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The speed of light is sometimes referred to as the speed of causality, and it seems like it's more of a fundamental speed limit on the propagation of events or

by bramen 9y ago

The speed of light is sometimes referred to as the speed of causality, and it seems like it's more of a fundamental speed limit on the propagation of events or information through space.

deepnotderp 9y ago
+1 to this comment, it would remove a lot of mysticism to have called it "the speed of causality" instead. https://www.sciencealert.com/watch-why-the-speed-of-light-is-not-about-light https://www.sciencealert.com/watch-why-the-speed-of-light-is...
reubenswartz 9y ago
IIRC, everything moves through spacetime at c. Things with mass like people, planets, etc, move through the time portion as well as the space portion. As you go faster through space, you travel less through time, though at non- relativistic speeds you don't notice (GPS satellites do have to account for this). Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space, so we say they travel at the "speed of light."
- Swizec 9y ago
  > Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space, so we say they travel at the "speed of light." This part comfuses me. If they don't travel in time, how do they have a speed? Light is a type of electromagnetic wave right? And it takes many years to travel to us from a nearby star. If we can measure or calculate the time it takes for light from some place to reach us, does that not imply traveling through time?
  - neom 9y ago
    This might help: https://simple.wikipedia.org/wiki/Space-time https://simple.wikipedia.org/wiki/Space-time
  - azag0 9y ago
    Very trivialized: in some sense, you could say that for light itself, there is no time. In the same sense as there is no space for things that do not move (in space).
  - erikpukinskis 9y ago
    Think about a wave on a lake. It may appear to be moving in time. The water particles certainly move up and down. But if nothing is in it's "path" is the wave really moving? It's actually just there, the wave undulates and that creates the perception of motion, but really the thing you see moving is just a visual effect on the surface of a field the size of the entire lake. A field which is not moving at all. Photons are similar. You see the peak of the wave moving around, but the wave itself is everywhere and eternal... until other forces get involved anyway.
    - bramen 9y ago
      I'm not sure about this analogy. You can argue that the apparent motion of the wave crests is an illusion being pieced together by our brains when we see the totality of the elliptical movements of water particles at the surface. But at the moment when you drop a pebble into a pond, there are definitely parts of the surface which are moving and parts which are not, and the influence of the energy you introduced with the pebble can clearly be seen to spread outward over time. Granted this doesn't map directly onto electromagnetic waves because the mechanisms involved in wave propagation are different.
    - Koshkin 9y ago
      This picture is incorrect: the electromagnetic wave has a mechanical momentum in the direction of its propagation, which means that something is moving in that direction.
      - erikpukinskis 9y ago
        Does it have momentum before we measure it? I thought momentum was a property of the collapse event, not a property of the wave?
        Koshkin 9y ago
        According to the classical electrodynamics - it sure does. From the quantum mechanical point of view, it also does - in the sense that we can always measure it (i.e. it is an observable). The "property" in this case is not so much a particular outcome of such measurement as much as the expectation value; actually, I'm afraid that the use of the word "property" in this context can only lead to confusion as it effectively conflates several different things: the (quantum-mechanical) state, the observable, and the particular value observed.
  - jfjdiriri73737 9y ago
    Basically to establish time a measure has to be taken. Either by a human with our units for time, or by interaction with some force or object to establish that "this happened then". We commonly think of time in the linear time line sense. It's more accurate to think of it as a big mesh of points of interaction. Think more Cartesian space than left->right
  - speeder 9y ago
    Another way to think about it, is how time effects the object itself. Photons are completely immutable, while they travel they don't change at all, if a photon was a "smergsboard" it would remain "smergsboard" during the whole trip. One of the most interesting ways I saw explaining this, is imagine 'spacetime' as a cartesian space. You have 4 axis, X, Y, Z and time. EVERYTHING has speed of 'c', so you use trigonometry and rotations to figure the values, light, that have a speed of 'c' in the 3 space axis, then obviously have speed of '0' in time axis. ---- Now, one interesting application of that knowledge is how they figured the speed of neutrinos... As I just wrote, if something is travelling at speed of light, it is 'frozen', never changing... But 10 years or so ago people figured that neutrinos change mid-flight, there are 3 (or more... people are unsure yet) 'flavors' of neutrinos, and during tests people noticed that even if you make a machine that generates only one specific flavor, what reaches on the other side is not necessarily that flavor, meaning they changed mid-flight... But if they change, then they have some speed in 'time', this means then that the speed in space must be smaller than light. Right now there are couple experiments where people are trying to use the changes in neutrinos to calculate their speed in 'time', and then by elimination figure their speed in space. I find it quite interesting, how people can use math to figure physics when our instruments aren't precise enough.
    - sscarduzio 9y ago
      I wish HN had "reddit gold". Thanks for jotting this down for us, super clear and interesting.
    - platz 9y ago
      photons don't freeze in time in their own reference frame, and one doesnt get to priviledge any particular reference frame including those that are different from the photon's
      - platz 9y ago
        actually i'm reading now that photons do not even have their own reference frame simply by definition/axiom. Interesting..
      - 9y ago
  - TheOtherHobbes 9y ago
    It's fine to be confused, because the idea that "photons don't experience time" is physically meaningless. If you plug c into the Lorentz transformation you get an infinity, which doesn't tell you anything particularly useful. There's no physical way to accelerate to light speed, so it's meaningless to make assertions about how the "experience" of travelling at light speed would be different to the (presumably simpler) experience of travelling at < c. The problem is that relativity is a classical theory, and it says nothing about the underlying physical processes of photon creation/destruction and propagation. Maybe one day a Theory of Quantum Gravity will fix that problem and provide a detailed low-level picture of what actually happens when things move through spacetime. But we're not going to get there for a while. In the meantime, we'll carry on using concepts like "position" and "time" without really understanding the mechanisms that generate them. And if that sounds obvious, it really isn't. It's astounding that the universe knows where everything is and where it's going. Not only does it somehow keep track of all those changing spacetime relationships within a self-consistent system, but it also generates the counterintuitive geometry described by relativity. How does it do that? No one knows.
    - meric 9y ago
      But some believe it's God who does this.
      - TimTheTinker 9y ago
        This sounds a lot like the common "God of the gaps" argument that Hitchens and others describe, in which a deity or deities are supposedly invoked to explain what we do not yet understand. Yet it is fascinating that (1) any system of thought (including science itself) must rely on axioms; (2) by Godël's incompleteness theorem, no system of thought can prove its own axioms; and (3) thus it would seem that faith is inescapably required to believe in anything at all. When evaluating world views, perhaps the best metric is to evaluate which of them requires the least faith. For my part, when considering the known universe's mere existence, atheism seems to require a lot more faith than theism.
        9y ago
- raattgift 9y ago
  > everything moves through spacetime at c No. Everything has its own worldline through spacetime, and between two events at point p and q on a worldline through a given spacetime we can measure the interval dS between p and q. When we normalize the interval against a set of coordinates and a chosen metric signature (here +++-) we can have three types of interval: dS^2 = 0 is lightlike, dS^2 > 0 is spacetlike and dS^2 < 0 is timelike. A concrete example using the Minkowski metric for a set of Cartesian coordinates dS^2 = dx^2 + dy^2 + dz^2 - cdt^2. If we have a test object that always remains at the (x=0,y=0,z=0) origin of the coordinates then as the "t" coordinate increases with the passage of time, -cdt^2 is the only nonzero component of dS^2. From t=0 to t=10000 (where t is in, say, seconds) is perfectly timelike interval. However, any way we vary x, y, and z, (measuring the coordinate distances in, say, light-seconds) if the changes are small compared to the constant factor c, we will have a timelike interval. Light itself, conversely, follows a lightlike interval. If we restrict a beam of light to move only on the x axis, then we have (in (light-)seconds and seconds) x=c, t=1; x=2c, t=2; x=3c, t=3; and so forth; the -c factor cancels out the change in x at each step, so dS^2 = 0. But bear in mind here that the Minkowski metric is just one of many known exact solutions to the Einstein Field Equations, and there are many many many known approximate solutions. Moreover, we are free to use arbitrary coordinates. The Minkowski metric looks different in spherical polar coordinates, for example. We are also free to use arbitrary units. We can even use the metric signature (-,-,-,+) if we like. However, when we take all of these into account, we're left with the same distinction based on the interval: they're either lightlike, timelike, or spacelike. A lightlike worldline is one in which intervals on the worldline are always light-like; a timelike worldine is one in which intervals on the worldline are always spacelike. We have strong evidence and stronger theoretical reasoning to expect that massless objects will always have lightlike worldlines (and that light itself is massless) while massive objects will always have timelike worldlines. So: > Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space No, they have lightlike worldlines. An interval between any two points on the wave's worldline will be lightlike. This generally means that changes in the spacelike coordinates will exactly match the change in the timelike coordinate multiplied by the constant factor c. However, under most reasonable choices of coordinates, the "t" coordinate will certainly vary from point to point along its worldline. However, one has free choice to decide which axis is timelike or spacelike, and different choices may seem like the natural ones to different observers. In order to cope with these sets of choices we write down the laws of physics in a generally covariant manner. This has been one of the greatest successes of relativity; any proposed theory that cannot be written down in generally covariant form is almost certainly unphysical in some way. Lastly, the value of "c" is determined empirically, and will vary depending on one's choice of units. Relativists will often use a system of units in which c is set to unity (c=1), for example, in order to simplify the form of equations. > (GPS satellites do have to account for this) The theory side of GPS relies upon covariance matrices.
- colordrops 9y ago
  So if you reach the speed of light does that mean you'll reach the end of the universe, being that time stops for you and speeds up for everything else? Speaking of which, is a black hole just a window into the end of the universe?
  - lomnakkus 9y ago
    Well, you can't reach c unless you're massless. (Anything with non-zero mass would require infinite energy to reach c.)
  - ajross 9y ago
    It's more a sci-fi way of expressing things, but yes, sort of. Time dilation becomes infinite at c, so massless particles do not "experience" time. This is the reason that photons on a Feynman diagram are traditionally drawn horizontally. But the black hole part is actually wrong. Time dilation approaches infinity at the event horizon, not the singularity. So to extend your metaphor the interior of a black hole forever exists "beyond time" from our perspective.
- QAPereo 9y ago
  That's more or less how you work it out on paper, with the hope that when you add it all up it comes out to c, (usually tuned to "1" or unity), but that isn't necessarily what is physically happening. There isn't some part of us that's compensating temporally, for a lack of spatial velocity, it's just that when you add up the numbers or draw something like a spacetime diagram, it should come out a certain way.
tannhaeuser 9y ago
Would you know if (the observable effect of) quantum entanglement is expected to travel faster than the speed of causality?
- fish_fan 9y ago
  They entangle next to each other, and they move apart at max the speed of light. you'll have already paid the price for transferring that bit, so to speak. Information cannot move faster than the speed of light, period.
- Filligree 9y ago
  Depends on your model of quantum physics. In none of them can information travel faster than light, but that isn't a satisfactory answer, since one half of an entangled pair still has to "know" what happens to the other in order to give the right result from measurements, even though that doesn't let you send information. In hidden-variable models, you can argue that the experiment outcome is defined "up-front". In the many-worlds model, both sides have both outcomes but the inconsistent ones "cancel out" as they meet, and pilot-wave interpretations are just many-worlds with one configuration picked out as "real". But in most of the rest, yes, something travels faster than light. That's a common argument against e.g. collapse interpretations.
- marcosdumay 9y ago
  It is that question that does not have much meaning. If you observe one of a pair of entangled particles, you will see one of its possible values. Entanglement only means anything when you compare it's value with its pair's value, and that comparison is limited to the speed of light. So, yes, in a sense quantum entanglement is free of all the causality issues brought by GR. But it does not really exist until the pair can communicate.
  - grepthisab 9y ago
    So why not communicate via quantum entanglement? Kind of like FTL TCP.
QAPereo 9y ago
Also, yes, gravitational waves travel at c.
- deleted 9y ago
  [deleted]
- Filligree 9y ago
  (Caution: Pedantry ahead.) Gravitational waves are believed to travel at C, the theory says they should travel at C, and we're slowly narrowing in on C in measurements, but our ability to measure gravity waves is poor enough that we aren't yet quite sure. Which is one thing this observation would fix, assuming it's real.
  - raattgift 9y ago
    General Relativity (GR) is a metric theory of gravitation, with one metric to which everything couples. In GR gravitational waves (GW) have lightlike worldlines. Consequently, a source emitting both electromagnetic and gravitational radiation will have its GWs and EMWs (or more generally its optical image and the direction in which things indicating its gravitational influence point) line up. This has been well-tested observationally, for example by watching the deflection of light from distant objects (like quasars) around Jupiter (whose mass, orbit, and distance from us are all very well characterized). However, one can write down a bimetric theory of gravitation with different couplings. It's possible to write down a bimetric theory in which gravitational waves move more slowly or more quickly than electromagnetic waves. It was fairly popular some years to take this kind of approach to solve some cosmological problems relating to the homogeneity within the horizon [1]. These were often cast as "variable speed of light", for aesthetic reasons fixing the speed of the gravitational interaction. However, it is perfectly reasonable to call the same models "variable speed of gravitational radiation" fixing the speed of light, as one has many freedoms with respect to coordinate conditions in General Relativity. The problem is that these "variable speed of gravitational radiation" theories do not match observations of the galaxy-filled parts of the universe that we can see, and also does not match what we see in the Cosmic Microwave Background. (Some bimetric models fail to match the results of laboratory-scale physics experiments too.) Viable bimetric theories thus have the second metric decay in the very very early universe, such that in the galaxy-filled epoch the speeds of light and gravitational radiation are identical, and physics becomes (outside of the very early universe) indistinguishable from their "standard" single-metric General Relativity based generally covariant formulations. Such decaying-bimetric theories usually are designed to do away with cosmic inflation, but it becomes difficult to distinguish between cosmic inflation and viable bimetric-decay models because the observables eventually have to become identical, and the time at which they can differ gets pushed back further as we develop observatories which can resolve objects at ever higher redshifts, or as we can get better data on the anisotropies of the CMB. > we're slowly narrowing in on C in measurements We should determine c empirically, but we have already done so to exquisite precision. However, we can also fix c to some exact value (e.g. the CODATA value, or 1) and be mindful of the side effects of doing so. This is, by far, the most common approach; you will be hard-pressed to find any formulation of a physical law which introduces uncertainty into the value of c, although it's certainly doable. The fixed CODATA value is extremely good. The relative uncertainty in the speed of light is principally driven by the uncertainties in interferometry, which at the time of the 1983 redefinition of the metre was less than 0.1 part per billion (and is now less than a part per trillion, and so for all practical purposes is unimportant at scales of the observable universe). Finally, one should note that in a general curved spacetime, while the constant factor "c" arises everywhere, it can only be taken as a speed when comparing two objects that co-occupy exactly the same infinitesimal point in spacetime. Comparing the speeds of distant objects is something that one should avoid in General Relativity. However, everywhere in every spacetime, in vacuum conditions one should find the same "c" as the upper limit of relative speeds of objects just as they enter, co-occupy, and exit the same point. - -- [1] https://www.wikiwand.com/en/Horizon_problem https://www.wikiwand.com/en/Horizon_problem
amelius 9y ago
But the universe itself is expanding faster than the speed of light, [1] :) [1] http://curious.astro.cornell.edu/about-us/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/616-is-the-universe-expanding-faster-than-the-speed-of-light-intermediate http://curious.astro.cornell.edu/about-us/104-the-universe/c...
- frutiger 9y ago
  The reason this isn't paradoxical is because expansion doesn't have a speed, and the phrase "X is expanding faster than Y" doesn't have a proper meaning.
- andars 9y ago
  Speed of light has units of distance per time. Expansion rate has units of (distance per time) per distance. For more info on why this statement makes little sense, see Sean Carroll's post here: http://www.preposterousuniverse.com/blog/2015/10/13/the-universe-never-expands-faster-than-the-speed-of-light/ http://www.preposterousuniverse.com/blog/2015/10/13/the-univ...
  - amelius 9y ago
    See the article I linked for a possible interpretation.
  - cygx 9y ago
    And recession velocities have units of distance per time and exceed c at the Hubble sphere. Such coordinate velocities are largely meaningless, though: The more interesting quantity is the relative velocity as evaluated via parallel transport along the trajectory of the photon you use to observe the receeding object, which goes to c at the cosmic event horizon.

by bramen 9y ago

The speed of light is sometimes referred to as the speed of causality, and it seems like it's more of a fundamental speed limit on the propagation of events or information through space.

deepnotderp 9y ago

+1 to this comment, it would remove a lot of mysticism to have called it "the speed of causality" instead. https://www.sciencealert.com/watch-why-the-speed-of-light-is-not-about-light https://www.sciencealert.com/watch-why-the-speed-of-light-is...

reubenswartz 9y ago

IIRC, everything moves through spacetime at c. Things with mass like people, planets, etc, move through the time portion as well as the space portion. As you go faster through space, you travel less through time, though at non- relativistic speeds you don't notice (GPS satellites do have to account for this). Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space, so we say they travel at the "speed of light."

Swizec 9y ago
> Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space, so we say they travel at the "speed of light." This part comfuses me. If they don't travel in time, how do they have a speed? Light is a type of electromagnetic wave right? And it takes many years to travel to us from a nearby star. If we can measure or calculate the time it takes for light from some place to reach us, does that not imply traveling through time?
- neom 9y ago
  This might help: https://simple.wikipedia.org/wiki/Space-time https://simple.wikipedia.org/wiki/Space-time
- azag0 9y ago
  Very trivialized: in some sense, you could say that for light itself, there is no time. In the same sense as there is no space for things that do not move (in space).
- erikpukinskis 9y ago
  Think about a wave on a lake. It may appear to be moving in time. The water particles certainly move up and down. But if nothing is in it's "path" is the wave really moving? It's actually just there, the wave undulates and that creates the perception of motion, but really the thing you see moving is just a visual effect on the surface of a field the size of the entire lake. A field which is not moving at all. Photons are similar. You see the peak of the wave moving around, but the wave itself is everywhere and eternal... until other forces get involved anyway.
  - bramen 9y ago
    I'm not sure about this analogy. You can argue that the apparent motion of the wave crests is an illusion being pieced together by our brains when we see the totality of the elliptical movements of water particles at the surface. But at the moment when you drop a pebble into a pond, there are definitely parts of the surface which are moving and parts which are not, and the influence of the energy you introduced with the pebble can clearly be seen to spread outward over time. Granted this doesn't map directly onto electromagnetic waves because the mechanisms involved in wave propagation are different.
  - Koshkin 9y ago
    This picture is incorrect: the electromagnetic wave has a mechanical momentum in the direction of its propagation, which means that something is moving in that direction.
    - erikpukinskis 9y ago
      Does it have momentum before we measure it? I thought momentum was a property of the collapse event, not a property of the wave?
      - Koshkin 9y ago
        According to the classical electrodynamics - it sure does. From the quantum mechanical point of view, it also does - in the sense that we can always measure it (i.e. it is an observable). The "property" in this case is not so much a particular outcome of such measurement as much as the expectation value; actually, I'm afraid that the use of the word "property" in this context can only lead to confusion as it effectively conflates several different things: the (quantum-mechanical) state, the observable, and the particular value observed.
- jfjdiriri73737 9y ago
  Basically to establish time a measure has to be taken. Either by a human with our units for time, or by interaction with some force or object to establish that "this happened then". We commonly think of time in the linear time line sense. It's more accurate to think of it as a big mesh of points of interaction. Think more Cartesian space than left->right
- speeder 9y ago
  Another way to think about it, is how time effects the object itself. Photons are completely immutable, while they travel they don't change at all, if a photon was a "smergsboard" it would remain "smergsboard" during the whole trip. One of the most interesting ways I saw explaining this, is imagine 'spacetime' as a cartesian space. You have 4 axis, X, Y, Z and time. EVERYTHING has speed of 'c', so you use trigonometry and rotations to figure the values, light, that have a speed of 'c' in the 3 space axis, then obviously have speed of '0' in time axis. ---- Now, one interesting application of that knowledge is how they figured the speed of neutrinos... As I just wrote, if something is travelling at speed of light, it is 'frozen', never changing... But 10 years or so ago people figured that neutrinos change mid-flight, there are 3 (or more... people are unsure yet) 'flavors' of neutrinos, and during tests people noticed that even if you make a machine that generates only one specific flavor, what reaches on the other side is not necessarily that flavor, meaning they changed mid-flight... But if they change, then they have some speed in 'time', this means then that the speed in space must be smaller than light. Right now there are couple experiments where people are trying to use the changes in neutrinos to calculate their speed in 'time', and then by elimination figure their speed in space. I find it quite interesting, how people can use math to figure physics when our instruments aren't precise enough.
  - sscarduzio 9y ago
    I wish HN had "reddit gold". Thanks for jotting this down for us, super clear and interesting.
  - platz 9y ago
    photons don't freeze in time in their own reference frame, and one doesnt get to priviledge any particular reference frame including those that are different from the photon's
    - platz 9y ago
      actually i'm reading now that photons do not even have their own reference frame simply by definition/axiom. Interesting..
    - 9y ago
- TheOtherHobbes 9y ago
  It's fine to be confused, because the idea that "photons don't experience time" is physically meaningless. If you plug c into the Lorentz transformation you get an infinity, which doesn't tell you anything particularly useful. There's no physical way to accelerate to light speed, so it's meaningless to make assertions about how the "experience" of travelling at light speed would be different to the (presumably simpler) experience of travelling at < c. The problem is that relativity is a classical theory, and it says nothing about the underlying physical processes of photon creation/destruction and propagation. Maybe one day a Theory of Quantum Gravity will fix that problem and provide a detailed low-level picture of what actually happens when things move through spacetime. But we're not going to get there for a while. In the meantime, we'll carry on using concepts like "position" and "time" without really understanding the mechanisms that generate them. And if that sounds obvious, it really isn't. It's astounding that the universe knows where everything is and where it's going. Not only does it somehow keep track of all those changing spacetime relationships within a self-consistent system, but it also generates the counterintuitive geometry described by relativity. How does it do that? No one knows.
  - meric 9y ago
    But some believe it's God who does this.
    - TimTheTinker 9y ago
      This sounds a lot like the common "God of the gaps" argument that Hitchens and others describe, in which a deity or deities are supposedly invoked to explain what we do not yet understand. Yet it is fascinating that (1) any system of thought (including science itself) must rely on axioms; (2) by Godël's incompleteness theorem, no system of thought can prove its own axioms; and (3) thus it would seem that faith is inescapably required to believe in anything at all. When evaluating world views, perhaps the best metric is to evaluate which of them requires the least faith. For my part, when considering the known universe's mere existence, atheism seems to require a lot more faith than theism.
      - 9y ago
raattgift 9y ago
> everything moves through spacetime at c No. Everything has its own worldline through spacetime, and between two events at point p and q on a worldline through a given spacetime we can measure the interval dS between p and q. When we normalize the interval against a set of coordinates and a chosen metric signature (here +++-) we can have three types of interval: dS^2 = 0 is lightlike, dS^2 > 0 is spacetlike and dS^2 < 0 is timelike. A concrete example using the Minkowski metric for a set of Cartesian coordinates dS^2 = dx^2 + dy^2 + dz^2 - cdt^2. If we have a test object that always remains at the (x=0,y=0,z=0) origin of the coordinates then as the "t" coordinate increases with the passage of time, -cdt^2 is the only nonzero component of dS^2. From t=0 to t=10000 (where t is in, say, seconds) is perfectly timelike interval. However, any way we vary x, y, and z, (measuring the coordinate distances in, say, light-seconds) if the changes are small compared to the constant factor c, we will have a timelike interval. Light itself, conversely, follows a lightlike interval. If we restrict a beam of light to move only on the x axis, then we have (in (light-)seconds and seconds) x=c, t=1; x=2c, t=2; x=3c, t=3; and so forth; the -c factor cancels out the change in x at each step, so dS^2 = 0. But bear in mind here that the Minkowski metric is just one of many known exact solutions to the Einstein Field Equations, and there are many many many known approximate solutions. Moreover, we are free to use arbitrary coordinates. The Minkowski metric looks different in spherical polar coordinates, for example. We are also free to use arbitrary units. We can even use the metric signature (-,-,-,+) if we like. However, when we take all of these into account, we're left with the same distinction based on the interval: they're either lightlike, timelike, or spacelike. A lightlike worldline is one in which intervals on the worldline are always light-like; a timelike worldine is one in which intervals on the worldline are always spacelike. We have strong evidence and stronger theoretical reasoning to expect that massless objects will always have lightlike worldlines (and that light itself is massless) while massive objects will always have timelike worldlines. So: > Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space No, they have lightlike worldlines. An interval between any two points on the wave's worldline will be lightlike. This generally means that changes in the spacelike coordinates will exactly match the change in the timelike coordinate multiplied by the constant factor c. However, under most reasonable choices of coordinates, the "t" coordinate will certainly vary from point to point along its worldline. However, one has free choice to decide which axis is timelike or spacelike, and different choices may seem like the natural ones to different observers. In order to cope with these sets of choices we write down the laws of physics in a generally covariant manner. This has been one of the greatest successes of relativity; any proposed theory that cannot be written down in generally covariant form is almost certainly unphysical in some way. Lastly, the value of "c" is determined empirically, and will vary depending on one's choice of units. Relativists will often use a system of units in which c is set to unity (c=1), for example, in order to simplify the form of equations. > (GPS satellites do have to account for this) The theory side of GPS relies upon covariance matrices.
colordrops 9y ago
So if you reach the speed of light does that mean you'll reach the end of the universe, being that time stops for you and speeds up for everything else? Speaking of which, is a black hole just a window into the end of the universe?
- lomnakkus 9y ago
  Well, you can't reach c unless you're massless. (Anything with non-zero mass would require infinite energy to reach c.)
- ajross 9y ago
  It's more a sci-fi way of expressing things, but yes, sort of. Time dilation becomes infinite at c, so massless particles do not "experience" time. This is the reason that photons on a Feynman diagram are traditionally drawn horizontally. But the black hole part is actually wrong. Time dilation approaches infinity at the event horizon, not the singularity. So to extend your metaphor the interior of a black hole forever exists "beyond time" from our perspective.
QAPereo 9y ago
That's more or less how you work it out on paper, with the hope that when you add it all up it comes out to c, (usually tuned to "1" or unity), but that isn't necessarily what is physically happening. There isn't some part of us that's compensating temporally, for a lack of spatial velocity, it's just that when you add up the numbers or draw something like a spacetime diagram, it should come out a certain way.

tannhaeuser 9y ago

Would you know if (the observable effect of) quantum entanglement is expected to travel faster than the speed of causality?

fish_fan 9y ago
They entangle next to each other, and they move apart at max the speed of light. you'll have already paid the price for transferring that bit, so to speak. Information cannot move faster than the speed of light, period.
Filligree 9y ago
Depends on your model of quantum physics. In none of them can information travel faster than light, but that isn't a satisfactory answer, since one half of an entangled pair still has to "know" what happens to the other in order to give the right result from measurements, even though that doesn't let you send information. In hidden-variable models, you can argue that the experiment outcome is defined "up-front". In the many-worlds model, both sides have both outcomes but the inconsistent ones "cancel out" as they meet, and pilot-wave interpretations are just many-worlds with one configuration picked out as "real". But in most of the rest, yes, something travels faster than light. That's a common argument against e.g. collapse interpretations.
marcosdumay 9y ago
It is that question that does not have much meaning. If you observe one of a pair of entangled particles, you will see one of its possible values. Entanglement only means anything when you compare it's value with its pair's value, and that comparison is limited to the speed of light. So, yes, in a sense quantum entanglement is free of all the causality issues brought by GR. But it does not really exist until the pair can communicate.
- grepthisab 9y ago
  So why not communicate via quantum entanglement? Kind of like FTL TCP.

QAPereo 9y ago

Also, yes, gravitational waves travel at c.

deleted 9y ago
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Filligree 9y ago
(Caution: Pedantry ahead.) Gravitational waves are believed to travel at C, the theory says they should travel at C, and we're slowly narrowing in on C in measurements, but our ability to measure gravity waves is poor enough that we aren't yet quite sure. Which is one thing this observation would fix, assuming it's real.
- raattgift 9y ago
  General Relativity (GR) is a metric theory of gravitation, with one metric to which everything couples. In GR gravitational waves (GW) have lightlike worldlines. Consequently, a source emitting both electromagnetic and gravitational radiation will have its GWs and EMWs (or more generally its optical image and the direction in which things indicating its gravitational influence point) line up. This has been well-tested observationally, for example by watching the deflection of light from distant objects (like quasars) around Jupiter (whose mass, orbit, and distance from us are all very well characterized). However, one can write down a bimetric theory of gravitation with different couplings. It's possible to write down a bimetric theory in which gravitational waves move more slowly or more quickly than electromagnetic waves. It was fairly popular some years to take this kind of approach to solve some cosmological problems relating to the homogeneity within the horizon [1]. These were often cast as "variable speed of light", for aesthetic reasons fixing the speed of the gravitational interaction. However, it is perfectly reasonable to call the same models "variable speed of gravitational radiation" fixing the speed of light, as one has many freedoms with respect to coordinate conditions in General Relativity. The problem is that these "variable speed of gravitational radiation" theories do not match observations of the galaxy-filled parts of the universe that we can see, and also does not match what we see in the Cosmic Microwave Background. (Some bimetric models fail to match the results of laboratory-scale physics experiments too.) Viable bimetric theories thus have the second metric decay in the very very early universe, such that in the galaxy-filled epoch the speeds of light and gravitational radiation are identical, and physics becomes (outside of the very early universe) indistinguishable from their "standard" single-metric General Relativity based generally covariant formulations. Such decaying-bimetric theories usually are designed to do away with cosmic inflation, but it becomes difficult to distinguish between cosmic inflation and viable bimetric-decay models because the observables eventually have to become identical, and the time at which they can differ gets pushed back further as we develop observatories which can resolve objects at ever higher redshifts, or as we can get better data on the anisotropies of the CMB. > we're slowly narrowing in on C in measurements We should determine c empirically, but we have already done so to exquisite precision. However, we can also fix c to some exact value (e.g. the CODATA value, or 1) and be mindful of the side effects of doing so. This is, by far, the most common approach; you will be hard-pressed to find any formulation of a physical law which introduces uncertainty into the value of c, although it's certainly doable. The fixed CODATA value is extremely good. The relative uncertainty in the speed of light is principally driven by the uncertainties in interferometry, which at the time of the 1983 redefinition of the metre was less than 0.1 part per billion (and is now less than a part per trillion, and so for all practical purposes is unimportant at scales of the observable universe). Finally, one should note that in a general curved spacetime, while the constant factor "c" arises everywhere, it can only be taken as a speed when comparing two objects that co-occupy exactly the same infinitesimal point in spacetime. Comparing the speeds of distant objects is something that one should avoid in General Relativity. However, everywhere in every spacetime, in vacuum conditions one should find the same "c" as the upper limit of relative speeds of objects just as they enter, co-occupy, and exit the same point. - -- [1] https://www.wikiwand.com/en/Horizon_problem https://www.wikiwand.com/en/Horizon_problem

amelius 9y ago

But the universe itself is expanding faster than the speed of light, [1] :) [1] http://curious.astro.cornell.edu/about-us/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/616-is-the-universe-expanding-faster-than-the-speed-of-light-intermediate http://curious.astro.cornell.edu/about-us/104-the-universe/c...

frutiger 9y ago
The reason this isn't paradoxical is because expansion doesn't have a speed, and the phrase "X is expanding faster than Y" doesn't have a proper meaning.
andars 9y ago
Speed of light has units of distance per time. Expansion rate has units of (distance per time) per distance. For more info on why this statement makes little sense, see Sean Carroll's post here: http://www.preposterousuniverse.com/blog/2015/10/13/the-universe-never-expands-faster-than-the-speed-of-light/ http://www.preposterousuniverse.com/blog/2015/10/13/the-univ...
- amelius 9y ago
  See the article I linked for a possible interpretation.
- cygx 9y ago
  And recession velocities have units of distance per time and exceed c at the Hubble sphere. Such coordinate velocities are largely meaningless, though: The more interesting quantity is the relative velocity as evaluated via parallel transport along the trajectory of the photon you use to observe the receeding object, which goes to c at the cosmic event horizon.