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18 Sep 2020 07:12

Watsisname wrote:
midtskogen wrote:
Source of the post What I don't quite catch here is that the black hole could make me see the redshifted things behind me in two different directions, once directly (behind) and once bent around the black hole (in front).  Therefore I would expect bands.

Aye, I think I see your confusion, and it's my fault for not explaining the special relativistic aberration effect very well. Yes, the black hole generates many images of the same object, because light rays may circulate around many times near the photon orbit before spiraling back to reach you. But the special relativistic red or blueshift of the image due to your velocity does not depend on whether the source of that light was behind or in front of you, but rather only on the direction from which the light ray ultimately intersects you, and aberrated (appearing to come more from the direction you are flying to). Normally in special relativity this distinction wouldn't matter, but with gravity bending the paths of light rays, it is surely confusing.

So an image that was lensed by the black hole to appear in front of you -- of an object that is actually behind you -- will be seen to be blueshifted, not redshifted (if you're hurtling toward the black hole with a great initial velocity). This is because the change in the photon's energy did not depend on the path it took around the black hole (that's what I mean earlier by the path independence due to gravity being a conservative force), but you are "driving into it" (invoking the driving in rain analogy for aberration), and because you can't measure a faster speed of light you instead see it have a higher energy (bluer color). You'll get multiple images, but they'll progressively go from redder appearing behind you, to bluer appearing more directly ahead.

hmmm this sounds a lot like how the sound of a train whistle changes pitch to an observer on a platform (but in reverse, since the observer in that case is the stationary one.)
 
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18 Sep 2020 08:34

Watsisname wrote:
Source of the post the change in the photon's energy did not depend on the path it took around the black hole (that's what I mean earlier by the path independence due to gravity being a conservative force), but you are "driving into it" (invoking the driving in rain analogy for aberration), and because you can't measure a faster speed of light you instead see it have a higher energy (bluer color).

Thanks.  Light behaves intuitively in this situation, then.  Like if you're flying fast towards a cliff, and a sound overtaking you from the behind will have its frequency shifted down, and when you hear the echo from the cliff a bit later, the same sound will be shifted up.
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19 Sep 2020 00:47

midtskogen wrote:
Source of the post Like if you're flying fast towards a cliff, and a sound overtaking you from the behind will have its frequency shifted down, and when you hear the echo from the cliff a bit later, the same sound will be shifted up.

Yes! Excellent analogy.

A-L-E-X wrote:
Source of the post hmmm this sounds a lot like how the sound of a train whistle changes pitch to an observer on a platform (but in reverse, since the observer in that case is the stationary one.)

Indeed. This is essentially the relativistic Doppler effect. :)
 
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19 Sep 2020 11:49

What is the habitability of this world around a gas giant? Sun-like star like ours, the gas giant is in the habitable zone. It has 4% more gravity than our Earth's, 1% less oxygen in it's atmosphere. It is a captured moon of this gas giant and orbits in a highly inclined, retrograde orbit. It would be beyond the tidal locking zone, I imagine.
 
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31 Oct 2020 12:51

I guess this video is intentionally somewhat provocative:

I guess so, as it triggered 14,000 comments in the first 8 hours (which I'm not bothered to read).

As soon as it was clear where the video was heading I thought of how the speed of light was first measured centuries ago by observing how one of Jupiter's moon's orbit apparently depends on Earth's season.  Which is of course nonsense if not the one-way speed of light was measured, and a good enough proof by reductio ad absurdum to me.  Isn't it?  If c depends on direction, so much else in astronomy would fall apart.  Cosmic microwave radiation, and so on.

Certainly, cosmology rests on the assumption that the universe is isotropic and homogeneous.  And isotropy may be difficult to prove in the general case, but for the speed of light?
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31 Oct 2020 15:21

:D  The relativity of simultaneity strikes again.  Many weird "paradoxes" in special relativity stem from it, but this consequence may be one of the most surprising.
 
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31 Oct 2020 19:58

I remember awhile ago someone asked, how long would it take for the earth to stop revolving around the earth if the sun disappeared?  Some thought it would be instantaneous but in reality it would take 8.3 min, the same amount of time as it would take for all sunlight to disappear from the planet.  It seems kind of funny that the sun could suddenly disappear but the planet would still be revolving and be lit for another 8.3 minutes.
 
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31 Oct 2020 23:30

I don't find it hard to wrap my mind around that our everyday concept of simultaneity breaks down with relativity, but more specifically, the isotropy of the speed of light, what's the problem with proving it by observing the orbits within our solar system?

Centuries ago one could, I suppose, argue that we couldn't know that the orbits actually didn't slow down or speed up and the speed of light varied depending on the direction, but today we can have probes around Jupiter and Saturn observing the moons.  Meanwhile on Earth we observe the transits and occultations of the moons accurately and we get reports from the probes that, no, the orbits did not change despite what we observed.  Therefore the one way speed of light did not change with direction, only our distance to the planets.

I mean, we get special relativity precisely because the speed of light is assumed to be isotropic, so the problem of simultaneity doesn't to me immediately imply that the isotropy cannot be observed.
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01 Nov 2020 04:29

midtskogen wrote:
Source of the post I don't find it hard to wrap my mind around that our everyday concept of simultaneity breaks down with relativity, but more specifically, the isotropy of the speed of light, what's the problem with proving it by observing the orbits within our solar system?

I totally agree here. How is it possible that all observable evidence would agree both with a non-isotropic speed of light and one that is isotropic? Is not easy to believe for me that this would result in the same universe we see? I might need Watsisname explanation here ;(

Image

Also, let's imagine an experimental device where you place two mirrors around a light source and at the same distance to it, so the light bounces on both and goes to the observer's eyes (located far away in the normal to the line passing through both mirrors). The distance can be measured with a ruler, and the length of the optical path for a photon that goes to mirror A and then to the observer is the same as the one that goes to the mirror B and then to the observer since the observer is at the same distance to both mirrors and the light source is the same distance to both mirrors also. The only difference would be that light would have to travel in different directions to reach the observer, so that a non-isotropic speed of light could be detected with a sufficiently precise measurement on a clock (or just by making both rays to interfere and watching the interference pattern). Why wouldn't some experimental setup like this reveal this anisotropy?

Okay, let me try; the total displacement in the y direction is zero for both paths (just like in a round trip). So looking to the y-component of the displacement: the first part of the trip (from source to mirror), any real speed that light might have in that direction might be counteracted by the complementary speed in the opposite direction. And this is true for both paths, regardless of which balance of speeds they might have (which might be different for each path since they go in different directions). Now for the x-components of the total path, here they in both cases we don't perform a round trip and in both cases the distance travelled is the same so we can't expect any difference. Is this correct? I've assumed the speed of light is always counteracted by the speed in the opposite direction so it looks like half the round-trip speed is [math] just like in the examples of the video, and I've also assumed that the the velocity vector can be decomposed in the x and y direction. Ahhhggg maybe it is true that there is no way around this thing in the end.

Another issue I have getting to understand this is; okay we have to at least impose that the speed of light is homogeneous so that in my experimental setup we can counteract the different speeds of light due to anistropies by the different paths taken to the observer. So, the speed of light is homogeneous but could be non-isotropic, wouldn't the break in the symmetry imply the non-conservation of some quantity that Noether's theorem points to in an isotropic-speed-of-light universe? Couldn't we observe this quantity not being conserved as evidence of a non-isotropic-speed-of-light universe? Why this test would also fail to recognize the difference between both scenarios?

As a final comment. If this is true (that the one-way speed of light can't be experimentally confirmed and thus could be anything that allows for a round trip speed of [math]) the main point here will be: How awesome is relativity (and the entirety of physics) that it really doesn't care about what the actual speed of light is!!!? How awesome is that the speed of light might not be a physically determined thing at all and just a part of a conventionalism that can be modified without any change in the material world?

This makes the speed of light seem more and more like the thing relativity claims it is, not just the speed at which light propagates, but something more fundamental of the geometry of space-time (that goes beyond light and other particular phenomena of nature). A metaphor that I always liked is the one that says that the speed of light is like the poles on Earth, you can't go farther north at the north pole (because of the geometry of a sphere and not because of the technical difficulty of performing such a feat), just as you can't go faster than the speed of light because of the geometry of space-time and not because of the difficulty of breaking that speed barrier. And now I can see that we could add some more meaning to this metaphor by saying that the north pole is also, in fact, just a convention. That you can define the poles on a spherical grid at any position on the sphere you want. We chose to use the convention that defines the poles on Earth as the points where the rotational axis intersects the surface of Earth, because it was easier to talk about climatic zones but not because they were special in any geometrical aspect to any other antipodal points on the surface. Just like we took the speed of light to be half the round-trip average speed of [math] because it was simpler to convene that the speed of light was isotropic, while in reality it doesn't matter at all. Any speed of light in a non-isotropic world (that allows for round-trips that make an average speed of [math]) would yield the exact same results. You can't go faster than light in any case (as you can't go to the north of the north pole) because speed is relative to convention and frames of reference (just like the north direction is relative to the coordinate system you are using or what pole you consider is the northern one by convention).
 
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01 Nov 2020 06:29

I thought we proved all this many decades ago with the Michaelson-Morley experiment.  Why do people keep questioning it- maybe it's because of the clash with people's every day experiences which are classical Newtonian physics, and they can't think of speed on an Einsteinian level?  In any case, popular science is also to blame for some of this, because you dont have to search very hard to find articles about how quantum mechanical actions like teleportation function at many times the speed of light.  The key here is, yes QM is faster, but no information can be transferred at those speeds.
 
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01 Nov 2020 09:43

midtskogen wrote:
Source of the post I don't find it hard to wrap my mind around that our everyday concept of simultaneity breaks down with relativity, but more specifically, the isotropy of the speed of light, what's the problem with proving it by observing the orbits within our solar system?

At what time was light from different planets along their orbits emitted if it is reaching us right now? To know, there must be a network of synchronized clocks, but any synchronization process that will actually allow you to measure the one-way speed of light requires knowing the one-way speed of light.

To make this concrete, consider a satellite in a circular orbit of radius r about the observer and with uniform velocity v (or angular velocity ω). If the speed of light is isotropic, then this situation is easy to analyze. The true angular position of the satellite over time is θ(t) = ωt = vt/r. The apparent angular position is equal to that but with a time delay of r/c, and hence the motion still appears uniform. 

Now let's consider a direction-dependent speed of light. Suppose it is infinity in the direction from θ=0 and c/2 in the other (θ=180°). Then the light from when the satellite is at 0° reaches us instantly, and we see it there "in real time", while there is a delay of 2r/c from when the satellite was at 180°. Clearly what we will see is nonuniform motion, which seems to contradict physical laws. Ah, but what will the form of those physical laws be if the one-way speed of light depends on direction? Will motion along circular orbits still be uniform? Will a clock on the satellite still tick at a uniform rate?

A-L-E-X wrote:
Source of the post I thought we proved all this many decades ago with the Michaelson-Morley experiment.

No. The Michelson-Morley experiment proved that the two-way speed of light is the same in all directions regardless of the velocity of the detector. That result is important and is one of the key observations that motivates special relativity. :) The one-way speed of light, however, is neither measurable nor physically meaningful in relativity.

FastFourierTransform wrote:
Source of the post Okay, let me try; the total displacement in the y direction is zero for both paths (just like in a round trip). So looking to the y-component of the displacement: the first part of the trip (from source to mirror), any real speed that light might have in that direction might be counteracted by the complementary speed in the opposite direction. And this is true for both paths, regardless of which balance of speeds they might have (which might be different for each path since they go in different directions). Now for the x-components of the total path, here they in both cases we don't perform a round trip and in both cases the distance travelled is the same so we can't expect any difference. Is this correct? I've assumed the speed of light is always counteracted by the speed in the opposite direction so it looks like half the round-trip speed is cc just like in the examples of the video, and I've also assumed that the the velocity vector can be decomposed in the x and y direction. Ahhhggg maybe it is true that there is no way around this thing in the end.


:D 

Very fine thought experiment! Yes, even knowing that the light was emitted along the different paths by a single event (i.e. emitted by a point source at a unique location in spacetime), and knowing the proper distances along the various paths taken to reach us, will not help us, because variations in the speed of c in different directions will all cancel out along those paths. In order to bypass this problem, we need multiple observers at different points in space, and then collate their measurements, but then that requires synchronizing their clocks. Doh!


FastFourierTransform wrote:
Source of the post This makes the speed of light seem more and more like the thing relativity claims it is, not just the speed at which light propagates, but something more fundamental of the geometry of space-time (that goes beyond light and other particular phenomena of nature).

Exactly!

The very concept of measuring the one-way speed of light means to know the time at which a signal sent at the speed of light reaches another known point in space. So we are essentially measuring the location in spacetime of another event that is separated from us precisely along that boundary defined by the light cone, or a null surface. But where lies the null surface on our spacetime diagram? And where on the null surface is the event where our signal reaches the destination point? Relativity shows us that events on the null surface can be transformed anywhere along the null surface, even onto the origin! And the null surface itself is defined by the speed of light, which is what we are trying to measure! 

So the only thing we can actually measure is the two-way speed of light, by allowing our signal to be returned back to us, such that we can measure the time it took for the signal to go both ways according to the same clock, moving along our axis of one spacetime diagram.
 
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01 Nov 2020 11:47

In a way this reminds me of one of the tenets of the Uncertainty Principle.  The unavoidable fact is the observer actually becomes part of the experiment!  In effect we are using the speed of light to measure the speed of light!  The key point is that since this is the maximum speed of information transfer, no faster speed can be measured (whether it exists or not is another matter, like in QM teleportation or entanglement.)  Being part of the geometry of the universe and us also being part of the universe leads to this inescapable conclusion.

Wat, I'm not even sure a stable universe could be constructed without this speed limit.  Could it?  If such a hypothetical universe were to form, wouldn't it collapse in on itself and back into a singularity?  I believe the Cosmic Censorship Conjecture postulated that naked singularities can't exist (in our universe anyway.)
 
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01 Nov 2020 13:11

A-L-E-X wrote:
Source of the post The key point is that since this is the maximum speed of information transfer, no faster speed can be measured

Not quite, it is more subtle than the speed of information, and we would be able to measure faster speeds (either speeds faster than light one-way, or speeds faster than light or c two-way). 

The problem for measuring a one-way speed of light is how we determine what time it is "now" at distant locations in space. That is, how to synchronize clocks, because we require multiple clocks to know when the signal arrived at the other point, whereas measuring the two-way speed of light can be done with just one clock. Synchronizing clocks is problematic because there is no invariant meaning to now across distant regions of space. That is the relativity of simultaneity. The best we can do is use the invariance of the two-way speed of light, and then choose the one-way speed of light to be the same as a convention for synchronizing clocks for one frame of reference.

If we had a way to communicate (both ways) at arbitrarily fast speeds, then we could use those signals to synchronize all clocks everywhere, and then measuring the one-way speed of light would be easy. But relativity says nasty things about signals that can go faster than c -- this means connecting events that are separated more in space than in time, but by the Lorentz transformations, the ordering of those events is ambiguous. In other words, if we could use arbitrarily fast signals, then this violates the causal structure of spacetime.
 
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01 Nov 2020 13:25

Watsisname wrote:
A-L-E-X wrote:
Source of the post The key point is that since this is the maximum speed of information transfer, no faster speed can be measured

Not quite, it is more subtle than the speed of information, and we would be able to measure faster speeds (either speeds faster than light one-way, or speeds faster than light or c two-way). 

The problem for measuring a one-way speed of light is how we determine what time it is "now" at distant locations in space. That is, how to synchronize clocks, because we require multiple clocks to know when the signal arrived at the other point, whereas measuring the two-way speed of light can be done with just one clock. Synchronizing clocks is problematic because there is no invariant meaning to now across distant regions of space. That is the relativity of simultaneity. The best we can do is use the invariance of the two-way speed of light as a convention for synchronizing clocks for one frame of reference.

If we had a way to communicate (both ways) at arbitrarily fast speeds, then we could use those signals to synchronize all clocks everywhere, and then measuring the one-way speed of light would be easy. But relativity says nasty things about signals that can go faster than c -- this means connecting events that are separated more in space than in time, but by the Lorentz transformations, the ordering of those events is ambiguous. In other words, if we could use arbitrarily fast signals, then this violates the causal structure of spacetime.

Wat, isn't this what Cerenkov radiation is all about though?  You can measure speeds faster than light, but not faster than light in a vacuum.  Could we conduct an experiment in which two spheres were immersed in some kind of non vacuum medium and then measure hyperluminal speeds- but this still wouldn't be able to sync clocks in "real time."
And that's right about time, I've conducted thought experiments trying to figure out how to synchronize time across advanced civilizations that exist many light years apart, but it just isn't possible to "now" because time is also relative.  You can only sync time to an event that already happened, not to "now." And "now" has no meaning across vast distances because the measurement itself has a speed limit- c.   And you can't use quantum mechanics temporal entanglement to sync time across vast distances because it doesn't carry information, correct?  There is no such thing as absolute time except in our own minds.  You know I intensely dislike causality and have tried to get around it in different kinds of mind models (such as the entire history of a universe might be predetermined therefore there is no cause and effect, because all pasts, presents and futures would co-exist and can't be changed.  Is such a universe with no speed of light limit even possible or would it "die on arrival" and collapse in on itself because without cause and effect you can't have a working universe?)  It sounds like even the Alcubierre drive that uses the universe's own hyperluminal expansion rate can't get around this because it would need exotic matter to work and we haven't found any evidence of it.  If it actually were possible, we could not only make hyperluminal space ships, but also time machines that go backwards in time.  But time doesn't behave like spacelike dimensions and doesn't exist along a 'timescape' in which all temporal possibilities (all the pasts, presents and futures) coexist (as far as we know anyway.)


BTW even adjusting our local clocks by the signal from the official atomic clock in Colorado isn't done in real time.  Even though the distances involved are extremely small compared to spatial distances, and there is a very high degree of accuracy, it still isn't perfect and can't ever be.  "Now" as measured by the atomic clock ends the very same instant it came into being.
 
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02 Nov 2020 01:04

Watsisname wrote:
Source of the post Ah, but what will the form of those physical laws be if the one-way speed of light depends on direction? Will motion along circular orbits still be uniform? Will a clock on the satellite still tick at a uniform rate?

OK, so you're basically saying that it all boils down to Einstein's insight that there is no universal time, no way to peel space and time apart, no fixed reference for either can be established?

Does it mean that it's ultimately a convention when we say that the distance from A to B is equal to the distance from B to A?
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