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In an article published on arXiv.org [Full article available] California-based Raytheon engineers Ulvi Yurtsever and Steven Wilkinson say that any interstellar spacecraft traveling at near-light speed would leave distinct light signatures in its wake.
While special relativity imposes an absolute speed limit at the speed of light, our Universe is not empty Minkowski spacetime. The constituents that fill the interstellar/intergalactic vacuum, including the cosmic microwave background photons, impose a lower speed limit on any object traveling at relativistic velocities. Scattering of cosmic microwave photons from an ultra-relativistic object may create radiation with a characteristic signature allowing the detection of such objects at large distances.
(Score: 4, Interesting) by wonkey_monkey on Saturday April 11 2015, @03:49PM
IANAP, and it would be awesome if one was around to clarify this for me.
The constituents that fill the interstellar/intergalactic vacuum, including the cosmic microwave background photons, impose a lower speed limit on any object traveling at relativistic velocities.
How can that be? If there is a "lower speed limit," what is it relative to? (don't say the luminiferous aether)
Is it because the CMB acts as a sort of base reference frame? Does the CMB look different - red/blue shifted along the axis of travel - if you travel fast enough? And is most stuff in the universe travelling slowly relative to the frame in which the CMB looks balanced?
systemd is Roko's Basilisk
(Score: 2) by wonkey_monkey on Saturday April 11 2015, @03:58PM
Thinking about it I guess it does just mean local matter. Throwing in the CMB confused me a bit.
systemd is Roko's Basilisk
(Score: 3, Informative) by maxwell demon on Saturday April 11 2015, @05:38PM
Yes, it does. More exactly, it looks blue-shifted from the direction you travel in (relative to it), and red-shifted in the opposite direction.
In effect, you get a "CMB friction" just like you get an air friction. It's just that you have to go much faster for it to matter.
Indeed, it is. The speed of the solar system relative to the CMB is about 370 km/s. [stackexchange.com]
The Tao of math: The numbers you can count are not the real numbers.
(Score: 5, Interesting) by boristhespider on Saturday April 11 2015, @10:04PM
"If there is a "lower speed limit," what is it relative to?"
Speed of light in a vacuum. This quantity is an invariant in most (and all mainstream) theories of physics. It does not mean that the speed of physical photons themselves is always that of light in a vacuum - it might be better to say that when viewed on large enough scales/at low enough energies anything propagating along a null geodesic in spacetime travels at the speed of light; while any massless particle operating in a quantum regime will average out to this speed.
"Is it because the CMB acts as a sort of base reference frame?"
You can use it that way if you want. I'd emphasise that there's nothing physically fundamental about the CMB - it just happens to be an almost uniform bath of radiation permeating the universe. We could, if we had enough knowledge (which we can't; the impossibility of making observations outside of our past light-cone -- ie of things that would have had to travel faster than light in vacuum to be observable) base a theory of cosmology on CMB isotherms, 3d surfaces on which the CMB is at the same temperature. The normal to this surface would define a time coordinate, and then we'd have everything needed to unambiguously set up a description of all spacetime based on this stack of CMB surfaces. The 3+1 "gauge-invariant and covariant" approach to cosmology is often formulated on exactly these lines. Doing so literally treats the CMB as a sort of base reference frame - literally. The only caveat is that there's nothing special about the CMB compared to, say, the cosmic neutrino background or the cosmic gravitational wave background, except that we've observed the CMB, unlike the CNB and CGWB, and to high precision. (We could use the cosmic infra-red background but that's so recent that most people would much rather base it on the CMB, if they have to base their model on any background - and I'd point out that most cosmologists don't actually think this way, although they tend to implicitly assume a frame in which dark matter has no velocity, or else a slightly more abstract frame where cosmological relativity looks a lot like Newtonian gravity. I'd also comment that while the 3+1 GIC approach often repeatedly refers to the CMB as the reference frame, when calculations are done it's almost universally been done in a frame in which dark matter has no velocity. Entertainingly, and maddeningly, and depressingly, most cosmologists seem utterly and entirely unaware that CAMB, the most widely used cosmological code for CMB analysis by a very long chalk, is actually built on the GIC and locked to the dark matter. The practical consequences of this misbelief are minimal to none, but the conceptual background of the theory they've built and the code they're using are quite different and it makes me actually quite angry that so many cosmologists either care so little about or fail to understand the theoretical underpinnings of their topic. But anyway.)
"Does the CMB look different - red/blue shifted along the axis of travel - if you travel fast enough?"
Of course. There's nothing special about the CMB that would kill the Doppler effect. In fact if you look at http://aether.lbl.gov/www/projects/cobe/COBE_Home/phys_today_cover_big.gif [lbl.gov] that top image is showing a massive red splodge on the left hand side, and if the colour scheme were less shit would be showing a hot spot in the lower right. That's the Doppler signal on the microwave background (or rather, it's what's universally interpreted as a Doppler signal). The CMB is uniform to one part in a thousand, but if you look at that level, the entire anisotropy of the CMB looks like this -- it looks for all the world like a Doppler signal, as though we're moving (as maxwell daemon says, at about 330km/s) towards the lower-left of the image. There are of course other ways to induce this type of signal but they're all rather artificial and would either have to align with our motion with respect to the CMB, or otherwise assume that our velocity w.r.t. the CMB is negligible. Neither assumption is appealing, so attributing this signal to a Doppler shift is far and away the preferred interpretation.
"And is most stuff in the universe travelling slowly relative to the frame in which the CMB looks balanced?"
Pretty much. It comes out of the model - it's a perturbative model, and the CMB is the last visible remnant of when things were close to the background. In the modern universe the various ripples have grown large enough to make galaxies and galaxy clusters and people sitting at computers, but the model itself assumes that we're still pretty close to an average, background state. Since perturbations have an extremely strong tendency to grow under gravity, it's natural to assume they were smaller in the past, and that as we track back the universe was more and more uniform. (More concretely, in reality, the model is started when the universe was, say, a few seconds old, assuming it was uniform - an assumption strongly backed up by observations including the CMB - and then run forwards. With very few parameters and some large-scale simulations the result of mapping this to the current day looks suspiciously similar to the modern universe, so this isn't just unfounded hand-waving.) The point of *this* is that any velocity is a perturbation, as is any fluctuation in density (or indeed a gravitational wave). Until the relatively recent universe these will have been linear effects at most, and won't have grown *that* much since. Since the CMB reflects the background universe, the immediate implication is that on the whole, velocities relative to the CMB will still typically be relatively small.
Of course this doesn't always hold and we do periodically observe things that appear to be moving too fast w.r.t. the CMB (or a group of objects spread across far too broad a swathe of the universe, all moving coherently), but the statistical significance of such observations is always highly debatable.
(Score: 2) by wonkey_monkey on Saturday April 11 2015, @11:02PM
"If there is a "lower speed limit," what is it relative to?"
Speed of light in a vacuum.
I'm having a hard time picturing that. Doesn't everything move at c relative to any photon, since all photons move at c relative to everything else? Or does everything else move at 0 relative to all photons? Or is it one of those neither/both cases because for a photon there is no spacetime?
What I mean is: to say that the "lower speet limit" is relative to c sounds like it can't mean anything, since any speed below c that we choose in our reference frame could be any other speed below c in some other reference frame. No?
Perhaps what I meant by my question was "If there is a lower speed limit, what reference frame is it relative to?" And I'm not sure photons actually have one...
Have I got it right that the idea behind the article is this: that spaceships would be limited by "the constituents that fill the interstellar/intergalactic vacuum" to moving at, say, 0.9c relative to those (local) constituents? Otherwise those constituents (including CMB photons) become too fast/high energy and pose a threat to the ship?
So the speed limit a spaceship can safely fly at is relative to the matter velocity/photon energy in the immediate vicinity.
So, I think the answer to my clarified question is "the average reference frame of the local slow-moving matter" and/or "the reference frame in which the CMB has roughly uniform energy in all directions" or something like that.
Thank you for your kind indulgence in someone who finds physics like this endlessly fascinating, but usually only grasps the really fascinating parts for fleeting moments, and certainly only one at a time.
systemd is Roko's Basilisk
(Score: 4, Interesting) by boristhespider on Tuesday April 14 2015, @07:07PM
Overall your conclusions are more or less fine. Photons move at a speed of c relative to anything else. To a photon (if one could attach an observer to it) no distance is travelled. (The so-called gamma factor is 1/sqrt(1-v^2/c^2), which becomes infinite at v=c, and length is altered by L=L/gamma.) So it's not quite that to a photon there's no spacetime, but certainly to a photon there's no real concept of distance.
The point of special relativity - indeed, it's one of the axioms - is that there are no preferred reference frames. If there were a preferred reference frame with which to view photons, we could identify it as an aether (of some form). In special relativity, a photon is observed to travel at a velocity of c regardless of reference frame. Phrased another way, we cannot find a reference frame in which a photon is at rest. We can find one for (at least one species of) neutrino since we now know that at least one neutrino species has a mass even if it's exceedingly small, but we can't for photons. In general relativity it does become slightly clearer since spacetime is separated around any event (ie a unique time and position stamp) into three distinct areas -- the past and future null cones, which are mapped out by every photon that could possibly have hit you and every point a photon emanating from you could hit; the past and the future, which lie inside the null cones, and the "present" which is everything outside the null cones. Massive particles are restricted to travel along "timelike" paths, which are those that lie within the null cones. They *can never cross or coincide with* the null cones. If tachyons existed, and we have no reason to assume they do, they would be restricted to travelling along "spacelike" paths which are those that lie outside the null cones and can also never cross or coincide with them. Massless particles are those that travel on "null" paths. As a result, we can never attach ourselves to a photon.
[The "null", "timelike" and "spacelike" terminology comes from the Pythagoras theorem. In the flat spacetime of special relativity -- which is equivalent to the spacetime in the vicinity of any point, although that "vicinity" might be extraordinarily small... -- Pythagoras becomes ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2. A "timelike" path is one with ds^20. ds is in some manner of speaking a distance through the 4d spacetime. (And sign conventions ensure that we don't run into problems when ds^20 apparently implying an imaginary 'distance'.)]
So yes, the reference frame they'd be meaning is indeed that of the (averaged) local constituents and if the spaceship is getting up to significant fractions of lightspeed that reference frame will likely be almost indistinguishable from that of Earth.
Where it comes to the CMB it's slightly more complicated, since the CMB *does* provide an absolute reference frame, which is the frame in which there is no Doppler signal on the CMB. (We see quite a strong Doppler signal on the CMB - one part in a thousand, more or less - from which we can derive our velocity w.r.t. the CMB which is something like 350km/s I think.) However, again, most local constituents are going to be moving relatively slowly w.r.t. the CMB, simply because unless something is catastrophically wrong with cosmology (and despite my dislike of some of the conclusions of the standard model of cosmology it is far from catastrophically wrong) everything started off very nearly as smooth as the CMB and very nearly comoving with it. Not because of anything special about the CMB but simply because *everything* was basically smooth and comoving with everything else. The universe until very recently is extraordinarily well described by a Taylor series - just a smooth background g(t) plus some tiny perturbations delta g(t, x, y, z). That means that even though today perturbation theory has broken down - and it must have, or we wouldn't be here and neither would our galaxy cluster - most velocities are still pretty small as are most density fluctuations. Sure, there are massive local spikes, but on the whole things are still reasonably close to the background. There just hasn't been time for everything to be rocketing around w.r.t. the CMB.
Hope any of that at least interests you...
(Score: 2) by wonkey_monkey on Tuesday April 14 2015, @07:21PM
Hope any of that at least interests you...
It does indeed. I even gave you a mod point, but that's probably being undone by this post.
systemd is Roko's Basilisk
(Score: 3, Interesting) by boristhespider on Tuesday April 14 2015, @09:16PM
Mod points are not the most important of things :)
One point I wanted to make but forgot - the CMB provides an absolute reference frame, but doing so does not violate special relativity since it's a reference frame born of a particular physical setup rather than a fundamental tenet of the theory. In this instance, the reference frame comes because we model a cosmological setup with a (Friedman-Lemaitre-)Robertson-Walker metric, which you can view as basically filling up spacetime with a host of evolving flat 3d sheets, and adding in baths of massless or nearly-massless fluids means we'll have basically smooth distributions of particles that freeze out at different times. The cosmic neutrino background, for instance, if we could see it, would provide a totally different absolute reference frame. (Neutrinos froze out at a different time to photons and the CNB would be at something like 1.7K, I think, as opposed to the CMB's 2.7K). Putting photons into an arbitrary metric will not give you an equivalent reference frame.