Exploring the Paradox of Relative Truth in Special Relativity

[m4r35n357]

If we consider an event 'car hits tree' then there is definitely car and a tree at a spacelike distance.

This jumped out at me. The event (which is just four coordinate values) says nothing whatsoever about the car or the tree except that they coincided (0 spacelike distance there) at some point in spacetime. Don't know if this helps, but I thought I'd try.

 

[Ebeb]

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.

It might be interisting for the forum readers. As far as I can remember you call 'physical' only what is measured.
But this means one is not allowed to talk about a 3D universe of simultaneous events occurring now.
Which means we are not allowed to make a 3D cut though the apex of the lightcone.
Which also means we are actually not free to make 3D sections anywhere in 4D spacetime.

Then in post #126 you state <<no 3D world is physical. >>
If no 3D world is physical, then even a 3D world of the past, squeezed between the extent of the observer's past lightcone, is not physical.
Hence you contradict your "physical is only what is measured".

And you think it is all clear what you communicate? You might indeed think it, but that doesn't mean the reader agrees its all clear...

 

[Ebeb]

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/

All I can say about this article is that it doesn't give any insight al all. Nobody fully understands what you write there. As far as I can remember -correct me if I'm wrong- there was a forum thread where the article was also discussed, you participated, but you didn't like what was being said there you all of a sudden closed the topic. That suffices.

 

[Ebeb]

This jumped out at me. The event (which is just four coordinate values) says nothing whatsoever about the car or the tree except that they coincided (0 spacelike distance there) at some point in spacetime. Don't know if this helps, but I thought I'd try.

The event is not coordinates. The event is: car hits tree. Hence it contains car and tree.

 

[m4r35n357]

The event is not coordinates. The event is: car hits tree. Hence it contains car and tree.

OK, so you need to understand that the event is no more than a label: (t, x, y, z). There is no car, tree, or distance involved (spacelike or otherwise).

 

[weirdoguy]

but you didn't like what was being said there you all of a sudden closed the topic. That suffices.

As far as I recall closing thread is a decision made by whole mentors crew, not one. So I see no relevance of this comment, since most of mentors agreed to close it. And it's not so difficult to check and see why it was closed.

The event is not coordinates. The event is: car hits tree. Hence it contains car and tree.

Then you simply don't understand what an event is in relativity. An event is labelled by coordinates. To say something like "spacelike separated events" you need two events. By definition.

 

[Dale]

It might be interisting for the forum readers.

Then they are welcome to respond to you themselves on the topic.

 

[Mister T]

The idea would be that the measurement of the first event instantaneously influenced the outcome of the second event.

Instantaneously means no time elapses between the events. They are simultaneous. But that is relative. There are observers who will observe the second event occurring before the first! If you were on a jury would you convict an accused killer who shot the victim after he was killed?

 

[PeterDonis]

Nobody fully understands what you write there.

You might not, but that doesn't mean nobody does.

The event is: car hits tree. Hence it contains car and tree.

An "event" is a point in spacetime. Strictly speaking, "car hits tree" is not a single point in spacetime, so it's not a single event. For many purposes, we can idealize the car and the tree as point-like objects, and then "car hits tree" is the single point in spacetime where the two objects meet. But if you don't want to accept that idealization, then you cannot say "car hits tree" is a single event.

 

[PeterDonis]

As far as I can remember -correct me if I'm wrong- there was a forum thread where the article was also discussed, you participated, but you didn't like what was being said there you all of a sudden closed the topic.

If you think a thread was closed incorrectly, you can always use the Report button.

That suffices.

Suffices for what?

 

[name123]

@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.

So there are no people that consider it to be the case that prior to a measurement being taken of two entangled particles they are in a wave-like state and that the wave collapses upon measurement to give definite results? That Einstein with the EPR experiment suggestion wasn't suggesting that if there were no local hidden variables that it would imply "spooky action at a distance"? I thought he was and that "spooky action at a distance" implied a "spooky" process that enabled one event to cause an effect between spacelike separated particles.

 

[name123]

Instantaneously means no time elapses between the events. They are simultaneous. But that is relative. There are observers who will observe the second event occurring before the first! If you were on a jury would you convict an accused killer who shot the victim after he was killed?

Obviously it couldn't happen with a shooting because bullets don't effectively instantaneously teleport. But I thought that in quantum mechanics some interpret entangled particles to be in a wave like state before measurement, and that the wave like state collapses upon measurement. Obviously the simultaneity of the collapse would differ with relativity, and so causality would be a relative truth in such a case. Is it that relative truth seems implausible to you?

 

[name123]

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.

My point is that time is a distinct dimension. It seems to me to be operated on differently in the equations. The location in the time dimension is not invariant. There are concepts in relativity that are not invariant but relative. So just because causality (the idea that there is a process that connects the cause to the effect) would have to be relative given "spooky" action at a distance, so what? To get around that you seem to be calling for all relative concepts to be removed from relativity to avoid having causality as a relative truth. But it seems weird anyway, as you would seem to be suggesting that if a measurement was taken of an entangled particle, such that some would claim would lead the entangled particles' wave state to collapse then if a measurement of the second particle was taken such that the first measurement was in its past light cone, the wave collapse could be considered to have related the two measurements, but not if the second measurement was taken before the first measurement was in its past light cone. Even if you choose to state that, I do not understand why there could not be alternative interpretations.

 

[PeterDonis]

My point is that time is a distinct dimension.

"Timelike" is a distinct concept from "spacelike" (and "null"). That's true. I'm not sure that "time is a distinct dimension" is the best way of stating it, though.

The location in the time dimension is not invariant.

The time coordinate of an event is not invariant. (It might not even exist, if you're using coordinates that don't include a timelike one.) But again, I'm not sure that "location in the time dimension" is the best way to think of a time coordinate.

There are concepts in relativity that are not invariant but relative.

Yes, nobody is disputing that. But the concepts that are relative can't correspond to any physical observable, which means that you should beware of putting any significant interpretation on them.

But in any case, "causality" is not one of those concepts. See below.

just because causality (the idea that there is a process that connects the cause to the effect) would have to be relative given "spooky" action at a distance

Once again you are failing to read carefully. I didn't say causality had to be relative to account for spooky action at a distance. I said "causality" cannot be some single thing that satisfies both of the incompatible intuitions I described. Nothing can do that; the intuitions are incompatible. Which means that you can't just help yourself to the word "causality" in this context without specifying exactly what you mean by it. I have already explained what I mean by it. And what I mean by it is not relative.

It's possible that you could come up with some plausible meaning for the term "causality" that referred to a concept that is relative, but since such concepts can't correspond to any physical observable, why would you want to? Wouldn't it be a lot simpler to just focus on the invariants--the concepts that can correspond to physical observables?

you would seem to be suggesting that if a measurement was taken of an entangled particle, such that some would claim would lead the entangled particles' wave state to collapse then if a measurement of the second particle was taken such that the first measurement was in its past light cone, the wave collapse could be considered to have related the two measurements, but not if the second measurement was taken before the first measurement was in its past light cone

I have stated no such thing. I have stated that spacelike separated measurements must commute. I have not stated any requirement for measurements that are not spacelike separated. They might commute, or they might not. It happens that, for the particular case of measurements on a pair of entangled particles, the results commute regardless of whether the measurements are spacelike separated or not. (It's simple to see this by looking at the math, since the mathematical description of the measurement probabilities does not even include the nature of the interval between events--timelike, spacelike, or null.) So in this case, the results are the same whether one measurement is in the past light cone of the other or not.

 

[PeterDonis]

Obviously the simultaneity of the collapse would differ with relativity, and so causality would be a relative truth in such a case.

Which measurement happened first would be relative, yes. But since the measurement results commute (they are the same regardless of which happened first), the results, and the correlations between them, are not relative. Therefore, the effects of wave function collapse (if we adopt a collapse interpretation of QM) are not relative either.

 

[name123]

Once again you are failing to read carefully. I didn't say causality had to be relative to account for spooky action at a distance. I said "causality" cannot be some single thing that satisfies both of the incompatible intuitions I described. Nothing can do that; the intuitions are incompatible. Which means that you can't just help yourself to the word "causality" in this context without specifying exactly what you mean by it. I have already explained what I mean by it. And what I mean by it is not relative.

I am not totally clear on which incompatible intuitions you are referring to but you had written:

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.

If they are the intuitions, then I had mentioned that I thought Everett's Interpretation had the idea that spacelike separated events can't causally affect each other and the intuition that correlations that violate the Bell inequalities imply some kind of relationship.

But the issue was whether the idea that spacelike separated events can't causally affect each other is not debatable. But I have been pointing out that with the Copenhagen Interpretation of Quantum Mechanics, a measurement of entangled pair of particles would be thought to be cause the collapse of their wave function. With that interpretation and the relativity interpretation, there could be scenarios where it would be considered a relative truth which measurement caused the collapse of the wave function. But you seem to disagree that this would be the case with the Copenhagen Interpretation. Perhaps you could point out my misunderstanding of it.

It's possible that you could come up with some plausible meaning for the term "causality" that referred to a concept that is relative, but since such concepts can't correspond to any physical observable, why would you want to? Wouldn't it be a lot simpler to just focus on the invariants--the concepts that can correspond to physical observables?

It isn't an issue of coming up with a meaning for the term causality that is relative. It is simply an issue of keeping the same meaning as the term as ever had. If you want a term that means something different then pick a new term. You seem to simply be advocating something akin to a logical positivist approach, and that is fine, but I don't think it is compulsory. There are lots of interpretations in physics.

 

[name123]

Which measurement happened first would be relative, yes. But since the measurement results commute (they are the same regardless of which happened first), the results, and the correlations between them, are not relative. Therefore, the effects of wave function collapse (if we adopt a collapse interpretation of QM) are not relative either.

But which measurement led to the collapse could be.

 

[PeterDonis]

I am not totally clear on which incompatible intuitions you are referring to

The ones you explicitly stated, to which I responded in post #166. Are you reading what anyone else writes in this thread?

If they are the intuitions

They are. See above. I've already responded to what you say after this. Again, are you reading what others write in this thread? You keep on repeating statements of yours that others have already addressed.

which measurement led to the collapse could be.

Which measurement led to the collapse is not an observable, and has no physical meaning. Yes, it could be considered "relative", but that just means you should quit trying to think about it and focus on invariants instead.

 

[Mister T]

Obviously the simultaneity of the collapse would differ with relativity, and so causality would be a relative truth in such a case. Is it that relative truth seems implausible to you?

What's impossible is one event being the cause of another when those events have a spacelike separation. What seems implausible to me is an effect occurring before its cause, so if one event is said to be the cause of another that's a statement that can be assigned a value of either true or false. I don't know the meaning of relative truth.

 

[Dale]

So there are no people that consider it ...

If there are, then they are not publishing it in the modern professional scientific literature. (To my limited knowledge)

In any case, this remains wholly irrelevant to a classical object like a brain.

a "spooky" process that enabled one event to cause an effect

It is not considered a cause-effect relationship because of the commutation that @PeterDonis mentioned.

you seem to be calling for all relative concepts to be removed from relativity

Can you please stop making completely disingenuous remarks about other people’s comments. If you think someone is saying something then quote them exactly. Where exactly did he say to remove all relative concepts from relativity? Nowhere. It is a complete fabrication about his position.

 

[PeterDonis]

What's impossible is one event being the cause of another when those events have a spacelike separation.

The issue, though, is that correlations between spacelike separated quantum measurements can violate the Bell inequalities, which means there is no way to account for them using the intuitive model of "causality" that you are describing here, where all you need is data in the past light cone of a given measurement to account for its result. These are the two incompatible intuitions I referred to in earlier posts in response to @name123.

As I've said in other posts, this does not mean the concept of causality is no longer valid, or that it is relative. It just means you have to be careful how you define that concept if you insist on a precise definition.

 

[name123]

The ones you explicitly stated, to which I responded in post #166. Are you reading what anyone else writes in this thread?

(Small note but for clarification the intuitions weren't ones I had brought into the conversation, they were introduced by PeterDonis in post #154)

A slightly strange reply, since I offered a quote from you and asked you whether they were the intuitions you were talking about, to which you replied:

They are. See above. I've already responded to what you say after this. Again, are you reading what others write in this thread? You keep on repeating statements of yours that others have already addressed.

I don't think it takes a detective to work out that I had obviously read them to quote them. You seem to be reverting to a tactic you have used before, in claiming that what I am asking has already been answered, and that I am not reading the replies, then shutting down the thread.

In post #166 you simply repeated your claim that the intuitions were incompatible

You're still not getting it. These two intuitions, in themselves, are not compatible.

While again failing to point out why Everett's interpretation is not compatible with them.

With Everett's interpretation (as I understand it) the intuition that spacelike separated events can't causally affect each other is satisfied because there is no faster than light influence. But each measurement leads to a "split in the universe". In one half of the split the measurement measured a +1/2 spin and in the other it measured a -1/2 spin, and that is the case for each particle irrespective of what the other measurement was. So the first measurement does not influence the second, thus the spacelike separated events don't causally affect each other. So it is compatible with the first of your so called incompatible intuitions.

But what about the second? Those splits then propagate at the speed of light through the universe, and when they meet, both sides of the splits which carried the +1/2 spins measurements marry up with the sides of the splits that carry the -1/2 spin from the other measurement. So it offers a causal explanation for the violation of the Bell inequalities.

So perhaps either explain where I am wrong with Everett's interpretation being compatible with the intuitions you claim are incompatible, or concede that you were wrong that they were incompatible, and had just ignored what I had wrote when I repeatedly pointed out Everett's interpretation.

Which measurement led to the collapse is not an observable, and has no physical meaning. Yes, it could be considered "relative", but that just means you should quit trying to think about it and focus on invariants instead.

To you. To you it has no physical meaning, because you have adopted a logical positivist like attitude to the issue. You didn't point it out though when you initially claimed that there could be no spacelike separated causal relations. You effectively deny causality. You deny that you do, but that is because you redefine the term causality to mean something different. You do deny causality as it is commonly conceived. In which there is a relation between a cause an effect. But not everyone takes a logical positivist type attitude. And without redefining causality, and instead using the common usage, with the Copenhagen Interpretation spacelike events can be causally related. So how do you feel you were correct in claiming that it isn't debatable that they can be given the Copenhagen Interpretation which I thought was a quite commonly held interpretation of quantum mechanics, and the one I assume you were taught at university?

 

[name123]

If there are, then they are not publishing it in the modern professional scientific literature. (To my limited knowledge)

Does the Copenhagen Interpretation of quantum mechanics not suggest that the measurement of either of the spacelike separated entangled particles would cause the collapse of the wave function resulting in each of the particles having definite values for what was measured?

It is not considered a cause-effect relationship because of the commutation that @PeterDonis mentioned.

It would be with the Copenhagen interpretation though. The @PeterDonis version of causality is a redefining of the term. In which there is neither a cause nor an effect. But I am not using that redefined version of causality, and I don't think you were when you wrote:

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

The point is that some interpretations like the Copenhagen Interpretation of quantum mechanics does as far as I am aware suggest that spacelike separated events can be causally related. The measurement being the cause the of wave function collapse and of the particles having the properties that they could subsequently be measured to have.

Can you please stop making completely disingenuous remarks about other people’s comments. If you think someone is saying something then quote them exactly. Where exactly did he say to remove all relative concepts from relativity? Nowhere. It is a complete fabrication about his position.

I may have misinterpreted him, but I wasn't trying to fabricate anything. He had written:

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".

But what was wrong with the truth about causation being relative? He went onto write:

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.

Notice that for @PeterDonis the well defined concepts were those that were invariant and not relative. His argument against the concept of "causally related" was that it was not defined in an invariant manner. If he believed the argument had any weight, then why would he not also be using it against other relative concepts in relativity?

 

[PeterDonis]

While again failing to point out why Everett's interpretation is not compatible with them.

And you still are not reading what I actually wrote. Go back and read my post #166.

Those splits then propagate at the speed of light through the universe

I don't know where you're getting this from, but it's not part of the Everett interpretation. The "worlds" in that interpretation are just terms in the universal wave function. Terms in the universal wave function don't propagate; the concept doesn't even make sense.

To you it has no physical meaning, because you have adopted a logical positivist like attitude to the issue.

No, I am simply pointing out what relativity--the basic theory, not any "interpretation" put on it--says. It says all of the physical content of the theory is contained in invariants, i.e., things that are not relative. That is why Einstein said the theory was misnamed; it should have been called the theory of invariants.

If he believed the argument had any weight, then why would he not also be using it against other relative concepts in relativity?

I am. Did you read what I wrote? I said you should not focus on any relative concepts.

You need to read @Dale's comment at the end of post #195. This thread is going on and on because you keep talking about your own misinterpretations instead of what others are actually telling you.

 

[PeterDonis]

Thread closed for moderation, to evaluate whether further discussion would be productive.

 

[PeterDonis]

After moderator review, this thread will remain closed.