God vs The Multiverse

Click here for God vs The Multiverse: a rational argument for the Existence of One God who intelligently designed one universe.

Sunday, July 15, 2012

God vs The Multiverse (Part 10: Mathematical Wonderland)

In the previous post, we suggested that multiverse theory is not truly science, but is bad philosophy. We did not mean that the average technical paper on multiverse theory reads like a philosophy paper. This is certainly not the case, as they certainly appear like mathematical physics papers. Rather, we mean that multiverse theory is rooted in a bad philosophy, which renders all the rigorous mathematics as details of a false system.  Confusing rigorous mathematics for the science of physics is a serious philosophical and scientific error, that leads to the decay of the physicist's mission of discovering the true reality of our universe.

The following video is from Max Tegmark, who is featured prominently on the Wikipedia multiverse page for his classification of different types of multiverses.  The main focus of this post will be on the last 4 minutes of the video (from the 10:45 minute mark), as other posts in this series deal with his first two levels of multiverse.  (If you only watch the last 4 minutes of the video, you can skip the next two paragraphs.)

Tegmark's level 3 multiverse is the semi-popular philosophical interpretation of quantum mechanics called the Many Worlds Interpretation.  We do not take up the standard understanding of this theory in depth as it has no bearing on the fine tuning of the constants, since the laws of nature and the constants do not change in the different worlds/multiverses.  It is similar to his level 1 multiverse, in the sense that while it posits an infinite number of alternate universes that are each ordered, it does not try to posit a combination of randomness and infinite tries to explain apparent order.

There are some physicists (Hawking as elaborated on by Sidney Coleman) who try to apply Quantum Mechanics to yield the constants themselves.  This approach uses Quantum Mechanics in an unconventional manner (as a meta law that determines the fundamental constants, as opposed to a law which governs the interactions of energy) to try to provide a model for the number generator that multiverse theory requires.  We aren't going to focus on this point, as our main problem with multiverse theory is not that it has a speculative model for the random number generator.  There are bigger problems.

What is particularly disturbing about this interview is that it is being conducted under the pretense of a true representation of reality, as determined by science.  The interviewer tells Tegmark that he is seeking reality and is coming to Tegmark to find out from him what is real. Tegmark proceeds to present his level 4 multiverse which he says would be nuts if it were not true.


Tegmark confuses mathematical possibility with physical reality.  Mathematics is a special language which is used to quantitatively describe the physical world we observe.  Mathematics is not physics.  The theory that every conceivable, mathematically consistent law is actually real is not even wrong.  It is simply crazy.

This theory implicitly undermines all truth that science has discovered or will ever discover, by granting equal existence in reality to every possibility that any mathematician can imagine.  What truth value do the scientific discoveries of General Relativity and Quantum Mechanics have, if they are just two laws out of the infinite set of all the laws that actually exist?  Faith in Mathematical Wonderland is tantamount to denial of the very Foundations and Pillar of the sciences.

While most scientists do not believe in this theory, Tegmark's respected place in the scientific community is truly astonishing to us.  (He is a professor at MIT with over 200 publications, 9 of which have been cited over 500 times each.)  Tegmark's theory is an extreme form of a problem which exists in various degrees in all multiverse theories. The theory of Mathematical Wonderland reveals more about the current state of theoretical physics than it does about the rest of reality.

Putting aside the problems with Tegmark, there is a more general point with regards to all multiverse theories which posit an infinite number of actual physical universes.  It is no small claim that there exists an actual physical infinity.  This is a very questionable philosophical issue.  Infinity commonly arises in pure mathematics, but is usually a sign of a problem in a theory of physics which describes the real world. (See the Ellis/Carr article where even Carr doesn't seem to believe in it.)

Georg Cantor was one of the most important mathematicians who did believe in actual infinities. Cantor was the originator of set theory, and was the first to show (1874) that there are different levels of mathematical infinity.  He did so again in a more elegant manner with his diagonal argument (1891). Cantor also had a philosophical theory, whereby he equated the Absolute Infinite with god.

Mathematicians generally accept set theory and the levels of infinity in mathematics, but disagree with Cantor's philosophy.  The Wiki page on Cantor explains his philosophy in a way which seems very similar with Tegmark's statements:
Cantor's philosophy on the nature of numbers led him to affirm a belief in the freedom of mathematics to posit and prove concepts apart from the realm of physical phenomena, as expressions within an internal reality. The only restrictions on this metaphysical system are that all mathematical concepts must be devoid of internal contradiction, and that they follow from existing definitions, axioms, and theorems.
Carl Gauss, physicist and arguably the greatest mathematician ever, wrote "I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics.  Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction."

The great mathematician David Hilbert said "Let us draw the conclusion from all our reflections on the infinite. The overall result is then: The infinite is nowhere realized. Neither is it present in nature nor is it admissible as a foundation of our rational thinking."

Aristotle and Wittgenstein are among the many philosophers who emphatically denied the existence of actual infinities.  Any actual, countable (observable) infinity would come under Hilbert's Paradox of the Grand Hotel, in addition to many other absurd beliefs you are forced to accept when you realize what infinity really means.

Despite these serious philosophical issues, many multiverse theorists are quick to invoke infinitely many universes.  Perhaps it is because they don't realize that they are engaging in philosophy, but rather believe that they are involved in the discovery of scientific theories like Mathematical Wonderland.

Click here to continue to Stage 2b

40 comments:

  1. My impression watching the video is - only a culture that teaches its children that Santa Claus brings them presents if they are good, could be capable of having a mind thats quite intelligent but with a poor faculty to recognize fiction.

    DW

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    1. What Tegmark is saying is interesting but it seems like that's just his intuition about the nature of reality. He never mentions that he has some proof or anything (because you couldn't bring physical proof of those other realities). It is pretty faith-based.... ironic!

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    2. DW, and you came to this conclusion by actually investigating Max Tegmark's culture and generalizing over many examples or just sort of pulled it out of your, er hat?
      (If you actually cared to look shit up before making up wise pronouncements, you'd find out that his father was a Jewish math professor from Brooklyn. So while few biorgaphical facts are available, my bet is against Santa. Maybe Moses, though)

      Dr_Manhattan

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    3. Do you have anything to say about the blog post or are you just trolling again?

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    4. If by trolling you mean "dumping unsubstantiated statements confirming superioirity of one's tribal entity" I assume you're talking to DW.

      If you're talking to me, than yes, but I'm working on the previous post now. Not easy to keep up with this barrage holding down a job.

      Dr_Manhattan

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  2. Yes I am talking to you and you don't make too much of an effort to conceal your aggression. Furthermore, you tend not to respond or concede the point when your argument is weakened. Those two things put you squarely in the category of troll.

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  3. Dr. M,

    The Santa example is used as symptom of a lack of value of true critical thinking. It can easily be applied to jews who believe that elijah the prophet comes and drinks wine at everyones house seder night. The culture that we live in was my point and no tribal superiority was intended. Any culture that does not raise its children with the ability to filter fiction is going to produce intellictual idiots...This reminds me of something Richard Fynman spoke about. He was amazed to see the stupidity of ivy league professors and their inabiltiy to see in reality the very theories they were teaching! I dont have to get a degree in paranormal studies but I know that ghosts are fiction. As one studies an area his mind must guide him and part of the mind is the abilty to filter fiction even if a logical argument is presented. This does not mean we are always correct but it is the best that we have. If you are honest Dr. M I think that you can see from the tone of what you wrote that you are under the spell of some emotion which is clouding your mind. Try taking a deep breath and calming down. Perhaps you are too busy at work to properly comment on the blog. I have read many of your comments and you write many intelligent remarks but I think you would be better served if you were not so angry.

    DW

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    1. Apologies DW, I misunderstood your intention.

      As far as anger, yep, got that, and I have my reasons (they are not personal to the authors, but related to the influence of apologist school of thinking on my life, nuff said). I do not feel that my better questions get answered here, but since I enjoy thinking about stuff I'll keep it up.

      Dr_Manhattan

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    2. Dr_M, I have been following the back and forth, but just as a review, what are your remaining "better questions" that are unanswered?

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    3. The discussion is ongoing in post 9, please see there.

      Dr_Manhattan

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  4. Dr. M

    Alls good.

    DW

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  5. Bit off the topic question:

    "Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment."

    As someone with a BS in physics and Phd in math, can you just clarify what Einstein means by this...I thought all of physics was mathematical. Is there a qualitative aspect to Relativity that can be understood to the fullest extent without math? (And i guess Quantum Mechanics as well) Thanks.

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    1. Sure. Mathematics might be the language of nature, but that doesn't preclude somebody translating the concepts into a language you can understand.

      We would recommend Einstein and Infeld's book "The Evolution of Physics" which explains Relativity and more in English only.

      For a more modern book, read Brian Greene's "The Fabric of the Cosmos" which also uses a lot of English analogies but no equations. In it, he tries to explain Relativity as well as Quantum (plus a whole lot more).

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  6. I was thinking about this post and the mathematical nature of scientific theories and how Dr_Manhattan's objections are often couched in mathematical terms - specifically probability. I think that couching such philosophical assertions in mathematical terms is in large part what allows these theorists to consider their theories scientific rather than philosophical. Science is always explained in mathematical terms at its core. This is the refining of the theory which takes place after results from experiments have been analyzed and a true scientific theory has begun to crystallize. Probability, in particular serves the purpose of philo-sciencing well as it doesn't ever actually claim anything.

    I think that sounding scientific is being mistaken for being scientific.

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    1. > I was thinking about this post and the mathematical nature of scientific theories and how Dr_Manhattan's objections are often couched in mathematical terms - specifically probability. I think that couching such philosophical assertions in mathematical terms is in large part what allows these theorists to consider their theories scientific rather than philosophical.

      > I think that sounding scientific is being mistaken for being scientific.

      Well, this can certainly be true, but you're making a very general claim without backing it up in this specific case. It's in the same vein as claiming that someone is biased, without showing why they're wrong.

      Regarding probability specifically, it's pretty a pretty established method of thinking about science.

      "Probability: The Logic of science"
      http://omega.albany.edu:8008/JaynesBook.html

      "The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable
      man's mind."
      James Clerk Maxwell (1850)

      If I'm correct you're also suggesting that "this is philosophy, and throwing in mathematical terms just make it sound like science". I will try to write up my more general take on the scientific method, but briefly here I will suggest it's a bit of a false dichotomy. Science used to be called "natural philosophy", and for a good reason - while science has its useful rituals such as scientific method, there is no reason to draw a line and declare them completely separated domains. As a matter of fact this is the reason scientists developed an aversion to certain kinds of "philosophy" - b/c philosophers developed theories which had no apparent relationship to reality. In the extreme philosophy just became a lingiustic game, to the degree that a computer-generated giberrish paper got accepted to a major philosophy journal. Anyway, even taking for granted the fact that multiverse theories are not "testable" (which is not clear to me - see for example this article http://discovermagazine.com/2008/dec/10-sciences-alternative-to-an-intelligent-creator/article_view?b_start:int=2) they are still theories about reality (and not philosophical giberrish) and same methods, such as probability should apply.

      Dr_Manhattan

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    2. You said it was not clear to you whether multiverse theory was testable. What about that point is unclear?

      Are you referring to this part of the article: “If you measure something which confirms certain elaborations of string theory, then you’ve got indirect evidence for the multiverse,” says Bernard Carr, a cosmologist at Queen Mary University of London.

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    3. Perhaps it was from the other parts of the article you quoted:

      "When I ask Linde whether physicists will ever be able to prove that the multiverse is real, he has a simple answer. “Nothing else fits the data,” he tells me. “We don’t have any alternative explanation for the dark energy; we don’t have any alternative explanation for the smallness of the mass of the electron; we don’t have any alternative explanation for many properties of particles.

      “What I am saying is, look at it with open eyes. These are experimental facts, and these facts fit one theory: the multiverse theory. They do not fit any other theory so far. I’m not saying these properties necessarily imply the multiverse theory is right, but you asked me if there is any experimental evidence, and the answer is yes. It was Arthur Conan Doyle who said, ‘When you have eliminated the impossible, whatever remains, however improbable, must be the truth.’”

      Or is it this part:

      "On the other hand, if there is no multiverse, where does that leave physicists? “If there is only one universe,” Carr says, “you might have to have a fine-tuner. If you don’t want God, you’d better have a multiverse.”

      Great article. We highly encourage everyone to read it

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    4. Dr_Manhattan

      > you're making a very general claim without backing it up in this specific case.

      I wasn't really directing my comment to you. It was directed to the blog. I am aware that I have shown little proof for it. that is why I prefaced every point with "I think".

      > Regarding probability specifically, it's pretty a pretty established method of thinking about science.

      I am aware of this. I disagree with it as an abandonment of one of the essential aspects of the scientific method, which I will elaborate on below.

      > I will suggest it's a bit of a false dichotomy. Science used to be called "natural philosophy", and for a good reason - while science has its useful rituals such as scientific method, there is no reason to draw a line and declare them completely separated domains.

      This is exactly a root of your misunderstanding. You are correct in pointing out that science and philosophy were once linked. For centuries it was Aristotle's Physics upon which the world relied. Science, though, is a qualitatively different pursuit. Whereas philosophy and science are both pursuits of the mind and rooted in perceptions of the physical world, science differs by its adherence to experimental proofs.

      This is not a "ritual" or "false dichotomy". It is a very real distinction which allows for substantial reliance upon theoretical interpretations of the world. Philosophy does not lend itself to the precise variable constant distinctions necessary for experimentation. Science is bad philosophy as it fails to address the question "Why? and philosophy is bad science as it fails to address the question "What" with as much verification as science.

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    5. > "The actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable
      man's mind."

      I do not know that probability is widely accepted as "the true logic for this world" in the scientific community, but if it is, I lodge my complaint equally against them. Probability is a valid tool for describing many things (often relating to the as yet uncertain future).

      It is not however a valid tool for definition. It posits nothing. There is no "theory" which is correct 12% of the time. Such a theory is ruled out by the scientific method in favor of a theory which is correct more often.

      As I read your quote I was reminded of the video posted of Richard Feynman. In it, he very specifically avoids concluding that a theory is ever correct. He points out that it has only ever "not been disproven". This is the essence of the scientific method. We may not be able to determine the truth of a thing, but we can most definitely determine its falsity.

      With an underlying theory and valid experimentation, an idea can be shown to "not be false yet" or "certainly false". This is the strength of science. It is rooted in gaining knowledge through focused disproof. It is directly opposed to your quote, providing certainty sufficient to accept as false.

      Probability alone is simply an amalgamation of data points. it is a long string of facts. It barely qualifies as analysis. It points out recurrences but without any explanation or definition of what those recurrences are. According to you, science is a million monkeys on a million typewriters and then charting the results.

      Probability without context or defined limits, as you propose in arbitrarily judging one theory 3% possibility, is not even that. It is just nonsense.

      For example: there is a 13% chance that you are a cup. There is a 16% chance that you are a human. There is a 46% chance that you are simply a computer program. There is a 17% chance that I dreamed you up after eating some bad pizza. And there is a 37% chance that you are a quantum fluctuation of an infinite multiverse.

      What's that you say? How did I get these numbers? How can they add up to 129%? Where is my proof for any of it? What are my limits? When do I include a theory and when do I exclude one? How do I meaningfully assign values to each of these theories?

      Excellent questions. I'm waiting for your answers.

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    6. > In the extreme philosophy just became a lingiustic game, to the degree that a computer-generated giberrish paper got accepted to a major philosophy journal.

      I had never heard of this, so I looked it up. It turns out that a program was created at MIT called SCIgen which randomly generated research papers and won a submission to a journal. It was not a philosophy journal, though, it was a computer science journal.

      I would still accept your linguistic critique though, but I would apply it to all of academia, who generally hide behind long verbose words that convey little meaning (I feel SCIgen supports this assertion). Philosophers, scientists, and many others are guilty of this particular nonsense.

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    7. It exists for physics too: http://davidsd.org/2010/03/the-snarxiv/

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  7. Wow! "It was Arthur Conan Doyle who said, ‘When you have eliminated the impossible, whatever remains, however improbable, must be the truth.’” Seriously? God is an impossibility?

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    1. The one thing they have correct is that it's God or the multiverse.

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  8. Regarding infinite physical entities: Aristotle and Plato both held of some form of physical material that is eternal, which means that logically infinite time can exist. Why would infinite universes be less plausible?

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    1. The question of an actual infinity is a very deep problem. We'll go through some of our thoughts to your question, but our main objective is not to fully resolve the issue, but rather to show the serious problems inherent in actual infinities.

      It would seem that the simplest way to answer your question is that Aristotle conceived of time as an accident of motion, which itself was an accident of matter. Therefore, time being eternal is a result of its being a property of an eternal, necessarily existing, matter. This is an idea that can at least be thought in the mind, as opposed to an actual infinite extension or magnitude which can not be conceived of.

      The second way level to interpret your question might be as follows: How can you have an infinite sequence of cyclic causation in time which Aristotle did believe in(i.e., chicken egg chicken egg)?

      We think (but we're not sure) that the way Aristotle answered this was by saying that at any moment in time, only a finite number of beings exist. The next moment, these fade out of existence as time progresses. At no point do you simultaneously have an actual physical infinity.

      It would seem to us that this distinction is no longer relevant because of the relativity of simultaneity, which was shown by Einstein to be a logical consequence of the two postulates of special relativity.

      In so far as no moment in time has any special claim to reality, an infinite cycle of beings in time would be philosophically equivalent to infinite coexisting beings, and therefore according to Aristotle himself, should be impossible too.

      Our main objective is to show that if multiverse theorists want to posit infinite actual infinities, they need to address these major philosophical issues, especially in light of science's new understanding of space, time, and matter.

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    2. I want to see if I understand your point correctly. Aristotle would have no problem with infinity in time because the hotel problem won't come about. The hotel problem is only a problem because of concurrent contradicting states - such as occupied and unoccupied. But in an infinite time, there is no problem of concurrent contradiction because matter may freely contradict its past or present. But because of the concurrent existence of all matter (meaning it doesn't come and go as do seconds), infinity is fundamentally absurd.

      Additional question: I'm not an expert on special relativity. I know that it somehow treats matter and time as linked but I don't exactly know what that means. Could you elaborate on how special relativity merges the two? Also, how the merger demonstrates the finity of time rather than the subsequent infinity of matter?

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    3. You have an interesting formulation synthesizing Aristotle and Hilbert. It seems like another way of formulating the distinction in a framework of an absolute time. (Though it's not an idea of the past and present contradicting, as much as it is that the idea of an actual infinite magnitude is not conceivable.)

      It terms of special relativity, we were referring specifically to the relativity of simultaneity. (As an aside, it treats time and space equally, not time and matter.)

      See http://en.wikipedia.org/wiki/Relativity_of_simultaneity

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    4. I still need some clarification from your reply on June 20 - with the application of relativity of simultaneity, you seem to be saying that there is no difference between infinite cycle of beings in time and infinite coexisting beings. But if one can conceive of an eternal universe, wouldn't that mean there is an infinite cycle of causality? how does this infinite cycle differ from an actual infinity?

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    5. We're arguing that an infinite cycle does not differ from an actual infinity because of the relativity of simultaneity. We're not experts in Aristotle, but we think he differentiated them by saying that at any moment in time only a finite number of beings exists. It doesn't seem to us that this makes sense to say in light of our current understanding of time.

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  9. Don't some multiverse theories describe a process by which new universes spin off of current ones? Isn't this the kind of repeatable process that is within a reasonable understanding of infinity? There is some mechanism by which current universes give rise to new ones and this process occurs ad infinitum. Do the philosophers object to something like this existing in reality or is it limited to the simultaneous existence of an infinite number of physical entities?

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    1. Some finite number, x. But once this process (whatever it may be) takes place there will be x+1.

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    2. We think that the problem with the way you are conceiving it is that you are imagining an absolute time in which you can say right now only this number of universes are real.

      But according to special relativity, no moment in time has any greater claim to reality than any other moment. This means that each bubble universe is just as real as the next.

      In fact, if there is no causal relationship between the different universe, it doesn't even really make sense to say that one exists before or after any other universe.

      See the comment thread directly above this to RG which we think touches on a very similar issue.

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    3. That is pretty clever actually. I think the claim you are trying to make is that there should be a coordinate system in which all the new universe spawnings occur at the same time (simultaneously) Then an infinite process of new universes spawning in time will occur simultaneously in this CS raising a red flag among the philosophers.

      I have to think about this a little more but I'm not sure if according to special relativity that claim is strictly true. I think that the two events (say, universe 2 and 3 spawning) may be separated (in space and time according to the rest CS) in such a way that no CS will see them occur simultaneously. Even if there will always be such a CS, I'm not sure that it is so easy to link more than 2 events in this way.

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    4. We're not saying that there is a coordinate system where they all spawn simultaneously.

      We're saying that if there is no causal framework that unites the different multiverses, it certainly doesn't make sense to say one is real now and the other will be real in the future.

      And if there is a causal framework that unites them all, according to special relativity even the past, present, and future of our known universe have equal claims to reality. Certainly these other multiverses.

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    5. First of all, by causally related you mean that one event could have though did not necessarily cause the other, right? As in A and B are causally related if B is in the light cone with A at its vertex or vice versa? So for example, the existence of dinosaurs and my typing this message ARE causally related despite the commonplace usage of causation?

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    6. Or even if they share one common cause 'C', even though A and B do not have any direct causal relationship with each other (i.e., they could even be outside each other's light cone.)

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    7. With respect to quantum physics how can a particle be in two places at once? Isn't that logically impossible.

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    8. Logically impossible might be going too far. It would depend on your definition of a particle and time. But we agree that it doesn't make too much sense.

      We think a better way to attempt to understand it (No one really understands quantum) is as a model we use to describe the relationship between interactions. There is no "between interaction" as space and time have no separate independent existence outside of matter. This is in contrast to saying that the particle is in two places between interactions.

      This is getting into the area of a philosophical interpretation of quantum mechanics. There a few views in trying to make sense of it. For what it's worth, ours is based on our understanding of Einstein's explanation of general relativity and Feynman's explanation of the double slit in QED. The interpretation of quantum mechanics is not a simple matter. Great minds have been befuddled over the problems.

      While every way has its challenges, we certainly think that the Many World's interpretation is one of the worst, as it posits a near infinite number of multiverses to explain the probabilistic problem. We think that the probabilistic causality problem is easier to make sense of than the universe splitting and multiplying a near infinite number of times

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