Cosmology and the speed of light

We’ve blogged about the discovery of neutrinos that seemed to have traveled faster than light.  As scientists try to replicate and study that event, Joel Aschenbach has a good explanation of what’s at stake if light is not the fastest thing in the universe:

There is logic and beauty in a universe in which space, time, energy and matter are tightly associated with the speed of light. The special status of the speed of light isn’t like an Olympic record, something begging to be broken. Someone could come along who is faster than Usain Bolt, and it wouldn’t change the way we look at the world.

But the speed of light, according to Einstein, is an integral part of the geometry of four-dimensional space-time.

When we discuss the speed of light, we’re not talking about the characteristics of light so much as we’re describing the fabric of the universe. Light speed is the ultimate speed that anything (including things with zero mass, such as light or other electromagnetic radiation) can possibly go.

This also puts a limit on the speed of information, and, as such, helps enforce the fundamental law of causality. There’s an “arrow of time”: Splattered eggs on the kitchen floor don’t reassemble themselves in the shell and leap back onto the countertop.

“The melded nature of space and time is intimately woven with properties of light speed,” Greene says. “The inviolable nature of the speed of light is actually, in Einstein’s hands, talking about the inviolable nature of cause and effect.”

Michael Turner, a University of Chicago physicist, says the universe won’t seem as logical if there are particles that can move faster than light.

“In science we like surprises. We like big surprises. This one is too big to be true,” Turner said. “We really like things that rock the boat and turn us in a new direction, but this one turns the boat upside down and fills it with water.”

via Faster-than-light neutrino poses the ultimate cosmic brain teaser for physicists – The Washington Post.

Perhaps some of you can explain why breaking the cosmic speed limit would undermine cause and effect.  Aschenbach says “that” it would do so, but he doesn’t get into the “hows” and “whys.”

About Gene Veith

Professor of Literature at Patrick Henry College, the Director of the Cranach Institute at Concordia Theological Seminary, a columnist for World Magazine and TableTalk, and the author of 18 books on different facets of Christianity & Culture.

  • Dust

    the only thing I can think of is, if the “information” can get to the observer before they actually witness the event, since the info goes faster than light, then either the observer becomes clairvoyant, sort of, or it sort of “reverses” the normal flow of cause and effect in that you get the cause first (info) and then the effect (light) rather than our old fashioned method we use today…effect first, then surmise the cause?

    Hmm, well obviously a wild guess. but the clairvoyant thing sounds slightly interesting….we could be like a little god, knowing something is about to happen before it happens, since the cause gets to us before the effect?

    Or is it the other way around :)

  • Dust

    the only thing I can think of is, if the “information” can get to the observer before they actually witness the event, since the info goes faster than light, then either the observer becomes clairvoyant, sort of, or it sort of “reverses” the normal flow of cause and effect in that you get the cause first (info) and then the effect (light) rather than our old fashioned method we use today…effect first, then surmise the cause?

    Hmm, well obviously a wild guess. but the clairvoyant thing sounds slightly interesting….we could be like a little god, knowing something is about to happen before it happens, since the cause gets to us before the effect?

    Or is it the other way around :)

  • WebMonk

    The explanation is a bit hairy, but basically a signal can be sent where an observer can see it arrive before it was sent. As in, send it at time X and someone can see it arrive at a destination at X minus some time.

    The equations that show this are used constantly in technology all over the world and have been EXTREMELY highly tested and verified. They work just fine as long as things can’t go faster than light. However, as soon as something starts moving faster than light, the equations start showing major causality violations.

    The equations are correct as everyone demonstrates every time they use a computer. However, if causality starts to be violated, it shows that the equations (Relativity) is fundamentally flawed.

    Relativity is the most firmly demonstrated law we know of. The “Law of Gravity” doesn’t even come close to being so firmly tested and verified.

    It’s sort of weird – if FTL neutrinos existed, it would in many ways make no difference in any of our lives. Relativity works for _everything_ we do today, so no one would stop using it to build computers or anything else.

    On the other hand, it would show that there is something fundamentally flawed about Relativity and everything we understand about how the universe works would need to be completely remade from the ground up.

    Whatever that new understanding would be, would work just like Relativity in most ways (all the ways that we deal with today) just like the “Law of Gravity” still works today in most day-to-day activities even though it is incorrect. However, it would be fundamentally different than Relativity just as Relativity is fundamentally different than Gravity.

  • WebMonk

    The explanation is a bit hairy, but basically a signal can be sent where an observer can see it arrive before it was sent. As in, send it at time X and someone can see it arrive at a destination at X minus some time.

    The equations that show this are used constantly in technology all over the world and have been EXTREMELY highly tested and verified. They work just fine as long as things can’t go faster than light. However, as soon as something starts moving faster than light, the equations start showing major causality violations.

    The equations are correct as everyone demonstrates every time they use a computer. However, if causality starts to be violated, it shows that the equations (Relativity) is fundamentally flawed.

    Relativity is the most firmly demonstrated law we know of. The “Law of Gravity” doesn’t even come close to being so firmly tested and verified.

    It’s sort of weird – if FTL neutrinos existed, it would in many ways make no difference in any of our lives. Relativity works for _everything_ we do today, so no one would stop using it to build computers or anything else.

    On the other hand, it would show that there is something fundamentally flawed about Relativity and everything we understand about how the universe works would need to be completely remade from the ground up.

    Whatever that new understanding would be, would work just like Relativity in most ways (all the ways that we deal with today) just like the “Law of Gravity” still works today in most day-to-day activities even though it is incorrect. However, it would be fundamentally different than Relativity just as Relativity is fundamentally different than Gravity.

  • larry

    Logic is fundamentally based on time’s one direction, a constant and space or respect. If time becomes “pliable” (the faster objects), then so does the logic. A contradiction in logic according to Aristotle, for example, is that one cannot say of something that it is and that it is not in the same respect and at the same TIME.” This assumes time as a baseline unchangeable constant. I cannot say, “I am here and not here at 1535 edt”, in the same respect/space AND time. If time can be altered or multiple rather than singular and fixed, then the contradiction can occur by definition since time could be moved/manipulated. E.g. the particle could be in the act of arriving and be anticipated at X at 1535 AND since it can travel faster than light actually be there prior to its arriving and anticipated arriving of 1535. Thus, the normal logical contradiction of “here/not here at 1535” would be a truth not a contradiction.

    If you do away with logical contradiction, you do away with the most rudimentary elements of logic: cannot be both true and not true, identity of X, and excluded middle. Without these the rest of normal logic falls apart because these are assumed.

    Does, also, make interesting the issues surrounding the sacraments does it not, since God is in fact the Creator of time and space and not its bound servant.

  • larry

    Logic is fundamentally based on time’s one direction, a constant and space or respect. If time becomes “pliable” (the faster objects), then so does the logic. A contradiction in logic according to Aristotle, for example, is that one cannot say of something that it is and that it is not in the same respect and at the same TIME.” This assumes time as a baseline unchangeable constant. I cannot say, “I am here and not here at 1535 edt”, in the same respect/space AND time. If time can be altered or multiple rather than singular and fixed, then the contradiction can occur by definition since time could be moved/manipulated. E.g. the particle could be in the act of arriving and be anticipated at X at 1535 AND since it can travel faster than light actually be there prior to its arriving and anticipated arriving of 1535. Thus, the normal logical contradiction of “here/not here at 1535” would be a truth not a contradiction.

    If you do away with logical contradiction, you do away with the most rudimentary elements of logic: cannot be both true and not true, identity of X, and excluded middle. Without these the rest of normal logic falls apart because these are assumed.

    Does, also, make interesting the issues surrounding the sacraments does it not, since God is in fact the Creator of time and space and not its bound servant.

  • WebMonk

    Dust – you’re right, but it’s more extreme than that. The FTL message could be seen to reach the destination, not only before the could normally know about it, but also before the message was sent.

    If an FTL message were sent from Earth at 1/1/2012, an observer could see someone receive the message at 12/31/2011. (or some nearly arbitrarily large time before the message was sent depending on distance and speed and things like that)

    Send it from the Earth to Mars (at their furthest distance from each other), for example, and someone could see people on Mars react to the message seconds, minutes, or even hours before the people on Earth actually sent the message.

    Someone could see people on Mars react to the message, and send back a radio message to Earth saying they got the FTL message. Earth could receive that response before they ever sent their own message, and then not send their message.

    In that situation, Mars responded to a message that they received from Earth, but which Earth never sent.

    All sorts of nasty causality violations.

    If anyone wants the equations, you can look them up on Wikipedia. They’re pretty basic. You don’t need anything more than algebra to work them out yourself.

  • WebMonk

    Dust – you’re right, but it’s more extreme than that. The FTL message could be seen to reach the destination, not only before the could normally know about it, but also before the message was sent.

    If an FTL message were sent from Earth at 1/1/2012, an observer could see someone receive the message at 12/31/2011. (or some nearly arbitrarily large time before the message was sent depending on distance and speed and things like that)

    Send it from the Earth to Mars (at their furthest distance from each other), for example, and someone could see people on Mars react to the message seconds, minutes, or even hours before the people on Earth actually sent the message.

    Someone could see people on Mars react to the message, and send back a radio message to Earth saying they got the FTL message. Earth could receive that response before they ever sent their own message, and then not send their message.

    In that situation, Mars responded to a message that they received from Earth, but which Earth never sent.

    All sorts of nasty causality violations.

    If anyone wants the equations, you can look them up on Wikipedia. They’re pretty basic. You don’t need anything more than algebra to work them out yourself.

  • Tom Hering

    Would FTL travel necessarily be time travel from the present, here, to the past, elsewhere – or to the present, here, from the future, elsewhere? So if you traveled FTL to another star, you’d return before you left?

  • Tom Hering

    Would FTL travel necessarily be time travel from the present, here, to the past, elsewhere – or to the present, here, from the future, elsewhere? So if you traveled FTL to another star, you’d return before you left?

  • WebMonk

    Not quite that straight-forward, Tom. You both could and couldn’t, move into the past. From your own frame of reference, you wouldn’t be moving into the past, however, someone else would see you moving into the past.

    Which point of view is correct? They both are, and yet they are in complete contradiction to each other.

  • WebMonk

    Not quite that straight-forward, Tom. You both could and couldn’t, move into the past. From your own frame of reference, you wouldn’t be moving into the past, however, someone else would see you moving into the past.

    Which point of view is correct? They both are, and yet they are in complete contradiction to each other.

  • Tom Hering

    So when I get there, when am I?

  • Tom Hering

    So when I get there, when am I?

  • WebMonk

    According to your POV? You’ve arrived back home sometime after you left.

    According to someone watching from another POV? You’re there thirty minutes before you left, knocking yourself over the head and stopping yourself from going.

    ‘cuz you KNOW that’s exactly what you would do if you managed to travel back in time! :-D

  • WebMonk

    According to your POV? You’ve arrived back home sometime after you left.

    According to someone watching from another POV? You’re there thirty minutes before you left, knocking yourself over the head and stopping yourself from going.

    ‘cuz you KNOW that’s exactly what you would do if you managed to travel back in time! :-D

  • Tom Hering

    So I experience myself returning sometime after I left, but others experience me returning before I left. So when are they in relation to the returned me I experience?

  • Tom Hering

    So I experience myself returning sometime after I left, but others experience me returning before I left. So when are they in relation to the returned me I experience?

  • http://www.redeemedrambling.blogspot.com/ John

    My dad (graduate degree in Physics) was involved with the LIGO project for a while, and we had all kinds of interesting discussions about these things. One thing that people must remember is that “the speed of light” is not the velocity of photons, but is a theoretical construct in Einstein’s theory. Actual photons travel at different speeds depending upon the medium. The “speed of light” in SR is a theoretical speed limit that intends to model the speed of light in a vacuum. However, space is not a vacuum – in fact, current dark matter theories mean that space may be far denser than previous models allowed. If this is the case than smaller particles such as neutrinos may indeed travel at a faster speed. What is important to the viability of the theory is not the velocity at which photons travel, but a theoretical “top speed” of information delivery. Running out of space, but SR is about inertial frame of reference, and since at the time most spacial measurements were completed via visible light spectrum, SR deals with light, but it is really about information delivery.

  • http://www.redeemedrambling.blogspot.com/ John

    My dad (graduate degree in Physics) was involved with the LIGO project for a while, and we had all kinds of interesting discussions about these things. One thing that people must remember is that “the speed of light” is not the velocity of photons, but is a theoretical construct in Einstein’s theory. Actual photons travel at different speeds depending upon the medium. The “speed of light” in SR is a theoretical speed limit that intends to model the speed of light in a vacuum. However, space is not a vacuum – in fact, current dark matter theories mean that space may be far denser than previous models allowed. If this is the case than smaller particles such as neutrinos may indeed travel at a faster speed. What is important to the viability of the theory is not the velocity at which photons travel, but a theoretical “top speed” of information delivery. Running out of space, but SR is about inertial frame of reference, and since at the time most spacial measurements were completed via visible light spectrum, SR deals with light, but it is really about information delivery.

  • WebMonk

    Let’s say you travel back and blow yourself up just as your FTL travel begins, instead of knocking yourself over the head 30 minutes beforehand. It’s the same thing, but cuts down the number of different times we have to talk about.

    No, you never experience yourself – traveling out and back, arriving back sometime after you left. And yes, people see you blow your other self up stopping the trip. (they would actually see and not see it happen, maybe) What they see really happens, though. They are at the “same time” as you. Different inertial frame of reference (they’re moving quickly), but the “same time” as when you are blowing yourself up. They could be passing by 100 ft away when you blow yourself up and see it all happen.

    It is a major contradiction. Both are happening. Both can’t happen. Both are seen. Both can’t be seen.

    Contradictions. Impossibilities. What is “actually” seen and experienced is impossible.

    Which is why FTL is so problematic. The laws which predict the effect of FTL have been EXTREMELY well verified and are utilized in every computer, have been tested in thousands of experiments, and observed throughout the universe.

    Those same laws would say that impossible contradictions would happen if FTL travel were to be possible.

    So, nothing would change if FTL were to be possible, because Relativity works and is accurate down to a few thousand decimal places sort of accuracy. But, on the other hand, it would be incredibly, fundamentally false.

  • WebMonk

    Let’s say you travel back and blow yourself up just as your FTL travel begins, instead of knocking yourself over the head 30 minutes beforehand. It’s the same thing, but cuts down the number of different times we have to talk about.

    No, you never experience yourself – traveling out and back, arriving back sometime after you left. And yes, people see you blow your other self up stopping the trip. (they would actually see and not see it happen, maybe) What they see really happens, though. They are at the “same time” as you. Different inertial frame of reference (they’re moving quickly), but the “same time” as when you are blowing yourself up. They could be passing by 100 ft away when you blow yourself up and see it all happen.

    It is a major contradiction. Both are happening. Both can’t happen. Both are seen. Both can’t be seen.

    Contradictions. Impossibilities. What is “actually” seen and experienced is impossible.

    Which is why FTL is so problematic. The laws which predict the effect of FTL have been EXTREMELY well verified and are utilized in every computer, have been tested in thousands of experiments, and observed throughout the universe.

    Those same laws would say that impossible contradictions would happen if FTL travel were to be possible.

    So, nothing would change if FTL were to be possible, because Relativity works and is accurate down to a few thousand decimal places sort of accuracy. But, on the other hand, it would be incredibly, fundamentally false.

  • WebMonk

    John, the neutrinos were measured to have arrived faster than the theoretical light speed, not just the practical light speed through matter.

    Neutrinos could indeed be traveling faster than light travels through practical space. (they don’t, but at least in theory they could) But, that’s not what was measured. They measured the neutrinos arriving more quickly than even the theoretical limit of c.

    There are enough papers which have come out on the topic by significant scientists in the fields which propose very likely mundane solutions for which the original scientists didn’t account, that I am positive we’ll get a news story in the next couple years saying they figured out exactly which factor (or combination) was responsible for the measurement.

    I expect that in the next year we’ll also get some duplicate experiments carried out at other facilities which either show a slower than light speed for neutrinos, or shows a different FTL speed due to variations on the factors that affected CERN.

  • WebMonk

    John, the neutrinos were measured to have arrived faster than the theoretical light speed, not just the practical light speed through matter.

    Neutrinos could indeed be traveling faster than light travels through practical space. (they don’t, but at least in theory they could) But, that’s not what was measured. They measured the neutrinos arriving more quickly than even the theoretical limit of c.

    There are enough papers which have come out on the topic by significant scientists in the fields which propose very likely mundane solutions for which the original scientists didn’t account, that I am positive we’ll get a news story in the next couple years saying they figured out exactly which factor (or combination) was responsible for the measurement.

    I expect that in the next year we’ll also get some duplicate experiments carried out at other facilities which either show a slower than light speed for neutrinos, or shows a different FTL speed due to variations on the factors that affected CERN.

  • Jerry

    Expanding on John @10, the speed of light in physics as we know it is a fundamental constant which underlies all of the equations for the mechanisms on which the universe operates. Using the caveat of physics as we know it, if the speed of light in a vacuum was not constant or different than what it is, then the universe would not exist. It’s rather profound that God created light on the first day.

  • Jerry

    Expanding on John @10, the speed of light in physics as we know it is a fundamental constant which underlies all of the equations for the mechanisms on which the universe operates. Using the caveat of physics as we know it, if the speed of light in a vacuum was not constant or different than what it is, then the universe would not exist. It’s rather profound that God created light on the first day.

  • WebMonk

    Jerry, just to blow your mind a bit, it’s also possible that c is infinite in some direction and moves at 0.5c in the other. The equations get really, really funky, but they still work out. And it’s impossible to develop a test to tell if that’s really the case or not because all the results would be the same either way.
    :^D
    Your random bit of weirdness comes courtesy of the color slow.

  • WebMonk

    Jerry, just to blow your mind a bit, it’s also possible that c is infinite in some direction and moves at 0.5c in the other. The equations get really, really funky, but they still work out. And it’s impossible to develop a test to tell if that’s really the case or not because all the results would be the same either way.
    :^D
    Your random bit of weirdness comes courtesy of the color slow.

  • Dust

    John at 10….good points and had read about these things back at the time of the first article on something going faster than light. Looked up a bunch of stuff on the internet and it got into a discussion of whether or not something contained information. It was kind of a different perspective, but in any case, am pretty sure most of the scientists didn’t think the particles faster than light had any information quality. But you could say, what do they really know, ha!

    Webmonk….thanks for the good info too. Really liked the description of the messages going back and forth between Earth and Mars. It occured to me that if the Earth people got the response from the Mars people, even before they sent the message, they could change their mind and not send the message? Probably not, but it seems like it could be a possibility?

    In any case, all these paradoxes and what-ifs are the kinds of things that some of the different strange explanations of the essence of the universe try to explain, or at least what I always thought. Theories like string theory, super string theory, super duper string theory, parallel universes, infinite parallel universes, etc. etc. Isn’t it somewhat true that these wild theories of imagination try to explain all the strangeness out there? If so, it will only begat more strangeness, you can count on that?

    Finally, it’s kind of fun to think about the omniscience (is that the right word) of God…how does He do it? Well, that’s a rhetorical question, but an answer is just because, or because He is SUPERnatural?

    Cheers!

  • Dust

    John at 10….good points and had read about these things back at the time of the first article on something going faster than light. Looked up a bunch of stuff on the internet and it got into a discussion of whether or not something contained information. It was kind of a different perspective, but in any case, am pretty sure most of the scientists didn’t think the particles faster than light had any information quality. But you could say, what do they really know, ha!

    Webmonk….thanks for the good info too. Really liked the description of the messages going back and forth between Earth and Mars. It occured to me that if the Earth people got the response from the Mars people, even before they sent the message, they could change their mind and not send the message? Probably not, but it seems like it could be a possibility?

    In any case, all these paradoxes and what-ifs are the kinds of things that some of the different strange explanations of the essence of the universe try to explain, or at least what I always thought. Theories like string theory, super string theory, super duper string theory, parallel universes, infinite parallel universes, etc. etc. Isn’t it somewhat true that these wild theories of imagination try to explain all the strangeness out there? If so, it will only begat more strangeness, you can count on that?

    Finally, it’s kind of fun to think about the omniscience (is that the right word) of God…how does He do it? Well, that’s a rhetorical question, but an answer is just because, or because He is SUPERnatural?

    Cheers!

  • Dust

    Just had another thought….all those new fancy explanations of the universe that try to answer, at least in my opinion, some of the paradoxes of the current explanations, are really attempts to maintain and restore the cause and effect, or causality NATURE of the universe. One might even say, the theories extend the boundaries of what phenomena can be explained via a cause and effect view of the universe?

    Perhaps there is a need for some folks to be able to rationalize everything and explain it in the only terms available to them? If one theory seems to “undermine” cause and effect, well we’ll just come up with another theory that will restore the principle. It will explain the how’s and why’s of things that previously were thought to be unknown or unexplainable?

    So even if the writer thinks this has undermined that basic principle, it’s just a matter of time until someone clever comes up with something to explain it in terms we can understand using the logical constructs that are comfortable to us?

  • Dust

    Just had another thought….all those new fancy explanations of the universe that try to answer, at least in my opinion, some of the paradoxes of the current explanations, are really attempts to maintain and restore the cause and effect, or causality NATURE of the universe. One might even say, the theories extend the boundaries of what phenomena can be explained via a cause and effect view of the universe?

    Perhaps there is a need for some folks to be able to rationalize everything and explain it in the only terms available to them? If one theory seems to “undermine” cause and effect, well we’ll just come up with another theory that will restore the principle. It will explain the how’s and why’s of things that previously were thought to be unknown or unexplainable?

    So even if the writer thinks this has undermined that basic principle, it’s just a matter of time until someone clever comes up with something to explain it in terms we can understand using the logical constructs that are comfortable to us?

  • WebMonk

    if the Earth people got the response from the Mars people, even before they sent the message, they could change their mind and not send the message? Probably not, but it seems like it could be a possibility?

    Yes, it’s possible they could change their mind and not send the message. That’s what causes the paradox. It’s the exact same situation as someone going back and killing their grandfather or blowing themselves up before they leave on the trip to go back in time or, or, or. There are lots of examples of this sort paradox.

  • WebMonk

    if the Earth people got the response from the Mars people, even before they sent the message, they could change their mind and not send the message? Probably not, but it seems like it could be a possibility?

    Yes, it’s possible they could change their mind and not send the message. That’s what causes the paradox. It’s the exact same situation as someone going back and killing their grandfather or blowing themselves up before they leave on the trip to go back in time or, or, or. There are lots of examples of this sort paradox.

  • Ryan

    So… If true, Douglas Adams was a prophet and the Infinite Improbability Drive is just a little bit less improbable!? :)

  • Ryan

    So… If true, Douglas Adams was a prophet and the Infinite Improbability Drive is just a little bit less improbable!? :)

  • kerner

    This theory has always seemed flawed to me. Event X occurs at time Y, but the light that enables me to see it arrives at time Y+z. If some method of information enables me to learn of event X prior to time Y+z, but still later than time Y, I haven’t observed an event “before” it happened. I have merely observed it before the light from it would have otherwise reached me.

  • kerner

    This theory has always seemed flawed to me. Event X occurs at time Y, but the light that enables me to see it arrives at time Y+z. If some method of information enables me to learn of event X prior to time Y+z, but still later than time Y, I haven’t observed an event “before” it happened. I have merely observed it before the light from it would have otherwise reached me.

  • http://www.geneveith.com Gene Veith

    Webmonk and the rest of you guys who understand this stuff, many thanks for your explanations. I love science (and math) that doesn’t just make things clear but that blows my mind!

  • http://www.geneveith.com Gene Veith

    Webmonk and the rest of you guys who understand this stuff, many thanks for your explanations. I love science (and math) that doesn’t just make things clear but that blows my mind!

  • Paul

    The book “Special Relativity and Motions Faster than Light” by Moses Fayngold looks like a great resource for understanding what’s at stake. It also explains all sorts of relativistic and “faster than light” paradoxes. Chapter 8 discusses causality. In physics it is taken as a fundamental principle that cause precedes effect. It looks like this is formalized in physical models using the notions of information and its conveyance. There’s a nice quote from Chapter 8:

    “So here is the logical chain restricting the speed of causal interactions: the invariance of the speed of light requires the relativity of time; the relativity of time makes it possible for a succession of events to be different in different reference frames… However, if A and B are causally connected, then, according to retarding causality, their ordering must be the same for all observers, despite relativity of time. This requires the speed of any causal interaction between them not to exceed c [the speed of light]….”

    The invariance of the speed of light and relativity of time are both tied to a set of space-time “symmetries” called Lorentz transformations. Many experiments support the claim that our observable universe obeys equations invariant with respect to Lorentz transformations, e.g., Einstein equations of general relativity and Maxwell’s equations of electromagnetism. So if we want to assume an apparently reasonable principle of cause-and-effect in addition to these empirically-supported equations, then we conclude (using properties of Lorentz transformations) that faster-than-light information conveyance is ruled out. In short, the reason that breaking the “cosmic speed barrier” would undermine cause and effect comes down to the Lorentz invariance of physical laws. In order to see why, it is best to write down some Lorentz transformations and manipulate them.

    Lorentz invariance is responsible for relativistic effects such as time dilation, length contraction, etc. These consequences perhaps seems strange because in our day-to-day experience the world appears to exhibit Galilean invariance–foundational to Newtonian mechanics–instead.

    It looks like Chapter 8 of Fayngold’s book goes on to consider in detail the consequences of giving up causality…

  • Paul

    The book “Special Relativity and Motions Faster than Light” by Moses Fayngold looks like a great resource for understanding what’s at stake. It also explains all sorts of relativistic and “faster than light” paradoxes. Chapter 8 discusses causality. In physics it is taken as a fundamental principle that cause precedes effect. It looks like this is formalized in physical models using the notions of information and its conveyance. There’s a nice quote from Chapter 8:

    “So here is the logical chain restricting the speed of causal interactions: the invariance of the speed of light requires the relativity of time; the relativity of time makes it possible for a succession of events to be different in different reference frames… However, if A and B are causally connected, then, according to retarding causality, their ordering must be the same for all observers, despite relativity of time. This requires the speed of any causal interaction between them not to exceed c [the speed of light]….”

    The invariance of the speed of light and relativity of time are both tied to a set of space-time “symmetries” called Lorentz transformations. Many experiments support the claim that our observable universe obeys equations invariant with respect to Lorentz transformations, e.g., Einstein equations of general relativity and Maxwell’s equations of electromagnetism. So if we want to assume an apparently reasonable principle of cause-and-effect in addition to these empirically-supported equations, then we conclude (using properties of Lorentz transformations) that faster-than-light information conveyance is ruled out. In short, the reason that breaking the “cosmic speed barrier” would undermine cause and effect comes down to the Lorentz invariance of physical laws. In order to see why, it is best to write down some Lorentz transformations and manipulate them.

    Lorentz invariance is responsible for relativistic effects such as time dilation, length contraction, etc. These consequences perhaps seems strange because in our day-to-day experience the world appears to exhibit Galilean invariance–foundational to Newtonian mechanics–instead.

    It looks like Chapter 8 of Fayngold’s book goes on to consider in detail the consequences of giving up causality…

  • http://www.geneveith.com Gene Veith

    By the way, Webmonk, could you give us a link to those Wikipedia equations? I’d like to give them a try, even with my limited prowess in Algebra.

  • http://www.geneveith.com Gene Veith

    By the way, Webmonk, could you give us a link to those Wikipedia equations? I’d like to give them a try, even with my limited prowess in Algebra.

  • Dust

    Paul at 21, thanks for the explanation and especially the reference to the Fayngold book, am taking a peak inside on amazon and it reads very well! By the way, amazon shows he has another, more recent one too, “Special Relativity and How It Works” , do you know anything about it?

    Thanks very much again!

  • Dust

    Paul at 21, thanks for the explanation and especially the reference to the Fayngold book, am taking a peak inside on amazon and it reads very well! By the way, amazon shows he has another, more recent one too, “Special Relativity and How It Works” , do you know anything about it?

    Thanks very much again!

  • WebMonk

    http://en.wikipedia.org/wiki/Tachyonic_antitelephone

    There are several equations on that page, but the Two-Way path section walks you through each step of the way.

    Don’t get freaked out by the term Lorentz Transformation – it’s just a simple adjustment that describes the different effects seen as one is moving quickly in relation to another. It’s the formula for the spacetime dilation between differing frames of motion.

    Another quick tip on working the equations: measure all the velocities in terms of c. So, when v is seen in the equations, subsitute in 0.5, 1.0, 2.0, etc for half the speed of light, the speed of light, twice the speed of light, etc.

    Simplifies the calculations a bit more.

  • WebMonk

    http://en.wikipedia.org/wiki/Tachyonic_antitelephone

    There are several equations on that page, but the Two-Way path section walks you through each step of the way.

    Don’t get freaked out by the term Lorentz Transformation – it’s just a simple adjustment that describes the different effects seen as one is moving quickly in relation to another. It’s the formula for the spacetime dilation between differing frames of motion.

    Another quick tip on working the equations: measure all the velocities in terms of c. So, when v is seen in the equations, subsitute in 0.5, 1.0, 2.0, etc for half the speed of light, the speed of light, twice the speed of light, etc.

    Simplifies the calculations a bit more.

  • WebMonk

    kerner, you aren’t taking it far enough. It isn’t just a matter of messages reaching people before light could transmit the information, it’s messages arriving before they’re ever sent.

    For a nice, extreme example, let’s say the message isn’t just a radio message, but a world-shattering missile that is FTL. Earth shoots at Mars. Mars manages to deflect it back to Earth somehow. Someone flying by the Earth twenty minutes/hours/days/years before the missile was launched could see Earth be destroyed by the reflected missile which hasn’t yet been launched.

  • WebMonk

    kerner, you aren’t taking it far enough. It isn’t just a matter of messages reaching people before light could transmit the information, it’s messages arriving before they’re ever sent.

    For a nice, extreme example, let’s say the message isn’t just a radio message, but a world-shattering missile that is FTL. Earth shoots at Mars. Mars manages to deflect it back to Earth somehow. Someone flying by the Earth twenty minutes/hours/days/years before the missile was launched could see Earth be destroyed by the reflected missile which hasn’t yet been launched.

  • Dust

    Dr. Veith….you may want to visit amazon and take a “peak inside” the book recommended by Paul in 22. It’s very good, in my opinion and much of it requires no or little math?

    The other book by Fayngold on Amazon is worth a “peak inside” too, and especially the preface is guaranteed to have no Math, and it has a brief discussion of the early days of the relativity boom.

    In particular, it references a paper by John Bell “How to Teach Special Relativity” and if you Google that, you will find lots of good discussion and other papers that shed a lot of light (no pun intended) on the mystic that surrounds the Einstein theory and others.

    Good luck and even though you may not have the best Algebra skills, the most important Math to know is the ability to count one’s blessings :)

  • Dust

    Dr. Veith….you may want to visit amazon and take a “peak inside” the book recommended by Paul in 22. It’s very good, in my opinion and much of it requires no or little math?

    The other book by Fayngold on Amazon is worth a “peak inside” too, and especially the preface is guaranteed to have no Math, and it has a brief discussion of the early days of the relativity boom.

    In particular, it references a paper by John Bell “How to Teach Special Relativity” and if you Google that, you will find lots of good discussion and other papers that shed a lot of light (no pun intended) on the mystic that surrounds the Einstein theory and others.

    Good luck and even though you may not have the best Algebra skills, the most important Math to know is the ability to count one’s blessings :)

  • Paul

    Dust @ 23: To be honest I am not very familiar with either book by Fayngold. At the graduate level I have only seen general relativity as taught by mathematicians. While causality certainly does enter in, it is viewed as a consequence of the equations rather than a first principle of the physical universe. Having had my curiosity piqued by this post this morning, I searched a bit for a resource that would offer a physicist’s perspective and was fortunate enough both to find that Fayngold book that I quoted and to have full online access to it through my university :)

  • Paul

    Dust @ 23: To be honest I am not very familiar with either book by Fayngold. At the graduate level I have only seen general relativity as taught by mathematicians. While causality certainly does enter in, it is viewed as a consequence of the equations rather than a first principle of the physical universe. Having had my curiosity piqued by this post this morning, I searched a bit for a resource that would offer a physicist’s perspective and was fortunate enough both to find that Fayngold book that I quoted and to have full online access to it through my university :)

  • WisdomLover

    larry-

    Logic does not depend on time. The laws of logic would still be true in a world without time.

    On the OP-

    The speed of light has nothing to do with times arrow. The laws of electrodynamics cannot distinguish the case where the egg splatters and where it re-assembles.

    I’ve heard two stabs at providing an arrow of time for physics.

    First, it is a result of the second law of thermodynamics. It is the direction of increasing entropy. But since entropy decreases in a contracting universe, that would seem to suggest that time’s arrow would reverse in a contracting universe. And that doesn’t seem right.

    Second, the arrow of time might be provided by quantum wave collapse. As things are observed, the superimposed probabilities that comprise the quantum state are pruned away. This seems more likely. It seems that time’s arrow would keep the same direction even in a contracting universe.

    Also, this is more closely linked with real time…that is, the order in which we remember and anticipate events.

    There are actually other contenders of the arrow of time, but I suspect most of them reduce to the thermodynamic arrow.

    On the FTL paradoxes-

    It seems pretty clear to me that if you were able to arrive before you left, or send a signal to a time before you sent it, you would be in no danger of creating a contradiction.

    Why not?

    Well, any of a million ordinary things would prevent you from blocking what has already occurred and whatever you do is already woven into the past of the time you left from. Supposing, for example, that you went into the past to try to kill yourself before leaving. You might well make it into the past, but you’d fail for, some ordinary reason, to kill yourself.

    How do I know this?

    Because you left on your journey.

    BTW, travelling into the past does not even require FTL travel, Kurt Godel has provided solutions to the equations of General Relativity that allow one to travel always forward in time, but arrive back at the same place but at an earlier time.

  • WisdomLover

    larry-

    Logic does not depend on time. The laws of logic would still be true in a world without time.

    On the OP-

    The speed of light has nothing to do with times arrow. The laws of electrodynamics cannot distinguish the case where the egg splatters and where it re-assembles.

    I’ve heard two stabs at providing an arrow of time for physics.

    First, it is a result of the second law of thermodynamics. It is the direction of increasing entropy. But since entropy decreases in a contracting universe, that would seem to suggest that time’s arrow would reverse in a contracting universe. And that doesn’t seem right.

    Second, the arrow of time might be provided by quantum wave collapse. As things are observed, the superimposed probabilities that comprise the quantum state are pruned away. This seems more likely. It seems that time’s arrow would keep the same direction even in a contracting universe.

    Also, this is more closely linked with real time…that is, the order in which we remember and anticipate events.

    There are actually other contenders of the arrow of time, but I suspect most of them reduce to the thermodynamic arrow.

    On the FTL paradoxes-

    It seems pretty clear to me that if you were able to arrive before you left, or send a signal to a time before you sent it, you would be in no danger of creating a contradiction.

    Why not?

    Well, any of a million ordinary things would prevent you from blocking what has already occurred and whatever you do is already woven into the past of the time you left from. Supposing, for example, that you went into the past to try to kill yourself before leaving. You might well make it into the past, but you’d fail for, some ordinary reason, to kill yourself.

    How do I know this?

    Because you left on your journey.

    BTW, travelling into the past does not even require FTL travel, Kurt Godel has provided solutions to the equations of General Relativity that allow one to travel always forward in time, but arrive back at the same place but at an earlier time.

  • Dust

    WisdomLover at 28….interesting perspective! Just a few clarifications please:

    1. You say: “you would be in no danger of creating a contradiction.”

    Question: How would you define a contradiction in this world that allows seemingly contradictory paradoxes in the first place? Am aware sort of, how to do it for a Mathematical proof, but how would you do it in these situations? Honestly, it seems kind of difficult, because almost any set of conditions that would be a contradiction in one system could just be explained away by saying that doesn’t happen in this new system? And it doesn’t seem fair just to say, “it seems pretty clear to me” and it would be clear for me if you explain it a bit more precisely, thanks!

    2. You say: “whatever you do is already woven into the past of the time you left from. ”

    Clarification: So does this imply a sort of predestination? Does this mean that my decision to come back in time is already woven into the past, since it’s part of everything I do? How does the past know which technologies will be available in the future? If everything is already woven into that past, that includes my return? Actually, it seems to me that if everything is woven into that past, then my return is woven into that past? Everything that I would do during that visit would have to be woven into that past, correct? So obviously, killing myself is not woven into that past, else would not be there. But what about all my other actions? How could I do anything, since everything is connected and woven into that past? Just doing anything would upset a million other connections in that fabric? It seems to me I could not do anything but observe since any other action would somehow upset the stuff woven into the past? Or whatever I did is predetermined since it is woven into that past? Yadda, yadda, yadda, hopefully you get my point?

    Forgive me, but am sure if I work on this long enough will come up with a contradiction, once you define that term :)

    This is meant to be fun, so thanks for any reply!

  • Dust

    WisdomLover at 28….interesting perspective! Just a few clarifications please:

    1. You say: “you would be in no danger of creating a contradiction.”

    Question: How would you define a contradiction in this world that allows seemingly contradictory paradoxes in the first place? Am aware sort of, how to do it for a Mathematical proof, but how would you do it in these situations? Honestly, it seems kind of difficult, because almost any set of conditions that would be a contradiction in one system could just be explained away by saying that doesn’t happen in this new system? And it doesn’t seem fair just to say, “it seems pretty clear to me” and it would be clear for me if you explain it a bit more precisely, thanks!

    2. You say: “whatever you do is already woven into the past of the time you left from. ”

    Clarification: So does this imply a sort of predestination? Does this mean that my decision to come back in time is already woven into the past, since it’s part of everything I do? How does the past know which technologies will be available in the future? If everything is already woven into that past, that includes my return? Actually, it seems to me that if everything is woven into that past, then my return is woven into that past? Everything that I would do during that visit would have to be woven into that past, correct? So obviously, killing myself is not woven into that past, else would not be there. But what about all my other actions? How could I do anything, since everything is connected and woven into that past? Just doing anything would upset a million other connections in that fabric? It seems to me I could not do anything but observe since any other action would somehow upset the stuff woven into the past? Or whatever I did is predetermined since it is woven into that past? Yadda, yadda, yadda, hopefully you get my point?

    Forgive me, but am sure if I work on this long enough will come up with a contradiction, once you define that term :)

    This is meant to be fun, so thanks for any reply!

  • Dust

    WisdomLover at 28….really like Godel myself (he was raised a Lutheran and was always spiritual, like Einstein) and wanted to add something per your comment:

    “BTW, travelling into the past does not even require FTL travel, Kurt Godel has provided solutions to the equations of General Relativity that allow one to travel always forward in time, but arrive back at the same place but at an earlier time.”

    Can’t remember exactly how it went, but Godel was famous for a saying that went something like “just because you can ‘prove’ something, doesn’t make it true. and likewise, there are many things that are “true” that you can’t prove them to be true.” Thought that may apply to his clever tricks with GRT? Did he do something similar with SRT?

    Cheers!

  • Dust

    WisdomLover at 28….really like Godel myself (he was raised a Lutheran and was always spiritual, like Einstein) and wanted to add something per your comment:

    “BTW, travelling into the past does not even require FTL travel, Kurt Godel has provided solutions to the equations of General Relativity that allow one to travel always forward in time, but arrive back at the same place but at an earlier time.”

    Can’t remember exactly how it went, but Godel was famous for a saying that went something like “just because you can ‘prove’ something, doesn’t make it true. and likewise, there are many things that are “true” that you can’t prove them to be true.” Thought that may apply to his clever tricks with GRT? Did he do something similar with SRT?

    Cheers!

  • WisdomLover

    Dust-

    Taking your points in reverse order. I think you are referring to Godel’s argument for the incompleteness of arithmetic.

    Up until Godel, the presumption that almost everyone had been working with was that all the truths of arithmetic could be logically derived from a finite set of axioms. What Godel showed was that any finite set of axioms capable of ‘proving’ every truth of arithmetic would also ‘prove’ propositions like 1=0. His argument is basically a variation of the famous liar’s paradox (i.e., “This sentence is false”).

    There’s a curious fact about deductive proof that’s often a major stumbling block for people. This is that fact that, if you start with inconsistent premises, then any conclusion whatsoever follows deductively from them. In fact, some logicians have gone so far as to define “consistency” by saying that a set of propositions are consistent precisely when there is something you can’t prove from them.

    So what Godel showed was that the only finite set of propositions that would allow one to deductively derive all the truths of arithmetic is inconsistent. At the same time, arithmetic itself is consistent. So the only axiomatization of arithmetic that is possible is where there are infinitely many axioms.

  • WisdomLover

    Dust-

    Taking your points in reverse order. I think you are referring to Godel’s argument for the incompleteness of arithmetic.

    Up until Godel, the presumption that almost everyone had been working with was that all the truths of arithmetic could be logically derived from a finite set of axioms. What Godel showed was that any finite set of axioms capable of ‘proving’ every truth of arithmetic would also ‘prove’ propositions like 1=0. His argument is basically a variation of the famous liar’s paradox (i.e., “This sentence is false”).

    There’s a curious fact about deductive proof that’s often a major stumbling block for people. This is that fact that, if you start with inconsistent premises, then any conclusion whatsoever follows deductively from them. In fact, some logicians have gone so far as to define “consistency” by saying that a set of propositions are consistent precisely when there is something you can’t prove from them.

    So what Godel showed was that the only finite set of propositions that would allow one to deductively derive all the truths of arithmetic is inconsistent. At the same time, arithmetic itself is consistent. So the only axiomatization of arithmetic that is possible is where there are infinitely many axioms.

  • WisdomLover

    Dust-

    On the issue of what is woven into the past (for time travelers), my general point is that the law of excluded middle is true.

    Time travel aside, one of these two statements is true and the other false:

    1. On Monday, your Tuesday-self arrived from the future and bought a gun with which to kill your Monday-self.

    2. It is not the case that on Monday, your Tuesday-self arrived from the future and bought a gun with which to kill your Monday-self.

    Ordinarily, my guess would be that it’s item-2 that’s true, and item-1 that’s false. But there’s no guesswork involved in the claim that one is true and the other false, that’s pure logic.

    There’s no first-time-through or second-time-through time…there’s just what is and what might have been. But in order to kinda sorta express things in a way that might be somewhat helpful, if you did time-travel and buy the gun, then that was true ‘the first time through’ as were all the other actions of your future-self in its own past.

    Now, I conclude that anyone who travels into the past will fail to kill themselves while there. Why? Because they traveled into the past. Is it that the past somehow listens to the future. Well, under this assumption, there would clearly be retrocausation. Events in the future would have causal impact on past events. For example, your time-trip on Tuesday, does result in a gun shop owner being richer on Monday. So the past does ‘listen’ to the future in that sense.

    But I don’t think we need to conclude that there’s some sort of time guardian that keeps the past ‘in sync’ with the future. What happens between your Tuesday and Monday self happens. There’s nothing particularly special about it apart from the fact that it was time travel that brought your two selves into contact. On Tuesday, we know that your Monday-self was not killed on Monday by your Tuesday-self in the same way that, with or without time travel, we know that your Monday-self was not killed on Monday by anyone: Here you are on Tuesday…that’s how.

    Does this imply a freedom-denying-predestination or fatalism. No. Nothing that I’ve said, for example, implies that you don’t have the power to to kill your past self. It’s just that you won’t do it.

  • WisdomLover

    Dust-

    On the issue of what is woven into the past (for time travelers), my general point is that the law of excluded middle is true.

    Time travel aside, one of these two statements is true and the other false:

    1. On Monday, your Tuesday-self arrived from the future and bought a gun with which to kill your Monday-self.

    2. It is not the case that on Monday, your Tuesday-self arrived from the future and bought a gun with which to kill your Monday-self.

    Ordinarily, my guess would be that it’s item-2 that’s true, and item-1 that’s false. But there’s no guesswork involved in the claim that one is true and the other false, that’s pure logic.

    There’s no first-time-through or second-time-through time…there’s just what is and what might have been. But in order to kinda sorta express things in a way that might be somewhat helpful, if you did time-travel and buy the gun, then that was true ‘the first time through’ as were all the other actions of your future-self in its own past.

    Now, I conclude that anyone who travels into the past will fail to kill themselves while there. Why? Because they traveled into the past. Is it that the past somehow listens to the future. Well, under this assumption, there would clearly be retrocausation. Events in the future would have causal impact on past events. For example, your time-trip on Tuesday, does result in a gun shop owner being richer on Monday. So the past does ‘listen’ to the future in that sense.

    But I don’t think we need to conclude that there’s some sort of time guardian that keeps the past ‘in sync’ with the future. What happens between your Tuesday and Monday self happens. There’s nothing particularly special about it apart from the fact that it was time travel that brought your two selves into contact. On Tuesday, we know that your Monday-self was not killed on Monday by your Tuesday-self in the same way that, with or without time travel, we know that your Monday-self was not killed on Monday by anyone: Here you are on Tuesday…that’s how.

    Does this imply a freedom-denying-predestination or fatalism. No. Nothing that I’ve said, for example, implies that you don’t have the power to to kill your past self. It’s just that you won’t do it.

  • WisdomLover

    Dust-

    I’m not quite sure what you’re after here:

    How would you define a contradiction in this world that allows seemingly contradictory paradoxes in the first place? Am aware sort of, how to do it for a Mathematical proof, but how would you do it in these situations?

    A contradiction is when the selfsame proposition is both true and false. I deny that this or any world allows contradictions to exist. Though it’s probably better to say that there’s something radically nonsensical about the description of a world if that description implies a contradiction.

    I’m not sure what sort of mathematical proof you’re referring to here. One that proves a contradiction? There is no such proof.

    Or do you mean that you know that in Mathematical proof contradiction is impossible? If so, then yes. Indeed, the whole definition of deductive implication is this:

    The premises imply the conclusion if the assertion is contradictory that says that the conclusion is false while all the premises are true.

    (Note how this definition implies the curious fact about deduction that I mentioned two posts up.)

    In any case, if contradictions were possible all of deductive reasoning would be cast down.

  • WisdomLover

    Dust-

    I’m not quite sure what you’re after here:

    How would you define a contradiction in this world that allows seemingly contradictory paradoxes in the first place? Am aware sort of, how to do it for a Mathematical proof, but how would you do it in these situations?

    A contradiction is when the selfsame proposition is both true and false. I deny that this or any world allows contradictions to exist. Though it’s probably better to say that there’s something radically nonsensical about the description of a world if that description implies a contradiction.

    I’m not sure what sort of mathematical proof you’re referring to here. One that proves a contradiction? There is no such proof.

    Or do you mean that you know that in Mathematical proof contradiction is impossible? If so, then yes. Indeed, the whole definition of deductive implication is this:

    The premises imply the conclusion if the assertion is contradictory that says that the conclusion is false while all the premises are true.

    (Note how this definition implies the curious fact about deduction that I mentioned two posts up.)

    In any case, if contradictions were possible all of deductive reasoning would be cast down.

  • Joanne

    God created light and then created time by separating the light from the not-light, darkness. He organized his creation temporally by setting up periods of light and not light. The creation starts and stops. Time has a beginning and time has an end. The creator is not the created; he lives in his eternal now although he is in intimate relation with his creation. God sees all of creation now.

    How does the timeless communicate with the timefull. With great difficulty and constant limitation. God is. We will be, we are, we were. And God tells us that we are eternal and that we exist either with him or without him past the time of time.

    He says that he knows from before he created time who lives with him and who exists without him after time passes away. Our greatest misunderstandings of God involve time. We can partially understand God when he puts on a mantel of time, but he looses us when he speaks timelessly.

    What is living without time, outside of time? It’s eternally now; it’s eternally “I am.” But what is that like? The past, the present, and the future are now, here now. I am the God of Abraham, Isaac, and Jacob. Before Abraham was, I am. I imagin a time without time, but I don’t understand it and God knows I can’t.

  • Joanne

    God created light and then created time by separating the light from the not-light, darkness. He organized his creation temporally by setting up periods of light and not light. The creation starts and stops. Time has a beginning and time has an end. The creator is not the created; he lives in his eternal now although he is in intimate relation with his creation. God sees all of creation now.

    How does the timeless communicate with the timefull. With great difficulty and constant limitation. God is. We will be, we are, we were. And God tells us that we are eternal and that we exist either with him or without him past the time of time.

    He says that he knows from before he created time who lives with him and who exists without him after time passes away. Our greatest misunderstandings of God involve time. We can partially understand God when he puts on a mantel of time, but he looses us when he speaks timelessly.

    What is living without time, outside of time? It’s eternally now; it’s eternally “I am.” But what is that like? The past, the present, and the future are now, here now. I am the God of Abraham, Isaac, and Jacob. Before Abraham was, I am. I imagin a time without time, but I don’t understand it and God knows I can’t.

  • Dust

    Here’s a link to a very good video series, part of which contains a discussion of Godel’s work and implications. The panel includes a few Nobel Prize winners, a Harvard Professor and author of the latest biography on Godel, a very famous MIT Prof and others:

    There are 4 (?) other parts that are also real good….

    Cheers!

  • Dust

    Here’s a link to a very good video series, part of which contains a discussion of Godel’s work and implications. The panel includes a few Nobel Prize winners, a Harvard Professor and author of the latest biography on Godel, a very famous MIT Prof and others:

    There are 4 (?) other parts that are also real good….

    Cheers!


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