HN Gopher Feed (2017-08-26) - page 1 of 10 ___________________________________________________________________
Rumours swell over new kind of gravitational-wave sighting
174 points by indescions_2017
http://www.nature.com/news/rumours-swell-over-new-kind-of-gravit...___________________________________________________________________
[deleted]
andrewflnr - 4 hours ago
Normally, the scientific community is pretty careful about not
revealing results before they're fully baked (press
notwithstanding). Seeing how that control has broken down for this
incident, is it correct to infer that astronomers have pretty much
lost their minds over the possibility of capturing a neutron star
merger?Edit: calm down, people, I'm excited too.
evanb - 4 hours ago
LIGO didn't announce because they want to be sure. But one of
the most valuable aspects of LIGO is as a trigger for optical
astronomy of transient, time-sensitive events. So, when they see
something, they have to tell a wider astronomical community---the
other observers who look in non-gravitational channels---though
they might not be ready to make the information public. Each
observatory comprises hundreds of people. Suddenly your message
isn't contained to just the hundreds of people loyal to LIGO, but
to thousands of people. Moreover, these observatories tend to be
publicly owned and funded, and transparency and modern open-
science practices often mean live updating of the status of these
observatories. Finally, there are the scientists who have
nothing to do with this physics, but fought hard for some
observation time and had their scheduled observations interrupted
for something high-priority. These people can infer (or are
often told directly) why their allocation was preempted.
whoopdedo - 7 hours ago
> swell ... waveSomeone had fun writing that headline.
ChuckMcM - 7 hours ago
No doubt they will "crest" just before the announcement :-). And
opinions will "undulate" over whether or not they are valid
results.Perhaps we just need more drama in science classes to be
more inclusive, "Will this acid change the Ph level of the
solution? Or will its buffering protect it? Find out after the
break ..."
qubex - 4 hours ago
You will never believe what happens to this falling feather in
a vacuum!
Fifer82 - 6 hours ago
The sad thing is that I wouldn't be surprised. Then they can
show you the same 3 minute buildup after the break in case you
forgot.
MilnerRoute - 2 hours ago
"We are working hard to assure that the candidates are valid
gravitational-wave events, and it will require time to establish
the level of confidence needed to bring any results to the
scientific community and the greater public. We will let you know
as soon we have information ready to share."-- Statement from Ligo
http://www.ligo.org/news/index.php#O2end"This did not, in fact,
blow my sox off."-- Astronomer Peter Yoachim
https://twitter.com/PeterYoachim/status/901175225819176961
Koshkin - 3 hours ago
While I would have a trouble imagining a quantum of the space-time
curvature (the graviton), it is not hard to see that the changes in
the curvature could propagate in the form of waves. So, while yes,
an experimental discovery of these waves is an important event in
history of science, I am left curious as to whether it adds
anything to our present understanding of Nature...
raattgift - 2 hours ago
> trouble imagining ... the gravitonLet's start with a graviton
as a gauge boson, mediating the gravitational interaction
similarly to how the photon is a gauge boson mediating the
electromagnetic interaction.First, let's start with "gauge". We
can use as an analogy an air pressure gauge, one that measures
relative air pressures. Let's take it to a place with a
standard pressure (say, in conditions which are effectively STP)
and tune our pressure gauge so that it reads "0" at that air
pressure. As we wander to and fro reading our calibrated gauge,
we'll see pressures that are zero, positive or negative. If we
climb a tall hill we'll see a negative reading. If the
temperature drops we'll see a positive reading.If we contrive
things so that we can take a reading of a generalized pressure
with our pressure gauge everywhere in the universe at all times,
we can construct a (classical) gauge field. In deep space, the
gauge will read strongly negative. At the bottom of the ocean,
or deep in Jupiter's atmosphere, or at the core of the sun it
will read strongly positive. In the early universe, it'll be
strongly positive; in the far far distant future away from the
black hole that will dominate our patch of de Sitter vacuum, it
will read strongly negative. We'll get zero values in some
places, like near the Earth's surface through a lot of Earth's
history, or in the upper reaches of Jupiter's atmosphere through
a lot of its history.Our choice of "0" is not ideal, because "0"
is only rarely the value at any point in our gauge field that
permeates all of spacetime. Instead we should set "0" as the
value in extragalactic space, because then "0"s will dominate the
field (indeed it is possible that all readings will then be non-
negative). In effect, when we set our "0" at STP we normalized
the gauge field; when we decided instead to set our "0" in
extragalactic space, we renormalized it. We could obtain an
ideal renormalization if we could sample the whole of spacetime
and find the lowest reading of our pressure gauge, but we can
certainly get rid of practically all negative values by taking
far fewer samples in regions where we think the lowest readings
might be.Once we have settled on a decent normalization, we could
look at the propagation of nonzeros and study their statistics.
If they follow the Bose-Einstein statistics, we'd call them
"bosons". If they follow the Fermi-Dirac statistics, we'd call
them "fermions". If they follow some other statistics, we'd
assign them yet another name. (Our choice of generalized "air
pressure" probably follows some odd statistics.)Perturbative
quantum gravity works something like this. [2]We have a
background spacetime with a metric; we have a gauge that measures
the deviation from this metric. It'll be "0" at every point
where the arrangement of stress-energy exactly matches the
metric, and nonzero elsewhere. We are interested in modelling
the gravitational interaction as the arrangement of nonzero
values in our field. Patterns of nonzeros around
gravitationally interacting matter themselves evolve (under a
suitable decomposition of spacetime into 3+1 space and time) and
interact like (classical) waves (made up of many molecules), and
upon some study we can determine that these waves in our gauge
field form patterns that strongly suggest they have a rotational
symmetry of two, which we expect on theoretical grounds too
because the metric is a rank-2 tensor field so particles
representing the (change in the) metric field should be spin
2.Conveniently, in a quantum gauge group theory, a particle with
spin 2 is attractive of a particle with the same charge and
repulsive of a particle with the opposite charge. (Compare with
spin 1, where same-charges repel and opposite-charges attract).
[4] So we can identify the nonzero numbers in our metric gauge
field with gravitons. This is amenable to study with
perturbation theory.Unfortunately General Relativity is a non-
linear theory and in our perturbatively quantized gravity, when
you have a lot of high-energy gravitons they spawn more
gravitons. We would want to apply Wilson's thinking on
renormalization and reset our gauge to "0" in a cluster of these
high-energy gravitons by finding some suitable ground value in
the cluster. This is extremely successful up to a point [1],
but as the energies of the gravitons increases we have to take
more measurements to find a suitable ground value, and eventually
we have to take an infinite number of measurements to find one.
This is what is meant when you read "gravity is perturbatively
non-renormalizable".There are, as you suggest with ("... space-
time curvature ..."), other values related to the gravitational
interaction that we can turn into a quantum field [3], but most
suffer a highly similar fate: in some conditions we have to do an
infinite amount of work to make our field values sensible and
match observables.Finally the gauge field that we built on the
metric is fully relativistic and generally covariant, so it works
with any system of coordinates, choice of units, slicing of
spacetime into 3+1, etc. that we want, up to diffeomorphisms (we
have to remember that we chose a static background spacetime).
So even though it gives us useless readings in some regions of a
spacetime containing strong gravity, perturbative quantum gravity
is a useful and standard tool. However, it is not considered a
candidate for a fundamental theory (barring some unforessen
advancement in renormalization theory) rather than an effective
theory and moreover by implication it undercuts General
Relativity's claim to be a fundamental theory too.- --[1]
Relativists tend to define "strong gravity" at this point, since
we get correct results from renormalization at any energy lower
than it. Strong gravity only appears very close to
gravitational singularities (and in the case of black holes, that
means well inside the horizon). If we are using the path-
integral formalism then we'd find that we have "strong gravity"
in this sense in every Feynman diagram containing at least one
loop of gravitons.[2] https://arxiv.org/abs/gr-qc/0206071[3]
https://www.wikiwand.com/en/Canonical_quantum_gravity[4] One
might ask, "is there oppositely-gravitationally-charged matter
anywhere"? It's an OK question, and people have discussed it
seriously. Sabine Hossenfelder has touched on this a few times
on her blog, including http://backreaction.blogspot.com/2017/04
/why-doesnt-anti-mat... although while the photon has no
electromagnetic charge, the graviton itself (in perturbative
quantum gravity) has gravitational charge (this reflects the non-
linearity of General Relativity).
smhost - 7 hours ago
As a non-science person who occasionally watches PBS documentaries,
could this have any implications for Hawking radiation?
snissn - 6 hours ago
Potentially this neutron - neutron star merger or ones that are
detected in the future will result in the formation of a black
hole and in that event we may get more data to help refine models
of black holes and those refined models may give us insight into
the mechanics of black hole radiation - but it would be a bit
indirect and we'd have to get lucky. Also Hawking radiation is
"very slow" and may never be measured directly in interstellar
black holes
kobeya - 7 hours ago
I don't think so, no.
perseusprime11 - 2 hours ago
Someday could we ride these waves to Interstellar travel?
Panoramix - 43 minutes ago
No. The effect of the waves is so small that it required a
gargantuan project to detect the strongest events. The LIGO
detector is possibly the most sensitive instrument of any kind
humans have made.
legohead - 6 hours ago
The idea of two neutron stars colliding gives me shivers. To see
something like that would be mind boggling..
colordrops - 2 hours ago
I wonder if the gravitational wave would be physically noticeable
if one were near the event.
carbocation - 6 hours ago
My understanding is that black hole mergers are not expected to
have any optical-wavelength emissions, whereas neutron star mergers
should have emissions across the electromagnetic spectrum. Is that
distinction part of the excitement here?
raattgift - 5 hours ago
The matter and light radiated away from black hole (BH) mergers
will all come from the accretion discs of each BH. The accretion
discs of the BH masses for which LIGO (and Virgo) is most
sensitive will generally be fairly sparse, so the emissions will
generally be fairly dim.For a pair of similar-mass neutron stars
(NS) that merge into a BH, you can treat region of spacetime
close to the merger as being filled with extremely dense
accretion discs. The density of matter leads very bright
emissions, and the available geodesics produce radiation that
will escape to infinity rather than being quickly absorbed close
to the source (including within the dense matter around the newly
formed BH as it settles into an accretion disc). The picture is
slightly different where the NS masses are highly unequal.The Max
Planck Institute for Gravitational Physics at Potsdam Germany has
done many numerical simulations of NS mergers. NASA's animated
one [1] where the NS are of substantially different
masses:https://www.youtube.com/watch?v=vw2sLcyV7VcSystems of mass
that are barbell-shaped (a pair of heavy masses connected via an
arbitrarily thin bar; for orbiting stars and BHs we take the
limit as the bar goes to zero volume and zero mass) will radiate
gravitational waves when they are spun about an axis on an axis
perpendicular to the bar. These spinning NSes will be radiating
gravitational waves with increasing amplitude, and these radiated
GWs remove angular momentum from the rotating system, allowing
the NSes to move closer to each other. By the start of the
video, the GW radiation being emitted should eventually be
detectable by instruments at enormous distances; that radiation
has allowed the two NSes to reach a critical proximity.At this
point the smaller NS disintegrates under tidal stress and its
additional mass-energy-momentum that then begins falling onto the
larger NS causes the larger NS to collapse into a BH. A large
proportion of the smaller NS remains in the region near the new
BH and is swept up into an accretion structure alsong with s
small proportion of the larger NS that did not get trapped behind
the horizon. The accretion structure is briefly very bright,
especially in gamma rays, as the matter from the smaller neutron
star self-collides until it is entrained into a dense disc.
Those early gammas will be visible at enormous distances (e.g. we
can pick up extragalactic NS mergers with sky-scanning
instruments searching for gamma ray bursts [2]).By comparison,
the smaller of a pair of mass-mismatched black holes cannot
disintegrate (everything is stuck within each BH's horizon), and
the larger of the pair is likely to have a sparser accretion
disc, so the amount of disc-disc collision will be relatively
low. The reshaping of the accretion material around the merged
BHs may be driven principally by the dynamical spacetime around
the BH, with only occasional collisions. While such collisions
can be arbitrarily energetic (at the point where their geodesics
intersect bits of matter may be moving ultrarelativistically with
respect to each other), there are unlikely to be enough such
emissions to be reliably detectable at large distances.- --[1]
https://arxiv.org/abs/1001.3074[2] There is a timing-coincidence
argument about a short gamma ray burst detected in this way and a
detection by LIGO & Virgo that is circulating around the rumour
mill. Peter Coles blogged some detail
https://telescoper.wordpress.com/2017/08/23/ligo-leaks-and-n...
This may be an NS-BH merger, in which the picture is again
somewhat different, and depends on the density of the BH's
accretion disc both in terms of its matter content and in terms
of the momentum (e.g. if the NS and BH are counter-rotating,
collisions will be more frequent and more energetic).
mturmon - 4 hours ago
Thanks for this well informed comment. It links together some
of the observing strategies and motivations really well.
pducks32 - 6 hours ago
Mostly but also because we haven?t ?heard? the waves caused by a
Neutron star interaction before. So experimentally we still have
to confirm that they cause GWs.
raverbashing - 5 hours ago
Which would be surprising if they didn't produce GW
pducks32 - 4 hours ago
Yea that would be very surprising.
qubex - 4 hours ago
Of course they produce gravitational waves! The main point of
curiosity is likely that unlike black holes, that are
"hairless" entities of pure curvature, neutron stars are
complex objects with multiple, variable layers... and
consequentially (I presume) the gravitational waves
occasioned by their merger would both carry more information
about the objects' composition and likely be more complicated
(as well as less powerful at any given distance).I'm just
guessing though.
m1el - 6 hours ago
That is correct.
saganus - 6 hours ago
This might be a naive question, but I'd like to clear it out.Do
gravitational waves travel at the speed of light?I know the theory
says nothing can travel faster than light. I also know that photons
can be seen as quanta or as waves. So my guess is that
gravitational waves travel at most, at the speed of light.But do
they? or do they travel slower? faster? Is there a doppler effect
for GWs?I ask because I would think ripples in the space-time
fabric itself might be a bit different than light waves or other
more studied phenomena.Can anyone point me in the right direction?
sleavey - 6 hours ago
The most popular theories say that yes, they do travel at the
speed of light. Only a coincident detection of a gravitational
wave and an electromagnetic counterpart would confirm this (such
as from a binary neutron star coalescence; the binary black holes
seen so far by LIGO didn't emit any visible EM as far as we
know).
tzs - 6 hours ago
Would even a binary neutron star coalescence give us the
information we'd need to answer this? Interstellar space is not
actually empty. It contains a low density plasma, and so the
speed of light in it is slightly slower than the speed of light
in a vacuum.I have no idea if that plasma would also slow down
gravity waves, but even if it does it wouldn't necessarily be
the same amount [1].Maybe from the differences in arrival time
of light at different frequencies we could figure out enough
about the intervening plasma to figure out when the light would
have arrived if the space had been empty, and check if that is
when the gravity waves arrived?[1] Edit: I have done some
Googling. Gravity waves would not be slowed down by the
interstellar plasma. The slowdown of light through a medium
depends on the existence of positive and negative charges in
the medium that can form dipoles in response to the passing
electromagnetic wave. For gravity all the "charges" are
positive so there is no dipole formation.
yorwba - 5 hours ago
> For gravity all the "charges" are positive so there is no
dipole formation.I'm no physicist, but couldn't lack of
matter in some region otherwise filled with particles play
the part of "virtual" negative matter?
imaginenore - 5 hours ago
We could build a second detector, sync their clocks, separate
them, and measure the speed directly.
greglindahl - 4 hours ago
LIGO is 2 pairs of detectors.
diegoperini - 6 hours ago
Check out LIGO episode of PBS SpaceTime youtube channel. Some
very informative explanitions about gravity waves are given
there.
Sir_Cmpwn - 6 hours ago
+1 for PBS SpaceTime, easily one of the best channels on
YouTube. Gravitational wave episodes:https://www.youtube.com/wa
tch?v=1Tstyqz2g7ohttps://www.youtube.com/watch?v=gw-
i_VKd6Wohttps://www.youtube.com/watch?v=eJ2RNBAFLj0
erikpukinskis - 5 hours ago
I really wanted to like PBS SpaceTime. So many interesting
subjects and I love physics videos on YouTube. But there's
something about Matt O'Dowd that makes them unwatchable for
me. Something about the pacing, I just can't stay
focused.Another great channel is looking Glass Universe -
https://youtu.be/r0plv_nIzsQAnd Udiprod doesn't have a habit
of making physics vids, but this is my all time favorite
physics videos on YouTube which explains quantum waves better
than anything else I've seen - https://youtu.be/p7bzE1E5PMY
SidiousL - 4 hours ago
Your intuition is correct and the question of the speed of
gravitational waves is pretty complicated. The usual treatment
of gravitational waves is done by linearization of some non-
linear equations. This is a very good approximation for the
propagation of gravitational waves since they disturb the space-
time only very slightly (for example, the mirrors in the
interferometry experiment at LIGO get displaced by a tenth of a
nucleus of a hydrogen atom, during the passage of a gravitational
wave).In this linear approximation the gravitational waves are
governed by the same wave equation as for electromagnetism (only
the spin part is different since the spins of the gravitons and
photons are different). Since in the linear approximation we
recover the Lorentz symmetry, then the linearized wave equation
has to be Lorentz invariant. Then, one can apply results from
the representation theory of the Lorentz or Poincare groups;
there are two major types of representations: massless and
massive. They differ in striking ways when it comes to spin and
when it comes to propagation, for example massless particles
travel at the speed of light. If you want to have a massive
graviton then you need to get the mass somehow from your theory.
Einstein's theory predicts a massless graviton, which by the
argument above has to travel at the speed of light. We still
don't know experimentally if the graviton is massless (but last
time I looked at the Particle Data Book there was an upper bound
on the mass which was very small).Now, coming back to why your
question is complicated. Remember that in Einstein's theory
space-time itself is dynamical. Now suppose you follow the
propagation of a gravitational wave. Since this takes some time,
we need to take into account the fact that the shape of the
space-time itself has changed in the meantime. In such dynamical
situations it becomes complicated to even define what the speed
of propagation between two points is. One way this becomes
important is in cosmological situations. For example, the
expansion of the universe stretches the distances and this allows
us for example to see further that the distance you obtain
multiplying the speed of light by the age of the universe. This
being said, you can define the speed locally by studying
propagation for very short distances and times and this will be a
constant. However, you need to remember that the global
situation is more complicated.
neom - 5 hours ago
These PBS Spacetime episodes should help:The Speed of Light is
NOT About Light - https://www.youtube.com/watch?v=msVuCEs8YdoIs
Quantum Tunneling Faster than Light? -
https://www.youtube.com/watch?v=-IfmgyXs7z8The Quantum Experiment
that Broke Reality -
https://www.youtube.com/watch?v=RlXdsyctD50Pilot Wave Theory and
Quantum Realism - https://www.youtube.com/watch?v=RlXdsyctD50The
Future of Gravitational Waves -
https://www.youtube.com/watch?v=eJ2RNBAFLj0
programbreeding - 4 hours ago
Thank you for this. You linked to the youtube videos but I
watch the PBS app on my Roku all the time and it's horrible at
recommending what I should watch."Watched 'City in the Sky' [a
3-part series about airports and planes]? You'll love Downtown
Abbey or The Great British Baking Show!"I'm always looking for
some actual good/educational shows on there, and there's so
many great hidden gems, but they're all... hidden.
iaw - 2 hours ago
Setup your youtube account with liking/subscribing to the
content you're interested in (even if it's from PBS) and
you'll get some okay recommendations.
yk - 1 hours ago
Yes, though one has to go through quite a bit of trouble to
actually show that. The big problem is, that speed of light is
defined with reference to a background geometry and gravitational
waves are a distortion of this background geometry. (And this has
of course not be shown yet, however this observation, if the
rumors are true, would be evidence for that.)
bramen - 6 hours 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.
amelius - 4 hours 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/c...
QAPereo - 5 hours ago
Also, yes, gravitational waves travel at c.
Filligree - 4 hours 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 - 4 hours 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
measurementsWe 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
pcnix - 3 hours ago
I must admit, I really enjoyed reading your comments on
this thread. Good work, and thanks for the effort!
[deleted]
deepnotderp - 6 hours 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...
reubenswartz - 6 hours 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."
raattgift - 4 hours ago
> everything moves through spacetime at cNo. 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 spaceNo, 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.
CamperBob2 - 1 hours ago
That's a rather impenetrable, buzzword-laden way of saying
exactly the same thing as the grandparent post: everything
moves through spacetime at c, which is a velocity expressed
as a 4-vector of constant length. Increase one component
and the others have to decrease to maintain the length.Put
all your velocity into the time component and you can't
move in space. Conversely, if you put all of your velocity
into the spatial components, you will freeze in time like a
photon.
raattgift - 30 minutes ago
Sure, you can always choose useless systems of
coordinates.
[deleted]
nileshtrivedi - 2 hours ago
Can you recommend a book/resource that explains this from
first principles and introduces the math involved as well?
The books I've read either exclude math altogether or if
they don't, they assume that reader already knows and
understands all the math that is required for this.
raattgift - 2 hours ago
Just about any standard textbook on General Relativity
will cover the content of my comment in the first chapter
or so.I like Carroll's [ https://www.preposterousuniverse
.com/spacetimeandgeometry/ ] and indeed, you get to deal
with intervals and worldlines in chapter 1.It assumes you
know or are ready to learn some differential calculus and
how to read a formula with an integral but it (maybe a
bit steeply) teaches tensors (and some aspects of vectors
and scalars) across the first couple of chapters.
Carroll provides some (quasi-)samples under the "Lecture
Notes" tab, but the book itself has benefited from
editing. He also supplies links to alternatives that can
be had for free-as-in-beer.
spaceseaman - 2 hours ago
You would be interested in this
bookhttps://en.wikipedia.org/wiki/The_Road_to_RealityIt
is quite long and dense but explains the math from first
princples like you want.
SAI_Peregrinus - 1 hours ago
The classic text is "Grativation" by Misner, Thorne, and
Wheeler. It's very dense, but very thorough. The other
classic is "General Relativity" by Wald. They don't
really include the math background though, for that you
need texts on multivariable calculus.
gnaritas - 47 minutes ago
You are terrible at explaining things and are correcting
someone who actually explained it much better than you,
even if he is technically incorrect. Your jargon laden
overly verbose response is wildly out of place in
correcting a simple layman level description of something.
It's not appropriate to respond to a simple metaphor by
slinging general relativity equations, you've probably
instantly turned off anyone reading this from your position
and at the end of the day you aren't really saying anything
different, you're just trying to sound smart. If you are
saying something differently, you've utterly failed to
communicate it in any reasonable way.
Swizec - 5 hours 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?
[deleted]
speeder - 4 hours 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 - 26 minutes ago
I wish HN had "reddit gold". Thanks for jotting this down
for us, super clear and interesting.
neom - 5 hours ago
This might help: https://simple.wikipedia.org/wiki/Space-
time
azag0 - 5 hours 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 - 5 hours 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 - 4 hours 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.
colordrops - 2 hours 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?
tannhaeuser - 5 hours ago
Would you know if (the observable effect of) quantum
entanglement is expected to travel faster than the speed of
causality?
fish_fan - 5 hours 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 - 4 hours 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.
4ad - 5 hours ago
All massless particles like photons and gravitons travel at the
same speed, the speed of light. Yes, gravitational waves travel
at the speed of light, and yes, of course they are affected by
doppler shift.
pducks32 - 6 hours ago
Yea so the universe says nothing can move faster than a massless
particle in a vacuum. The photon is the most famous?hence the
speed of light?but any massless this can move at it. So GWs do
theoretically move at the speed of light, though checking to see
if they do requires a lot of analysis and is tricky to figure
out. But yes theoretically they do move at the speed of causality
(or the speed that things happen in the universe unless someone
slows them down) I?m a physicist who?s now listened to a ton of
LIGO?s founders talk about it.
pedro_hab - 3 hours ago
I have the same question, based on the Alcubierre Drive math,
(Wrap Drive) which is based on that space can travel at any
speed.But I also know that the Alcubierre Drive have some weird
implications, such as the inner of the ship is causally
disconnected from the space wrap, basically you can't control it
from the inside.Anyways, I'm curious if the gravitational waves
are "space waves", in that case it wouldn't have limit, as space
can move at any speed.