Why can’t I go faster than the speed of light?
gravityandlevity.wordpress.com
gravityandlevity.wordpress.com
Basically people ran the EFE "backwards" to see what matter distribution makes the wanted curvature. You get either negative mass-energy or the bubble doesn't travel ftl iirc.
We can’t do that either for now, but is way easier on the feasibility scale.
The Alcubierre drive is only a thought experiment that requires "exotic matter" (aka fairy dust) to work.
> They are only theoretically possible if you allow for negative mass and energy--not an engineering problem so much as a "need to find exotic matter"
Basically people ran the EFE "backwards" to see what matter distribution makes the wanted curvature. You get either negative mass-energy or the bubble doesn't travel ftl iirc.
Assuming constant acceleration to the 1/2-way point, flip, deceleration, and using http://www.projectrho.com/public_html/rocket/slowerlight3.ph... :
Time elapsed (in starship's frame of reference, "Proper time")
T = (c/a) * ArcCosh[a*d/(c^2) + 1] (given acceleration and distance)
year = 365.25*24*3600; c = 3E8; a=9.8; d=1.25*1_000_000*(c * year)
from math import acosh
T = (c/a) * acosh(a*d/(c*c) + 1)
print(T/year)
=> 14.3 years each quarter
=> 57 years round trip
Assuming the fully loaded RV weighs 5 tons, this means at max velocity the rest of the ship weighs 10 megatons, which is 10M cubic meters of water, or a cube 200m on each side.
That sounds like plenty of material, right?
The same Project Rho page links to https://arxiv.org/ftp/physics/papers/0610/0610030.pdf which calculates that at the relatively slow 0.995c "the penetration depth of protons of this energy will be ~40 m in water and ~10 m in titanium".
For 99.99999999993978% c, even 10M cubic meters isn't going to be enough.
E.g., to a photon moving at 1c, the whole universe has a contracted length of 0 meters, and it crosses the whole universe instantly. To us, observers at <1c, the whole universe has a non-contracted length of <a lot> and the photon takes <a long time> to cross the whole universe. By the time the photon's 0-second journey across the entire universe has finished (whatever that means), we're all extremely old. :D This is the time dilation meme of slowly-aging space travelers but taken to the extreme.
(1) 'light speed' as in the speed of light, not as in a sci-fi context of hyperspace jump/FTL jump.
Since the universe expands with >1c, I wonder if the photon actually crosses the whole universe. And if not, how it would look like from the prespective of the photon?
If I travelled at one percent of speed of light, same distance, i suppose 100 years would elapse for me, how much would elapse on earth? Odometer would still show one light year?
And what if I left earth at 50percent of light speed , traveled 1 light-year away and did a turn and came back to earth at same speed. For me, it would be 1 year, but if I had a twin brother who was waiting on earth, would i now be a year younger than him? And how is this possible?
His book was intended to help people understand these exact questions, without getting into any complex math.
Regarding "how is this possible?": This was experimentally verified in the 70s in the Hafele–Keating Experiment. Read more here: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experim...
From the photon's perspective, it passes earth immediately. From our perspective, it takes 7 or 8 minutes.
> And let's say, i travel one light-year at the speed of light, that should be instantaneous, right? The odometer would show 1 light-year, my watch would should 0 seconds and some decimals. How much would I have aged by the end of the journey?
You would have aged as much as your watch says you would have aged. Zero seconds.
>If I travelled at one percent of speed of light, same distance, i suppose 100 years would elapse for me, how much would elapse on earth?
I don't know how to do the math, but a very, very long time would have passed on earth.
> And what if I left earth at 50percent of light speed , traveled 1 light-year away and did a turn and came back to earth at same speed. For me, it would be 1 year, but if I had a twin brother who was waiting on earth, would i now be a year younger than him? And how is this possible?
Yes, you would be younger than him, and it's possible because that's just how relativity and time dilation work. It's even practically measurable in "real" life: http://www.leapsecond.com/great2005/tour/
> I don't know how to do the math, but a very, very long time would have passed on earth.
Eh, at .01c, not so much: https://www.omnicalculator.com/physics/time-dilation?c=USD&v...
(=100.005y, not even two days extra)
Is travelling at the speed of light, actually travelling a a fraction of the speed of time?
The 'speed of light' is nothing but a coefficient between seconds and meters (or in general, between units of time and units of distance and is equal to 1 in any sensible measurement system) since the spacetime in GR is unified
This is probably one of the more counter-intuitive simple calculations you can do in physics.
In special relativity, distance is given by:
ds^2 = dx^2 + dy^2 + dz^2 - (c^2)dt^2
dX^2 = dx^2 + dy^2 + dz^2
Further, your velocity is given by dX/dt. If you are traveling at the speed of light, you have:
dX/dt=c
dX^2 = (c^2) dt^2
dX^2 - (c^2) dt^2 = 0
ds^2 = 0
> just curious... does "time" have a "speed" ?
It is not clear how to parse this question. Traditional "speed" is defined as distance over time. We can give this meaning for time itself by realizing that there is no single notion of time in relativity. As such, you could consider the line parallel to the time axis in the coordinate system of observer A. Since dt=0 in the coordinates of observer A, the speed of this line is not well defined. However, we could consider the coordinates of observer B. Assuming B is moving relative to A, he would see this line as being slanted, with both a time component, and a space component. As such, B could compute the speed of this line as dX'/dt', where X' is the total displacement along B's 3 spatial dimensions, and dt' is the displacement in B's time dimension. As such, B could meaningfully answer "what is the speed of A's time". Assuming I didn't mess up on the math, dX'/dt' turns out to be the velocity of A relative to B. This is a curious result that I have never seen before, but I can't really see any physical significance to it.
B could also compute dt/dt', where t' is the time axis in B's coordinate system. This computation seems more useful as it gives a direct measure of time dilation. Unsurprisingly, it also works out to be the Lorentz factor.
- Time relative to an observer: Designating a non-accelerating massive object ("observer"), you get a coordinate system which assigns a time and distance to each event (point in spacetime). In this coordinate system, the observer moves along the time axis.
- Proper time: For an object taking any path through spacetime, you can measure the "subjective" time which has passed between two points on its trajectory.
The two notions coincide along the path of an observer: For each second of subjective time, the observer moves one second along the time axis in its coordinate system. Observer time moves at one second per second, if you will.
What you usually call "velocity" is distance/time in the coordinate system of some observer. For massive objects, this is always smaller than the speed of light. If you want, you can define another notion of speed, to illustrate the original commenter's point: distance in some coordinate system per proper time. This can be arbitrarily high, because at high velocities the proper/experienced time becomes shorter.
To get back to the speed of time: If you measure coordinate distance per proper time, it is only natural to also measure coordinate time per proper time. If you take earth as the observer and follow a spaceship, this is earth time per spaceship time. For a fast spaceship, time on board passes slower than on earth (time dilation), so reciprocally, the spaceship moves through (earth) time faster than 1s/s.
(Unfortunately, the notion of proper time becomes useless for massless particles moving at the speed of light: proper time along their trajectory is constant. They "do not experience time".)
Even the 5-dimension tesseract was a decent representation as well.
Matthew Mcconaughey using love to navigate through the 5-dimension is classic hollywood.
Another one would be cause and effect, if that had already happened it means it must happen again... and so whatever he does there it will succeed in setting events in motion again... Interesting bit would have been how it all started.
To go even further: to a photon's perspective, it is able to teleport instantly anywhere in the universe, because time doesn't elapse for it.
So, saying time stands still for the light is a misnomer.
The main ”paradox” found by experimention is that the speed of light is a constant, regardless of your velocity. The only way this could be true, if you do a thought experiment, is if time was dialating for you. As for the physical and mathematical “why is this happening”, that’s where Einstein comes in.
It’s an exponential. At 0.5c 100 years to you would be 115 years elasped to an observer, 0.9c 229 years, 0.999c 2,236 years, etc.
Here’s an online calculator for the dilation effect https://www.omnicalculator.com/physics/time-dilation
Both observers, looking at one another, would see the other moving near c. Neither would know who was ‘actually’ moving. Yet, you assume there would not be a symmetry in their respective views of the other’s passage of time.
Explain why.
In simpler terms, a twin in a c-speed rocket could very well assume he was still and the earth was moving away. He should expect to find a younger twin when the earth ‘returned.’ Yet the examples only have the earth twin age, so to speak, and not the rocket twin.
What actually matters is who travels the longest World Line a.k.a. the longest path in 4-d spacetime https://en.wikipedia.org/wiki/World_line . That is all.
A person on a non-curved geodesic spacetime path ages more quickly than a person on a curved non-geodesic spacetime path
https://m.youtube.com/watch?v=cPEwkMHRjZU (7 minutes)
It doesn’t answer your question directly, but the tricky part of a twin paradox is not that the earth twin observes his brother in a slow motion (the space twin also does that, thus a paradox). It’s because a space twin actually changes direction by acceleration at some point B, and at that time he skips over a big part of earth’s timeline. The video above only addresses why it’s NOT the earth twin who changes direction by acceleration, which you’re reasonably questioning. The universe somehow knows who is really “steering” and what remains more or less inertial. The pendulum example at the end may give a hint on why.
Edit: also, the space twin doesn’t have to experience any additional acceleration from the “engines” - looping around some gravity well would work too. E.g. an entire trip could be that the space twin goes to the orbit around the earth, gets slung away by a quickly passing blackhole, loops around a distant blackhole and returns, all in a complete free fall.
It's not intuitive but time actually warps and there is no true concept of "simultaneous" in a special relativity world.
This did my head in. Wikipedia has a great explanation.
Time slows down for the faster moving particles. And by time slowing down we mean all the particles in your body equally all start to move slower and more sluggishly in sync.
This is because it takes more energy to accelerate a particle as it approaches the speed of light. So if you had a pendulum clock moving almost at the speed of slight, that velocity of the pendulum at rest would be at X m/s, but if the whole system is already moving super fast the extra X m/s would take too much energy. So since the energy is constant the relative speed of the pendulum just becomes much slower.
So thinking about it, if you are traveling at that speed because of your inertial reference frame it is equivalent that everyone else around you is moving at (or near) the speed of light and they are moving slowly through time. This is the classic twin paradox and there is a resolution to it, which is that you can't instantaneously turn around.[0] Or in our case, we have to turn around to slow down.
Edit: the faster you go, the slower your own (inertial) time passes. That means the external time passes faster, and the factor grows to infinity the closer you get to C.
In fact, subjectively there is no speed limit. As you go faster, anything around you ages faster, but you yourself won't encounter any speed limit.
There is a subtlety not explicitly raised in the writeup, mainly that in General Relativity metrics do not superpose cleanly, in the sense of getting another solution to the Einstein Field Equations. We do not worry about this in the ultrasimplified twin-paradox model where the spacetime is flat in the sense that the Riemann tensor vanishes everywhere. However, if we want to consider the behaviour of gravitational waves with amplitudes outside of the weak https://en.wikipedia.org/wiki/Linearized_gravity limit, we are in a world of calculational pain.
Physicalizing this subtlety, if our travelling twin is travelling in our neighbourhood of the galaxy, it is probably in for a bumpy ride due to gravitational waves from nearby binary stars https://news.berkeley.edu/2021/02/22/binary-stars-are-all-ar... . We cannot easily extract how bumpy by adding in the uniform pseudogravitational field proposed by Weiss. On the other hand, we probably cannot quantify the effects of gravitational waves at all by simple adapatation of the other strictly Special Relativity analyses at the related Weiss link, https://www.desy.de/user/projects/Physics/Relativity/SR/Twin... (which lists among other the resolution in the minutephysics youtube link you provided above).
You're also right that the problem is one of reference frames. We are not obliged to use that of one twin as the spatial origin. In principle any will do, but some choices have advantages driven by features deliberately excluded from the Special Relativity twin paradox.
Let's consider the "(s!)" tacked on at the end of acceleration. We have not only that of the travelling twin's spacecraft engine, but also that which drives the expansion of the universe.
From within our galaxy we observe a highly spatially homogeneous and isotropic arrangement of extragalactic luminous matter (and cosmic radiation, locally) without distortions in the shapes of distant spiral galaxies that imply a spatially non-flat universe. The metric expansion of this, retaining bulk isotropy, gives us a preferred foliation (Wald's 1984 textbook develops this pp 92-93, but alternatively we could use Weyl's principle). Each twin is free to use a "cosmic fluid" observable (like the dipole-free temperature of the cosmic microwave background, which expands adiabatically), even while accelerating, to determine the https://en.wikipedia.org/wiki/Scale_factor_%28cosmology%29 . For example, each twin could consider the dipole pattern dT/T = v/c where T in the twin's proper time. Each twin can thus determine whether it is the relativistic traveller or not, even if it only wakes up occasionally and only long enough to look at a snapshot of the CMB. The travelling twin thus sees a clear breaking of the Copernican principle along the direction of its travel. Or more precisely, with respect to the bulk flow of matter and radiation in the universe, the non-travelling twin can conclude that it is effectively a Eulerian or comoving observer, while the relativistically-travelling twin cannot.
Moreover, the twins (and any third party) can use "cosmic fluid" observables to determine the scale factor when the twins are together at the start of the travel, and when they (or at least one and the other's remains) are together again at the end.
In this approach there is no paradox at all, there is only the consequences of one twin with a worldline with sections where the proper time is at a higher tilt to the cosmic time than the other twin's. We also avoid the difficulties in attaching a pseudogravitational field to a spacetime where there are gravitational waves of reasonably large amplitude, or relativistic stars and other massive compact objects.
We head into the land of apparent paradox by stripping out evidence of an expanding universe. We must also eliminate evidence of the aging of galaxy clusters through gravitational collapse (including the rate of star formation and the change in abundance of heavy elements). Indeed, we have to arrive in a setting in which neither twin can determine that it has departed from a point at which some reasonable generalization of the Copernican principle applies.
Indeed, the usual formulation of the apparent paradox gets rid of everything but the twins, so that one cannot even use Rindler/Unruh-like observables in flat spacetime, and this really emphasizes the "Special" in Special Relativity.
In that setting, as I said above, relying on the equivalence of being in uniform acceleration (even if it's instantaneous) and being immersed in a uniform (pseudo)gravitational field, is a reasonable way to eliminate the apparent paradox.
At our origin, S and E synchronize observe their identical atomic wristwatches coincidentally agree that it is "0". Light-years away, E and L come very close to one another and exchange timestamps showing that coincidentally their identical atomic wristwatches agree. Finally, L and S come very close to one another and compare timestamps from their identical atomic wristwatches. All the wristwatch times are identical to those at the three points in the diagram of the "instant turnaround" version of the twin paradox, we've just turned the travelling twin into two unrelated travellers on different trajectories.
The argument is that this "love triangle" is resolved because E & L are different travellers in uniform motion, so all parties must combine the times acquired in two different reference frames (E's and L's) to compare with the times acquired in S's reference frame. The further argument is that this duplicates the "instant turnaround" version of the twin paradox if we can have the travelling twin change direction without acceleration.
Firstly, we can still solve this with a pseudo-gravitational field popping up at the moment E & L exchange timestamps. It's no more of a coincidence than the identical timestamp when S & E are close.
Secondly, it's not clear that the paradox remains interesting in this case, because there is no expectation that S & L should be the same age when they are close to one another again. They aren't twins. Unless we add in accelerations, there is no way by which S, E, and L could all have been born at close to the same location in spacetime.
Thirdly, it's unclear that there can be an instant turnaround without acceleration. A couple flavours have been explored here and there.
One involves a slingshot around a star to change directions from away to towards the stay-at-home twin. In this picture the travelling twin is always in free-fall. But here we are substituting real gravitation (that of the star) from pseudo-gravitation. We've moved from everywhere-flat Minkowski space -- the spacetime of Special Relativity -- to something closer to Schwarzschild spacetime, which is only asymptotically flat. Moreover, we are using the near region of Schwarzschild to accomplish the slingshot.
Another substitutes the open flat Minkowski space with one in which there is a compact spatial dimension that curls back on it self. A universe with the geometry of a cylinder with infinite height and small circumference, or a torus, or a sphere would do. The cylindrical case has been explored recently : https://doi.org/10.1119/10.0000002 with comparisons to Minkowski space (the spacetime of Special Relativity), §IV (Conclusion) being pithy. Again, I see this as trying to substitute pseudo-geometry with real geometry, an adapted clock-comparison recipe, and a highly privileged frame for the traveller, in order to avoid a non-gravitational acceleration opening the door to a pseudogravitational field arising in the ultrasimplfied and thus strictly Special Relativity problem.
The pseudogravitational field approach comes from Einstein in 1918: https://en.wikisource.org/wiki/Translation:Dialog_about_Obje... which was fun to read.
Finally focusing on the latter part of my comment that I'm self-replying to (mostly for my own benefit), we have only done away with one acceleration by the returning twin. We still have the effects from the behaviour of matter in the expanding universe with which to clock S, E and L, removing the remaining paradox if we somehow contrive to have S, E & L expecting to age similarly. If we are abandoning Special Relativity in order to avoid acceleration by the returning without invoking outright magic, why only do it along one spacelike dimension, or by importing a very finely tuned third traveller?
Unless we invent a reactionless drive the idea of traveling between solar systems remains a pipe dream.
Oh, and all light from the universe is now gamma radiation focused intensely ahead of the spacecraft cooking the whole thing.
An atomic nucleus sitting in deep space becomes an apocalyptic collision at 99.99% light speed.
I assume people know how bad the penalty can be for going merely 10 MPH over the speed limit.
Don't worry about an individual photon except as part of an image in this example.
The light from the source hits the subject and is reflected toward your eyes at the speed of light.
That's why they call it the speed of light, and radio signals do it too between their source & receiver.
So now imagine you could travel faster than the speed of light to a planet a number of light-years away and you are going to get there from here.
Once you leave Earth orbit you will be able to accelerate up to and beyond c in the safest most gradual way directly toward your destination.
While still in orbit you look down on the traffic in your hometown, and everything is still moving at normal speed no matter how far it is down there, since you are a steady distance away from what it is you are looking at.
As you accelerate away from Earth and approach the speed of light itself you're beginning to catch up with the light that was reflected off your home planet quite a bit earlier than the light which is simultaneously being seen by those back in orbit.
So at half c you look out the window and it looks like everyone back in your hometown is moving at half speed. But naturally time marches on down there. You just can't be so sure any more. At that speed if you left 2 years earlier you will only be able to know additional things about your home which happened no more recently than 1 year ago at that point.
Of course you can't communicate with them about this in real time because of how long it takes the radio signal to get back & forth so you don't bother.
You keep going and reach full light speed which finally matches the rate the images are being reflected away from the Earth at, so now look back home and everyone appears to be standing still on Earth, as expected. Even though as far as you know they are still carrying on like normal.
OTOH, approaching the destination planet at the speed of light, that's pretty fast, but you have to realize their alien traffic is actually only moving half as quickly as it looks from your craft, whilst you are speeding so rapidly in their direction. Don't let that fool you, the aliens are only half as advanced as they look.
If you want to really see something, go faster than the speed of light and the planet you are approaching will be moving more than twice as fast as normal, and looking Earthward all you can see would be things moving backwards.
One thing that's happening is that you are always seeing images of these two planets where the light source originated from two different suns.
Once the distances get far enough, it's possible to launch a mission to a destination that actually no longer existed any more for quite some time before launch, only who knew?
In that case the earlier you make your reservations the more unwise it could be.
Arvin Ash has a cool video on this that is probably too complicated to describe in a HN comment:
:adjusts bow tie:
Welllll…combination of that and angular momentum. Combined with the masses of the sun, and the moon, the other planets, and all the other masses of the universe.
Fortunately, orbits factor in, too. Everything that orbits is essentially in free fall, wellll…until they get tooo eliptical and the oscillating accelerations get really noticeable.
And it all affects time. Time is a bunch of wibbly-wobbly…stuff.
(( Ok, ok: Matt Smith might not have been that wordy as The Doctor. ))
Think about it: when you are in free fall you feel 0 acceleration. You appear to be accelerating relative to the ground-- but you're actually motionless in an "inertial reference frame". (Similar to how the astronauts on the ISS don't "feel" acceleration despite accelerating rapidly relative to the earth.)
The "force" of gravity is often modeled as "gravity pulling you down" and the ground "pushing you back up". This works mathematically, but isn't quite logically consistent.
In reality, on the ground you're in a region of warped spacetime, so you feel constant upward acceleration despite not actually accelerating. (Thinking of this another way, standing on earth feels identical to being in a far away spaceship accelerating at 9.8 m/s².)
This is also why time "speeds up" near more massive objects. (Separate from "acceleration".)
We're so used to gravity this it doesn't seem weird. But when you consider the fact free-fall is when you're not accelerating... well pondering that from many angles is what ultimately led Einstein to his model of relativity.
(This is me trying to condense what could be a 10 minute explanation into a few sentences, so apologies if it's not particularly clear.)
It his, it just depends on the observer.
An external, stationary observer will never see you go further than 100 light years, but yourself? Assuming you are able to make your ship go any arbitrary speed approaching c, you could be traveling billions of light years.
It's just that when you stop (if you manage to stop), the universe around you will have aged billions of years, while you will only be a few years older.
We can parametrize (as in make parametric) arbitrary curves through spacetime however we like. Parametric representations of unique curves are generally nonunique.
Some of the infinite possible parametrizations of a chosen curve have useful properties, such as uniquely labelling every point on the curve with some monotonically ordering value and keeping the form of some set of equations reasonably simple.
For timelike geodesics, particularly in the Minkowski space of Special Relativity, proper time (being a Lorentz scalar) is a good option. However that is not true for all geodesics in Minkowski space (as you note, the proper time is everywhere zero on a null geodesic, and so a bad option), much less all curves through general curved spacetimes.
For null geodesics, following the logic of GP's question, we may wish to preserve the tangent vector under parallel transport; this requires the parametrization to be affine. Some gory details at https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics and a brief useful summary at https://www.reddit.com/r/AskPhysics/comments/9aenid/what_act...
As is noted below the comment directly pointed to by the second link, labelling a timelike geodesic with proper time is choosing one specific affine parametrization on that geodesic, and that this choice is driven by convenience.
One of the neat outcomes of affine parametrization is that we can take a point on an affinely-parameterized null geodesic and look at the derivative with respect to the affine parameter there, and define a momentum k^{\mu} = \dot X^{\mu}. In a Lorentzian spacetime, with curvature, we can compare the momentum at two different points on the null geodesic, giving us the gravitational redshift between those two points of the photon's wavelength equiv. frequency.
It stops being conserved if there's suddenly more or less energy inside the volume without the same amount crossing the boundary
Conservation of energy says that it is impossible for energy to enter this volume with that same amount of energy exiting the volume.
Consider what it would mean for this to be violated. For the sake of argument, assume that all particles must move forward in time by a non zero amount at all points along there path. Since the volume is bounded, any particle with an infinite path must eventually have a time coordinate beyond the largest time coordinated in the volume. Therefore, the particle must eventually exit the volume. If you were to work out the geometry more carefully, you could show with relative ease that the particle must exit the volume an equal number of times as it enters. If a particle were to enter the volume without exiting the volume, it would mean that said particle was destroyed within the volume. Similarly, if a particle were to exit the volume without entering, it would have to have been created within the volume. Both of these situations are possible if an interaction occurs within the volume, but the net energy of the particles leaving such an interaction, must be the same as the net energy of the particles entering the interaction.
Put another way, assume that all interactions obey the conservation of energy. If our original volume was V, we can construct a new volume V' from V by carving out sub volumes in which an interaction occurs. Since all such sub volumes obey the conservation of energy (by assumption), the net energy flow into and out of V' must be the same as for V. However, since no interactions occur withing V', all particles entering V' must exit V' an equal number of times, so the net energy flow of V' must be 0. Therefore the net flow of V must also be 0.
At the other end of the scale, you're travelling through space (or practically-C on a relativistic scale), and you're not experiencing time.
So the whole theory of zipping around space and coming home to find you've barely aged, is just spending more time at a higher "angle" than everyone else.
Traveling at the speed of light results in infinite time dilation. Which means that from the perspective of an outside observer, no time at all is passing inside the spaceship.
One way I like to think of this is the term 'sun-kissed'. From the perspective of the photon, the sun is actually giving you a kiss on a summer day.
I would like to see the map of the universe at different potential speeds (or thrusts). E.g. you choose a point in space nearby the sun. At thrust zero you only see hot sun everywhere, because there you go anyway. But at greater thrusts the sun turns into a circle and you start to see sections of the “sky” where you could land, given the thrust is constant. Some areas would be still black because of blackholes, orbits and event horizon. I always wanted that simulation but never found it. It would be much more interesting than just looking around via reversed photons flying into your eyes.
Xkcd style explainer: When you have two things going at noticeably different time rates, you typically prepend "relativistic" [0] to all interactions. "Relativistic collision" sounds almost like "changes into huge amounts of plasma escaping from contact point".
But then that sounds like I'm describing the speed of sound, no? Maybe I'm confusing two concepts.
For any space-time path, you can consider the coordinate system as an observer traveling that path would see it, in which that observer would see itself traveling through time at a rate of one second per second. Geometrically, if you were to draw where on the path the observer's clock ticks, the distance between ticks as measured along that path is constant regardless of the path.
The speed of light limit says something different. It limits what paths a physical observer can take.
Condsider a 1+1 dimensional universe (or our 3+1 universe with a test particle moving along a single spatial dimension).
Pick a non accelerating observer to construct the 'stationary' coordinate system. Plot spatial coordinates along the horizontal axis, and the time coordinate as the vertical axis. Pick units such that the speed of light is 1.
A particle moving at a constant velocity will follow a straight line. If the line is vertical the particle is stationary. If the line is at an angle, the speed of the particle is the inverse of the slope of the line. The speed of light limitation says that this line cannot be shallower than 45 degrees.
In more analytic terms, the distance metric for our 2 dimensional spacetime is given by ds^2 = dt^2 - dx^2. The speed of light limitation says that ds^2 cannot be negative for any path a particle actually takes.
In other words all particles must must have at least half of their travel be along the time dimension.
So given what you've described, that means that forces applied to bodies need to have a time component equal in magnitude to the spatial components. Forces must always exist along that 45° line. The limit of the force required to continue to rotate that spacetime velocity out of the time component and into the spatial components goes to infinity as the vector approaches that 45° line.
The fact that forces are unidirectional is the unexplained part. If they weren't, then we could rotate that vector further, and start traveling backwards in time. Then wouldn't B expect to see the objects moving apart, while A sees them moving closer together?
To me, the impossibility of the disparity in observations is a consequence of, dependant on, no-FTL, not an explanation thereof.
Addendum: I don't understand why you said 45° instead of 90°. I thought objects traveling at the speed of light would experience infinite time dilation, and thus be observed as having 0 passage of time.
Think about what the diagram shows: Every (s[pace], t[ime]) coordinate pair on the spacetime diagram shows an observation of a particle. So in natural units, a photon's wordline is given by s=t or s=-t (traveling in one or the other direction). If you draw that, it's a 45° line. It also gives you the light cone of the observer at (0, 0).
A horizontal wordline would be something moving at infinite speed, not the speed of light, as it is observed at every place at the same time.
The rate the simulators transmit data are irrelevant to our timeframe (since we’re a part of the computation).
I believe it’s more like a centralized interpreter with decentralized (NP) evaluation strategies. The limit reflects the minumium size of a recursive expression.
Consciousness (at least in this world) can perchance then be understood as the artifact of a feedback loop constructed by a (meta-circular) interpreter that converts the topologies of molecules into qualia, which then makes adjustment to the reflective tower (with physiological-changes-in-brain&body as correspondence).
Time perception then is the same consequence that follows relativity ie a direct result of this speed limit that reflects the minumium size of a recursive expression (but concerning only the viscosity and turbulence of neurotransmitters in relative to eletric signals?)
There was a talk with lawrence krauss I think, where he explained that at galaxy scales, everything is distributed, there's not one reality but an infinity since no point in space can be aware of far points in the universe.
I also wonder if there would be ways to tweak C.
(I also highly recommend their book "There Is No Antimemetics Division" if you're at all interested in SCP Foundation)
A very easy to read article, give it a try.
Also if you are curious why a moving charge creates a magnetic field watch this Veritasium video: https://www.youtube.com/watch?v=1TKSfAkWWN0
This way, the stationary observer will sure notice that there's F_B, but will also know that the charge moving alongside the (also moving) rod does not experience it.
[0] http://www.physics.louisville.edu/cldavis/phys299/notes/mag_...
Maybe what they really wanted to say is "there is a speed c at which the charge of a moving rod is indistinguishable of current running through stationary rod"? Now that would make a lot of sense.
But from the runner's perspective, the barn has length 5m long. What does she see happen when the doors are closed on her?
Also, relevant xkcd (what-if) https://what-if.xkcd.com/1/
Most likely from the runner's perspective the world turns white as they dissolve to plasma prior to reaching the barn.
No, they don't. I'd phrase it differently, e.g. “each door is shut for an instant when the end of the pole is just inside the door”. (Also, make it clear that the barn is long enough to fit a 10m pole between the two shut doors.)
When you put it as “shut the doors simultaneously”, it's more troll physics than a paradox.
Meta-puzzle: figure out how to still imply that the runner is completely enclosed for an instant, without incorrectly insinuating that it is so from her perspective.
If the doors actually don't open in time then the resolution for the fact that the pole doesn't physically fit is that nothing can be rigid at relativistic speeds. So either the door or the pole or both will deform (violently) to allow the pole to fit inside the barn.
But I think over longer distances there would be a time delay for the light of the explosion to reach the individual, so they would probably the light of a visually warped pole colliding with visually warped barn doors very briefly before disappearing into an explosion.
What one frame of reference sees as a simultaneous closure of the doors looks like non-simultaneous closure of the doors in another frame of reference.
Simultaneity means that two events coincide in time and space.
Different time and/or space means: not simultaneous!
Q2. How do black holes exist if time stops inside a black hole? That is, they continue to move through spacetime, even though spacetime is not moving within the hole? I accept that a black hole can form, and can stop time, I'm just curious how something that stops time continues to persist in the present. The way I'm visualizing this, is like a lava lamp about to bleb off some goo from the top [1]. As the object gets more and more dense, it curves and drags spacetime more and more, until eventually its density passes the Schwarzschild radius and blebs off.
[1] https://m.media-amazon.com/images/I/615deDvfDkL._AC_SS450_.j...
Truly, the Ship of Theseus was inside us all along. (Which is super convenient, considering how often we step into the same river twice!)
Regarding time, there's no universal global coordinate for time in General Relativity. Time is based on each observer's time coordinate. When time stops inside a black hole, it means time appears to stop in an outside observer's time coordinate.
This is because the spacetime curvature inside a black hole has been stretched so much that the stretched curvature approaching infinite long. See the pulled down funnel [1]. An object traveling in no faster than light speed in the infinitely long curvature takes forever and its time appears frozen to an outside observer.
But it's an illusion to the outside observer. The observer is seeing the light imprint emitted from the object, not the real object itself. See the diagram below.
BH << o. EH. . . . .......... >> P
Imagine the object o has a blinking light beacon at its tail, blinking every second by its clock, i.e. on for half of a second and off for half of a second. You can see the light every second and measure the object's time.
Since the speed of the light is constant, the photon traveling away from BH will take longer and longer to move across the stretched out space, as shown by the spaced out dots between EH and P. As o approaching EH, P will see the blinking light slows down because the photons take longer to move across the stretched space. P would conclude that o's time is slowing down. Passed EH, the photon is not coming out because the space is stretched longer than it can cover in its constant speed. At EH, the photon can still come out but at a very slow pace because the space is stretched matching the speed of light. The beacon is not blinking because the light stream been stretched to infinitely long. Object o appears frozen as its time has stopped by P's measurement of the blinking rate. But what P sees is the long stream of photons stretched out when o approaching EH. The object o has long gone in its forever falling across the infinitely stretched spacetime. Only its light imprint before EH is being observed as frozen.
[1] https://www.sciencenews.org/wp-content/uploads/2017/05/05121...
> basically make people whatever age I want by varying my speed.
No more so than making the Earth change shape by moving your physical location.
> Since the same 1 hour passes for me no matter the age for them I chose, it seems like I'm selecting an already existent future from a stack, not fast-forwarding the present I left.
Yeah these are more philosophical questions rather than a testable hypothesis. It’s an interesting way of viewing the world, but if you’re talking about a future “existing” scientifically and materially in concert with the present, then you’d need to devise an experiment to be able to enter or interact with that future beyond just waiting for that future to exist.
Otherwise time travel isn’t even necessary for this thought experiment. You could say the morning already exists and fall asleep and wake up and boom it’s morning time. But in reality all of the ticks of time happened between when you fell asleep and when you woke up, you just weren’t able to observe all of them at the same speed as someone who stayed awake all night.
You and I survey a building (plot of land, whatever) separately because we want to check each other's work. At then end we look at our data and disagree on every single coordinate except the origin. Ah, you're a crappy surveyor, I conclude. No, you are, you reply.
Then for whatever reason I ask what distance you compute for the distance from the origin to the corner of the desk. 3.183 meters. Huh, exactly same number I compute. Okay, what about the distance from the far corner of the room to the southmost window? 18.45 meters. Me too!
A bit more chatting and it turns out you used true North as the y-positive direction, and I used magnetic North. Opps. Our frames are just rotated in respect to each other.
Now, is it freaky and weird that I say the speaker is 2.78 meters in the y direction, and you say it is 2.619? No, we are just using different frames of reference. There is no 'reality' to any given y direction or coordinate. It is arbitrarily chosen, as our the units (I could use yards instead of meters, and have an entirely different number yet).
OTOH, what is real, and invariant, are distances. That's a physically real thing. hence we always comput the same distance between any two points, despite using different coordinates for our (x,y) tuple. If you want to be mathy about it we say the metric is s^2 = x^2 + y^2. Pythagoras, in other words, in a Euclidean space.
Well, we don't live in space, we live in spacetime, where time is a dimension. When we move at different speeds relative to each other our 4-D coordinate systems are rotated relative to each other. That includes time. So, if you rotate yours relative to mine, travel for awhile (time and space!), well, you will end up with different coordinates for x, y, z, and t. It's no odder than if you and I travel 'North' in your car, but you use true North and I use magnetic we end up in different places on the globe.
In 4D space what is 'real' is not coordinates or time, but events, and what is constant is the interval between events. Just like what is 'real' in 2D Euclid space is not some arbitrary y-direction, but the distance between two objects. Distance is invariant in 2D space, event intervals (space and time) are invariant in 4D Minkowski space (the space we live in absent of gravity).
There's a bit of handwaving in there, but that's pretty much the physics; any 7th grader can do it. The main part that will lead to bad conclusions is that the metric in Minkowski space uses a negative number for time; so s^2 = x^2 - c^2 t^2. That's hyperbolic, so if you use intuition from Euclidean space you may conclude that in some instance distance will contract when it expands, or vice versa.
So, finally, to your Q1, if I travel magnetic North, is the position I reach on the "same" Earth as the one where you use true North? Feels like a weird question that misses the point, right? Same Earth, just a different location than you expected because my frame was rotated wrt yours.
Note that every experiment we have ever carried out bares this out. Accelerate a clock, bring it to Earth, that clock is younger (I'm ignoring general relativity's effects here, but the experiments don't). Measure how long a very short living particles live that are created by other particles crashing into our atmosphere, and they live exactly as much longer as SR would predict. Etc. did that clock "select" a different version of you? No, it just travelled a different path in 4D spacetime than you, and hence ended up at different coordinates. To go deeper into that I'd have to introduce "proper time", but since the ending x,y,z are the same are your x,y,z, can you see that intuitively it must be the t coordinate that changed?
[1] https://www.eftaylor.com/spacetimephysics/ This book is released under CC, free to download and share, and utterly fantastic. All you need is junior high math to master the material.
Small relativity related tidbit: I hate when people say the phrase "the faster you go, time slows down for you." This is a problem because it implies that the moving observer notices their own time dilation which is reverse of the case. Of course, every non-accelerating observer is in their own rest frame, so it doesn't make sense to say "time slows down for you," because you are your own reference and there is no other frame to base your measurements on (I mean that was the whole point of relativity, there is no universal rest frame). Instead, when you measure the rate of change for other reference frames moving relative to you, their clocks move slower when measured by your clock. So the actual phrase should be something like "the faster others go, the slower their time appears to you."
That will be very comprehensible
Most people for whom this property of electricity and magnetism is well known, also know that the speed limit from general relativity comes from Maxwell's equations (which are on themselves a compilation of other previous rules).
I also dug deep into this problem a while back, but without proper physics background couldn't get too far. The speed of light comes directly from the Vacuum permeability and Vacuum permittivity, since light is an electromagnetic wave. If these were different, then the speed of light would be different. Both of these seem to be values of the behavior of vacuum in our universe (and possibly electron's [1]).
It is Maxwell's equations gives us that the speed of electromagnetic radiation needs to be c ^ 2 = 1 / (e * u) [2].
[1] https://en.wikipedia.org/wiki/Fine-structure_constant
[2] https://en.wikipedia.org/wiki/Electromagnetic_wave_equation#...
They do such a good job at using video to explain Special Relativity.
It's not that nothing can move faster than the speed of light, it's that nothing can accelerate to a speed faster than the speed of light.
If you could bring particles into being that already moved faster than light, they would not violate our understanding of relativity or the rest of physics. Hence ... the tachyon. https://en.wikipedia.org/wiki/Tachyon
I'll largely stick with the theory, which I guess is what you are interested in.[1]
The topic is in Part VIII (Chapter 35) of Misner, Thorne & Wheeler's Gravitation ("MTW"), which is the gold standard reference/textbook for General Relativity.
I will later try to briefly summarize the section.
Instead, first, at the root of my answer is the non-linear nature of the Einstein Field Equations, which imply that gravity self-gravitates. This is usually side-stepped by textbooks, which instead proceed to linearize the Einstein Field Equations, that is, they consider the weak limit of gravitation. This is usually to split a metric with a gravitational wave into some minimally-or-even-non-dynamical background and the wave-part, using the former to define the speed of the latter.
For strong gravitational waves, or a very dynamical background, we cannot do this. I think this regime is best studied in a vacuum solution, i.e., where there is only gravitation that self-interacts, although most of the work in this regime appears to have the aim of resolving questions about the distribution of matter in the very early universe (e.g. Misner's mixmaster). An interesting exact solution of the Einstein Field Equations is the https://en.wikipedia.org/wiki/Kasner_metric which can generate singularities and other features formed by gravitational-wave interactionsn. That is, there is manifestly non-linear gravitational self-interaction in the highly-dynamical Kasner chaos. (This is the worst case for the linearized treatments in textbooks).
The Kasner metric can be applied to a Lorentzian manifold (3 space, 1 time dimension), and so is consistent with our universe's causal structure. An interesting feature of this solution is that it engages only two constants in the Einstein Field Equations: c and G. The only velocity scale that we can construct from any combination of these two constants is c itself.
This is highly suggestive that in a universe like ours gravitational radiation must propagate at c.
Again, this is just an argument that there may be an answer within the theory of General Relativity itself, without treating the speed of gravitational waves as a postulate.
This argument is made without regard to the obvious craziness in a Kasner chaos universe compared to our own. General Relativity admits complete gravitational solutions for all sorts of craziness, including universes with any number of space and time dimensions as long as there are at least two total, stress-energy which is distributed very differently from ours (including negative energy, or energy that pops in or out of existence without a cause), and so forth. It is very General. (Special Relativity is very Special: it's defined on -- and only on -- a gravity-free (flat, no gravitational waves) spacetime of exactly 3 spatial and 1 timelike dimension.)
Returning to MTW, they conclude that the propagation speed instead can be no greater than c.
The authors develop an exact vacuum plane-wave solution in §35.9, where the only thing in the spacetime is single large pulse of gravitational radiation in otherwise totally empty flat spacetime, and a set of "test particles", which are well defined probes in General Relativity defined so as to not perturb the solution. They proceed to compare this solution to that of an electromagnetic plane wave in Special Relativity, and arrive at a more physical viewpoint where the gravitational plane wave, if it has anything like a physical source (e.g. a pair of masses in mutual orbit; they return to this in Ch. 36) should be more like a set of "ripples in the spacetime curvature ... propagating on a very slightly curved background spacetime ... The most striking difference between the background and the ripples is not in the magnitude of their spacetime curvatures, but in their characteristic lengths". There is a characteristic length of this background spacetime, determined by its (much much larger) radius of curvature.
They then grind out effective stress-energy tensors, which would couple with any matter in a non-vacuum environment. The argument is that anything in the stress-energy tensor must in certain causal structures (like the one in our universe) must propagate at no more than c.
Their treatment is the basis for a particular type of graviton (Ex 35.16), the scattering and redshift of gravitational waves (.17, .18), and various ways to express them without resort to an effective stress-energy tensor.
In these approaches, c is the limiting speed of gravitational radiation, but gravitational radiation may move slower than c in non-vacuum. In vacuum, the pure pulse may in some circumstances develop a trailing edge that propagates at less than c, but when this can even happen the effect is weak when the wavelength is short compared to the background length scale, or when the amplitude of the pulse is small. Perhaps gravitational astronomy can hope to find someday a high-enough amplitude wave to put this to the test.
For clarity, though, the linearization-is-good-theory claim is on solid footing. LIGO uses the linearized equations and have found agreement between the speed of gravitational waves they've detected to their theory to something around nineteen decimal places. A good multimessenger signal, which seems inevitable, will almost certainly improve that. There is no good reason to expect the speed of gravity in a full solution to the Einstein Field Equations to differ. One can make the same argument about the march of results from post-Newtonian expansions (as below) too. The only "wiggle" room is that cosmic inflation is probably much more dynamical, and the gravitational waves are of much greater amplitude.
- --
[1] The non-theory answer is that the behaviour of orbits in known astrophysical systems which are very post-Newtonian (think black holes, or extremely fast-moving galaxies containing predictable spectra from hydrogen or light curves from supernovae) are consistent with a speed limit on any gravitational interaction, and that the speed limit is very close to c. It turns out to be hard to measure the speed limit exactly. See e.g. Will @ https://arxiv.org/abs/astro-ph/0301145 which discusses light from quasars being gravitationally lensed by Jupiter and how it would look different under theories that admit a propagation speed c_{gravity} different from c_{electromagnetism}. One could also compare bimetric theories of gravitation in which in the early universe gravitational self-interaction propagates differently from electromagnetism, with a view to resolving some questions in the distribution of galaxies in our sky. These generally have to decay the additional metric (meaning gravitational radiation propagates like electromagnetism) in the very early part of the universe or we get something very different from the cosmic web of galaxies that we observe.
How do we know we're not already moving at 99% the speed of light (like our observable universe as a whole having that speed )?
I love this stuff, but it is so counter intuitive for the average human.
To you. There is no such thing as absolute speed. You say cosmic rays are crashing into the earth at 99% the speed of light. The cosmic ray says it is sitting still and you (and the Earth) are approaching it at 99% the speed of light. Some other particle moving at 70% relative to you will give a different speed for the cosmic ray. All of you are right.
So eg. if you hear about the particles at the LHC travelling at near the speed of light, it's implied that's relative to the Earth.
The speed limit comes in here: no-matter what nearby object you look at, its speed relative to you always be less than the speed of light. (Here, nearby means something like "within the local group of galaxies" - objects a long way away can be receding faster than the speed of light due to the expansion of space in between you and the object). You can accelerate as much as you like for as long as you like and when you stop accelerating and check, that'll still be the case.
Freaky, but true.
Not sure what you mean by relative time?
It is not logical if you really believe that speeds add linearly (that is, if you are going 5mph past an observer and throw a ball 5mph, that the result is the ball moving 10mph).
Speeds don’t actually add linearly like that, but they come very very very very close to doing so for all speeds humans are used to dealing with.
So, we all have very deeply held gut feelings that speeds should add linearly. Once you let go of that, it becomes much easier to understand many of the things that don’t feel logical about relativity.
Ultimately, it is logical, but from a different set of axioms than most humans tend to have.
We just don't realize we live in a 4D space where time is one dimension, so we think driving in opposite directions is a special case where we can add the speeds. but there is the fourth dimension, and we have to use an equation very similar to Pythagoras to get the right value.
I know you must know this, this is more for the benefit of the reader.
I wrote a long answer to someone else; I'm not going to retype it. But what is invariant in the 3D space you think you live in is distances. The distance of you from the kitchen is computed to be 8 meters no matter what we choose to say the x and y directions are, right? If we choose different directions for y, you may say the kitchen is 6 meters from you in the y direction, I say it is 3.7 meters in the y direction. No mystery, our frames are rotated. But we both get the same value for distances. Rotating a map doesn't change the reality of how far you are from the kitchen.
Well, you don't actually live in 3D space, you live in 4D space, where time is a dimension. So what is invariant is not distance (3 of the 4 dimensions), but intervals (time and distance between two events). when you travel at a significant fraction of light speed, you are rotating that 4D 'map'. If you rotate frames, you get different values for x, y, z, and t. But the intervals are still constant.
The intervals are the same for all observers. It is just the individual coordinates (x,y,z,t) that vary for different observers, just like (x,y) are different for you and me wrt your kitchen, but the distance we compute are the same.
edit: in summary, wouldn't you find it bizarre if I rotated the floor plan to your house and suddenly got a different distance from your couch to the kitchen? That would be absurd! Well, when you rotate in space time intervals are unchanged. IOW, the speed of light is unchanged. It would be bizarre if by a simple rotation you got a different value! You just don't 'see' (literally and figuratively) that time is a dimension, and the map rotation as non-relativistic speeds is so tiny that you don't realize that t changes along with x, y, z. But it does. It would be bizarre if it didn't.
Here is one aspect of the conundrum: a certain photon travelling at the speed of light from the sun reaches the earth, which is relatively stationary vs the sun, in approx 8 minutes. It will obviously reach our rocket (which at the moment the photon was fired from the sun was at the same distance as the earth from the sun) some time later, depending on its relative speed to the sun. However, once the photon hits the spaceship it supposedly has the same speed as the speed of light hitting the earth.
I realize this axiom seems to have been experimentally proven, and that I probably just have not found the right key for me towards the understanding of it. Looking forward to that day, which might also lead me to understand how to fit the fact that the blueshift/redshift observed in light allows us to actually determine relative velocities. As well as understand how the expansion of space is a different kind of speed than normal speeds, allowing for the speeds greater than light that it does.
In the meantime I find some solace in the fact that I'm not the only one to find this bizarre - hence that whole linked article as I understand it. But thanks for your effort.
This, I believe, is the general relativity view of spacetime.
What I like most about this is that it highlights the importance of understanding the domain of a function. The above shows how any object with rest mass has a space velocity domain of [0, c).
People really don't want this to be true so latch on to any wild theory that would seem to bypass this cosmic speed limit, be it wormholes, FTL drives or whatever. Pretty much all of these theories rely on taking an equation with a domain over real numbers and plugging in negative values for things like mass.
Garbage in, garbage out.
I mean if mass can be negative, why limit yourself to real numbers? Why not a complex number for mass?
As to why this is the case and how to reconcile it with a quantized view of spacetime... is beyond my pay grade.
Alice and Bob are in some spaceships by a long racetrack in space. Alice fires a very brief pulse of light down the racetrack, maybe we see the rays that don't go straight through successively illuminate some rings around the track. Alice challenges Bob to race another light pulse, Bob revs his engine.
As the countdown hits zero, Bob accelerates to speed c/2 relative to Alice, then checks the reflected light from these rings only to find out that the light pulse is still traveling at speed c away from him. So he drops a beacon at his current speed then accelerates to speed c/2 relative to that, but no dude: the light is still moving at c away from him. Bob realizes that he can never win, so tries to instead measure the speed of Alice, who he expects to be moving at speed c away from him, only to find that she is instead moving at speed 0.8 c away from him.
Now the question is, how can this be? Consider a much slower spaceship. When Alice fires the light pulse and Bob starts moving forward at a slow speed, Alice sees this bubble of light expanding in kind of a uniform sphere centered on her. (Say it reflects off of space dust instead of a track.) Since they were at the same position when the light Bob also sees an expanding bubble of light, with himself at the center. The weird stuff about time dilation and length contraction does not apply at low speeds, if Bob goes at c/1,000 say, then these are only one part per million.
They both basically agree on how far this bubble of light is from Bob, in the directions perpendicular to the motion. The motion is parallel to the bubble in those directions, and to first order those parallel lines will not get any closer or further away. (This is why I want Bob to move at a slow speed!) They only disagree along the motion. Alice thinks the light is receding from Bob at speed c–v ahead of him, at speed c+v behind him: Bob sees the light recede at speed c in both directions.
So they come back together to repeat the experiment and Alice decides to force the contradiction. Alice puts a clock ticking out every millisecond out at distance 1 light-second, but it will start at the moment she fires the pulse, stopping when the pulse hits it, showing 1000. She puts one of these in the direction Bob will travel, and in the opposite direction. Surely he must agree that the light started from here and that it intersected those two clocks when they both said 1,000.
Bob agrees that the clocks look synced up and films all of this with a high-speed camera to make sure that there is no funny business, and they repeat the experiment.
Right when the light hits, Bob accelerates at his usual 1,000,000 gees for 0.03 s, to get his final speed of c/1,000. (I need to rewrite this to make the numbers more reasonable LOL.)
Here's where something weird happens, and it is entirely contained to those first 30 ticks of both cameras, as Bob looks at them in his high-speed camera footage. Bob corrects for Doppler shift like you do, and agrees that these clocks appear to be ticking during the other 970 ms at one tick per ms, his camera has maybe microsecond resolution and not the nanosecond resolution you need to see time dilation.
But during those first 30 milliseconds when Bob was accelerating, even after correcting for the Doppler shift, his best guess is that Alice artificially slowed down the clock behind him and artificially sped up the clock ahead of him. Because the clock ahead of him definitely ticked 31 times in those 30 ms, while the one behind definitely only ticked 29 times. So Bob says the light did hit these clocks when they said 1000 ms, but the clock ahead of him should have said 999ms at that time, and the light should have gone past it a bit by 1000ms, while the clock behind should have said 1001ms, and the light was actually not yet there at 1000 ms.
This anomalous Doppler shift is proportional to both the distance of the clock you're looking at, and your acceleration. It is also called the relativity of simultaneity, and it is the only new prediction of relativity, in that length contraction and time dilation are second-order consequences of it.
IIRC there are a few things that go faster than speed of light (e.g. universe expanding).
"Spooky action at a distance" is also not known very well. That could also break the speed of causality law. While Bell's theorem hints that this is not the case, there are some exceptions to Bell's theorem.
Right now a lot in physics are just convention like energy conservation and symmetry.
We need another paradigm upgrade to understand these things.
Here: https://phys.org/news/2017-01-violations-energy-early-univer...
Here: https://phys.org/news/2015-02-space-faster.html - we are trying hard to reconcile this and categorize universe expanding as something else (e.g. not a movement that has speed because time itself is a dimension or something). But this is still up for debate, tbh.
Another example was one where we said CP symmetry was true (it was a law like a lot of things in physics) until it was violated by a weak nuclear force experiment.
And now we are holding the fort at CPT symmetry as the law.
In Physics, the evidence of anything is kinda light. A lot of reasonable extrapolations has been made. Still they are extrapolations (e.g. intelligent guess).
Even the big bang itself is just an extrapolation from the "theory" that the universe expanding.
To be fair, it is difficult to find good evidence because we can't dial back time, can't go observe things on Neptune, can't measure gravity at the subatomic scale, and etc. So, we have to work with what we can experimentally observe.
Our tools are getting better, and this is where the physics paradigm shift will come from.
You say like these are 100%. It is just a theory that we currently hold according to the little evidence that we have.
Failing to recognize that is straight up unscientific.
The articles you’ve linked to are interesting and there are clearly many scientific discoveries to be made by studying the early formation of the universe which will test our current models. However I don’t feel like convention is the right word for laws like the conservation of energy, even if there are some difficulties with tying up these theories and new experimental evidence from events at the scale of the Planck length.
Convention to me would mean something that has been accepted just because it’s always been done that way and people didn’t really bother to question why, but I don’t think that’s the case here. But we’re verging on pedantry now so no point going down that route any further.
You're wrong. The Thermodynamic laws are sort of axiomatic, meaning you really can't explain why energy is conserved. It's just experimentally shown to be maybe true, but no one knows why energy is conserved or has actually proved it to be true. It is totally "convention" as you defined it.
The caveat here is that entropy is not axiomatic. Entropy occurs as a consequence of probability. Probability is the real axiomatic assumption of the universe and entropy is a byproduct.
The thermodynamic laws were established before people fully understood the true nature of what was going on with entropy so these laws are sort of a hodge podge of axioms and derived theorems. From a temperature perspective these assumptions work so the laws still have their use. But the laws of thermodynamics aren't some elegant grouping of fundamental laws of the universe. It is a set of rules that are grouped arbitrarily.
>But we’re verging on pedantry now so no point going down that route any further.
I find this attitude rude. You called him a troll than apologized then gave your final answer and dismissed any further discussion as "pedantry." Like wow, you get the last word and shut down anything else he has to say? You were rude to assume he was in jest and you're being rude again by saying any further discussion after your final statement is pedantry.
Either way I disagree with you. It's not pedantry. This discussion is about convention and the conservation of energy. Your statement is wrong.
This means, and I assume, we can also base all of our equations on say "energy is not conserved and always increase by 1 Joule", though the physics equations might be much more complex.
Pro-science folks are too enthusiastic about current science to the point that they become unscientific. Pointing out that these theories/laws/conventions might become invalid in the future is getting downvoted.
Newsflash: physics theories/laws/conventions are getting invalidated all the time.
We can but this won't match with observations. We assume energy is conserved only because our current observations show that it has been conserved thus far.
Referring to the OP article, he's basically writing that the c being the absolute speed limit is not axiomatic. It's not something we just assume to be true. It is a theorem derived from the assumption (aka axiom) that the universe cannot produce inconsistent events.
As a standard example, take a wall at 1m distance and a flashlight. move the light spot at 1 m/s. If you put the wall at 2m, the same spot will now go 2 m/s. If you put it at 300 000 km, the spot will go at 300 000 km/s, slightly over light speed.
The problem is more one of information: For any action you take, no consequence can happen outside your light cone. All information you generate travels at c at max.
None of the examples you gave violates this: Even if the universe expands at more than c, nothing you do will have influence on things too far from you.
And what you point out is actually the speed limit of causality, instead of light. It just happens that light travel really fast.
Though the article wants to discuss the speed of light as you mentioned, so I focused on speed of light.
It doesn't consist of the same photons; the spot in the "new" position consists of photons which have been traveling in a straight line from your flash light at (assuming vacuum) a constant rate of C (and then reflected back to reach your eye again, also at a constant rate of C); they haven't traveled to or from the previous "spot" position at all, much less exceeded the speed of light at any point in the process of reaching the new position.
Right?
AFAIK Expansion of the universe is comparable. It pushes things away not by speed but by putting extra 'new' space between things.
Your sibling comment makes a variant of the same point:c is the maximal speed of information or causality. Light in a vacuum is just one of the things capable of reaching it.
I'v heard someone saying space is a big ball and outside of it is nothing. I imagine nothing as a black space but that actually is something. So there is something after all. And however weird or normal these other places are, it goes like this infinitely.
OK. How?