ecliptic plane is one such) but there's nothing in the laws of physics that picks it out.

That's why we call a 3d slice through 4d spacetime unphysical. Which one you pick depends solely on your choice of simultaneity criterion. There's no physical law that picks it out.

 

[Mister T]

So what if you can't "send knowledge of that outcome and have it arrive at the location of the second event before that second event occurs"? The issue was whether the two events can be interpreted as being causally related.

If news of the outcome of the first event can't possibly, even in principle, reach the second event before it occurs then the first event can't possibly be the cause of the second event.

 

[PeterDonis]

Everett's theory

Everett gave an interpretation, not a theory; his interpretation of QM makes the same predictions as all other interpretations of QM.

has the intuition that spacelike separated events can't causally affect each other and the intuition that correlations that violate the Bell inequalities imply some kind of causal effect does it not.

I don't think these conflicting intuitions are tied to any particular interpretation of QM. In fact I don't think they're tied to QM at all; they are leftovers from pre-quantum thinking that simply have to be discarded.

There is a difference between stating that you would choose to give up causality

I have never said I would choose to give up causality. You need to read more carefully.

relativity also seems to be open to the interpretation that spacelike separated events can causally affect each other

No, because "causally affect" is not well-defined.

and that causality is relative

I don't know where you're getting that from. All of the concepts that I said were well-defined in previous posts are invariants in relativity.

 

[name123]

If news of the outcome of the first event can't possibly, even in principle, reach the second event before it occurs then the first event can't possibly be the cause of the second event.

The idea would be that the measurement of the first event instantaneously influenced the outcome of the second event. Not that there was a delay. A word like "news" is confusing, as it tends to imply sending information from one conscious observer to another. The two things are quite different. There could be instantaneous causality (such as that in Bohemian Mechanics for example), and yet no way for observers to exploit it in order to send information to one another.
If there was no way to exploit it to send information to one another it does not imply that there is no instantaneous causality.

 

[Nugatory]

Well I think those experimental results have been interpreted as being the measurement of one particle causally influencing the measurement of another particle even though the events were spacelike separated, and so have been interpreted as contradicting the statement "spacelike separated events cannot be causally related".

"Have been interpreted..." by whom? I am aware of no serious peer-reviewed claim of that sort - if you think you've found one, chances are that the word "causal" is being used in a different way than you're understanding it.

As I understand it relativity does not prohibit spacelike separated events from being causally related because it does not prohibit particles of a negative mass from traveling faster than the speed of light.

Again, do you have a source for this claim? It's a popular misconception, but in fact the objection to causal relationships between spacelike-separated events is not based on the impossibility of faster-than-light travel. The argument goes the other way: landing my FTL spaceship at the destination is caused by, among other things, the spaceship having taken off in the first place so FTL travel requires a causal relationship between two spacelike-separated events, and this is not allowed by relativity.

The objection to causal relationships between spacelike-separated events is based on Tolman's paradox and similar time travel paradoxes. Attempts to work around these problems are highly speculative and by no means generally accepted.

 

[name123]

Everett gave an interpretation, not a theory; his interpretation of QM makes the same predictions as all other interpretations of QM.

Ok, but his interpretation has the intuition that spacelike separated events can't causally affect each other and the intuition that correlations that violate the Bell inequalities imply some kind of causal effect does it not?

I have never said I would choose to give up causality. You need to read more carefully.

You wrote that

The way to fix that is to give up the idea that "causally related" is a well-defined concept, and focus on the other well-defined concepts I gave.

I assumed you meant that we should give up the idea that there is a causal relation between events. The idea of there being a causal relation between events was what I thought was implied by the idea of causality.

I don't know where you're getting that from. All of the concepts that I said were well-defined in previous posts are invariants in relativity.

The concept of dimensions is used in relativity, and I thought a conceptual distinction was made between the three spatial dimensions and the time dimension, but an event's location in the distinct time dimension is not invariant for an event's location, only the spacetime interval is. The reason I suspect the theory is know as relativity is because it utilises concepts that are not invariant, but are relative.

Do you agree and think that are distinctions made between the 4 dimensions of spacetime or is their selection just arbitrary, like the dimensions of Cartesian space?

 

[name123]

"Have been interpreted..." by whom? I am aware of no serious peer-reviewed claim of that sort - if you think you've found one, chances are that the word "causal" is being used in a different way than you're understanding it.

Maybe, but could you explain what you thought Einstein was thinking when he used the term "spooky action at a distance" for such a result?

Again, do you have a source for this claim? It's a popular misconception, but in fact the objection to causal relationships between spacelike-separated events is not based on the impossibility of faster-than-light travel. The argument goes the other way: landing my FTL spaceship at the destination is caused by, among other things, the spaceship having taken off in the first place so FTL travel requires a causal relationship between two spacelike-separated events, and this is not allowed by relativity.

The objection to causal relationships between spacelike-separated events is based on Tolman's paradox and similar time travel paradoxes. Attempts to work around these problems are highly speculative and by no means generally accepted.

I just thought that relativity only ruled out faster than light travel for things with a positive mass. And that these particles never traveled less than the faster than the speed of light. And the issue isn't whether the things are accepted, it is whether they are debatable.

 

[PeterDonis]

his interpretation has the intuition that spacelike separated events can't causally affect each other and the intuition that correlations that violate the Bell inequalities imply some kind of causal effect does it not?

Go back and read my post again. I already answered this question.

I assumed you meant that we should give up the idea that there is a causal relation between events. The idea of there being a causal relation between events was what I thought was implied by the idea of causality.

Then you thought wrong. In quantum field theory, i.e., QM combined with special relativity, "causality" means that spacelike separated measurements must commute--their results can't depend on the order in which they happen. That's all it means.

I thought a conceptual distinction was made between the three spatial dimensions and the time dimension

No, a distinction is made between timelike, null, and spacelike separation between events. But that does not require you to label one specific "dimension" as the "time" dimension. The fact that this is usually done in treatments of SR is a convenience, not a necessity.

 

[name123]

Go back and read my post again. I already answered this question.

I did. But let me rephrase. Is Everett's interpretation compatible with the intuition that spacelike separated events can't causally affect each other and the intuition that correlations that violate the Bell inequalities imply some kind of causal effect does it not?

Then you thought wrong. In quantum field theory, i.e., QM combined with special relativity, "causality" means that spacelike separated measurements must commute--their results can't depend on the order in which they happen. That's all it means.

Ok, so (taking a slightly logical positivist's approach, which apparently Einstein later backed off of) in quantum field theory "causality" means that spacelike separated measurements must commute--their results can't depend on the order in which they happen. That's all it means. So on what basis are you claiming that there can be no causality between spacelike separated measurements?

Edit: So you are not claiming that there is no causality. Just that there is no relation between one event and another other than a correlation. But presumably the claim that there is no relation is debatable.

No, a distinction is made between timelike, null, and spacelike separation between events. But that does not require you to label one specific "dimension" as the "time" dimension. The fact that this is usually done in treatments of SR is a convenience, not a necessity.

I wasn't asking about distinction between spacetime intervals. The question was:

Do you agree and think that are distinctions made between the 4 dimensions of spacetime or is their selection just arbitrary, like the dimensions of Cartesian space?

The point being could I chose the x and y spacetime coordinates and arbitrarily decide that they are the x and t coordinates and use them in the equations?

 

[PeterDonis]

Is Everett's interpretation compatible with the intuition that spacelike separated events can't causally affect each other and the intuition that correlations that violate the Bell inequalities imply some kind of causal effect does it not?

You're still not getting it. These two intuitions, in themselves, are not compatible. So nothing else can be compatible with both of them. You have to give up at least one. Or, as I have suggested, you can give up the idea of "causal effect" between a specific pair of events as a single thing, and focus on the other things I have already mentioned several times that are well-defined instead.

on what basis are you claiming that there can be no causality between spacelike separated measurements?

I have not claimed that. You really, really need to go back and read what I've actually said more carefully.

could I chose the x and y spacetime coordinates and arbitrarily decide that they are the x and t coordinates and use them in the equations?

You can choose any coordinates you want. It doesn't change any invariants, including whether a given pair of events are spacelike, timelike, or null separated.

Also, the fact that you call a coordinate "t" doesn't mean it's a "time" coordinate. You have to look at invariants, such as whether events with the same $t$ coordinate are spacelike separated or not, to determine whether a "t" coordinate in a particular coordinate chart qualifies as a "time" coordinate. (Note also that it is perfectly possible to have a coordinate chart that has no "time" coordinate.)

 

[name123]

You're still not getting it. These two intuitions, in themselves, are not compatible. So nothing else can be compatible with both of them. You have to give up at least one. Or, as I have suggested, you can give up the idea of "causal effect" between a specific pair of events as a single thing, and focus on the other things I have already mentioned several times that are well-defined instead.

So with Everett's interpretation if I understand it, if not count it as a consideration of my own.

There is no faster than light influence. So one measurement does not influence the other directly. If it were a binary issue, there could event A outcomes of

1) 0
2) 1

and

event B outcomes of

3) 0
4) 1

And that 2 distinct universes would be created and in one (1) matches with (4) and in another (2) matches with (3).

So that that the A outcome didn't affect the B outcome, but that the resultant correlations were influenced by the result (of either A or B) because it influenced how they were matched. .

I have not claimed that. You really, really need to go back and read what I've actually said more carefully.

I realize that, tried to fix it in an edit, but did it presumably too late.

You can choose any coordinates you want. It doesn't change any invariants, including whether a given pair of events are spacelike, timelike, or null separated.

Also, the fact that you call a coordinate "t" doesn't mean it's a "time" coordinate. You have to look at invariants, such as whether events with the same $t$ coordinate are spacelike separated or not, to determine whether a "t" coordinate in a particular coordinate chart qualifies as a "time" coordinate. (Note also that it is perfectly possible to have a coordinate chart that has no "time" coordinate.)

So are you saying that if I there was a passer by traveling in the x direction that I could substitute their y coordinate (in which there is not change) for their t coordinate (for which there is a change) that it works out pretty much the same?

Edit: Such that you could describe the experience without knowing which way it was.

 

[PeterDonis]

So are you saying that if I there was a passer by traveling in the x direction that I could substitute their y coordinate (in which there is not change) for their t coordinate (for which there is a change) that it works out pretty much the same?

I said you can use any coordinates you want, but you still need to have a valid transformation from one chart to another. I'm not sure whether what you are describing is a valid transformation or not, because you haven't shown any math describing the transformation.

 

[Dale]

Maybe we disagree on the meaning of physical.

Yes, I think we do disagree on the meaning of physical. In that previous conversation I was very clear about what I mean by it. I have no desire to rehash it here.

 

[name123]

I said you can use any coordinates you want, but you still need to have a valid transformation from one chart to another. I'm not sure whether what you are describing is a valid transformation or not, because you haven't shown any math describing the transformation.

So imagine a change in x and t, but none in y and z, and provide a transformation for changing it to a change in x and y, but none in t or z, such that it makes no difference to what the experience would be expected to be.

 

[Dale]

In view of the confusion it is causing, I would recommend abandoning this language ("causally related"), as I explained in my previous few posts.

Well, I am not sure how to say it otherwise. Maybe: Any observable (including an “experience”) is a function only of events within its past light cone.

 

[PeterDonis]

imagine a change in x and t, but none in y and z, and provide a transformation for changing it to a change in x and y, but none in t or z, such that it makes no difference to what the experience would be expected to be.

This still doesn't give an actual mathematical description of the coordinate transformation. But if it's a valid coordinate transformation, then it won't change any invariants, which means it won't change any physical consequences of the theory, including what anyone will experience.

 

[PeterDonis]

Any observable (including an “experience”) is a function only of events within its past light cone.

This will work for classical SR, yes. If we include quantum mechanics, so that we are in the domain of quantum field theory, I think it would have to be rephrased as a statement about commutation relations, for example: any observable (including an "experience") can only fail to commute with events within its past light cone.

 

[Dale]

@name123 so there has been a whole bunch I missed today. Yes, I agree that it is “debatable” in the same sense that whether the Earth is round or flat is debatable. I.e. you will get people who argue any point. As @Nugatory mentioned, to the best of my knowledge this is not considered an open issue in the modern professional scientific literature.

Additionally, the brain is a classical object, governed by classical laws. See my recent post to @PeterDonis and his response. Although you have to use slightly weird language (regarding commutators) for quantum systems, you can be more straightforward for classical systems like the brain.

Bottom line: your experience at any moment is a function only of events in your past light cone at that moment, not of simuktaneous events. As such it is a relativistic invariant. Indeed, this is necessary because experience is an observable and all observable are invariants.

 

[PAllen]

This will work for classical SR, yes. If we include quantum mechanics, so that we are in the domain of quantum field theory, I think it would have to be rephrased as a statement about commutation relations, for example: any observable (including an "experience") can only fail to commute with events within its past light cone.

I beg to differ. The observation of correlation for entanglement is only based on setting of devices in its past light cone. Each local measurement's probability distribution needs only past light cone information. The weird part is that the observation of correlations depends on device setting events that were spacelike separated, and the correlation can't be explained by any model in which the local measurements are independent of each other.

However one is not forced to accept any generalization of strict SR causality. One unpalatable option (but enough to prove there is absence of necessity) is that the device settings are determined as of generation of the entangled particles.