Do we really travel through time with the speed of light?
backreaction.blogspot.com
backreaction.blogspot.com
One of the deep insights of special relativity is that these scalar and vector quantities are actually unified into a single, new entity called a "four-vector". Each four-vector has three spatial components and one temporal component. So in the two lists I wrote above, each scalar quantity gets paired with the corresponding vector quantity: time & position; energy & momentum; power & force; the electric & magnetic potentials. In Newtonian physics a rotation in three-dimensional space will transform one component of your position vector into another (say, some of your x-component becomes a bit of y-component). In special relativity observers moving at different velocities are related by a similar kind of transformation of their four-vectors --- a bit of the time component mixes with the spatial component and vice versa.
But what happens if you do this with velocity? Velocity is a vector. It's corresponding temporal quantity is a bit weird: change in time per change in time. But it's a little more subtle than that, because it's actually the change in coordinate time per change in proper time. Basically this is the ratio between how fast you observe a clock tick in an observer's reference frame relative to how fast they see it tick within that reference frame.
But the really weird thing about this particular four-vector is that it always has a magnitude of exactly the speed of light. No matter how fast you go, the magnitude of your four-velocity does not actually get larger. All you do by going faster is just mix some of the time component of your four-velocity into the spatial components. (This is why the clocks of moving observers tick more slowly.) And when you slow down, you just mix some of the spatial components into the temporal component. And when you're at rest the spatial components are all at zero, so the only component of your four-velocity is in the temporal direction. So at rest your four-velocity points directly in the future with a magnitude equal to the speed of light. This is what is meant by the statement that we travel through time at the speed of light.
This isn't weird. The magnitude of any four-vector is frame invariant in relativity. Lorentz transformations in relativity are the analogue of rotations in ordinary Euclidean space, and have the same property of preserving the magnitudes of vectors.
> All you do by going faster is just mix some of the time component of your four-velocity into the spatial components.
I think this is a misleading way of putting it. In a frame in which you are moving, the time component of your four-velocity is larger than it is in your rest frame, not smaller. So it's not the case that some of the time component in your rest frame got "moved" to a space component.
What this means is that the length of a relativistic four-vector [ct, x, y, z] is sqrt((ct)^2 - (x^2 + y^2 + z^2)).
It is not the same as the Euclidian magnitude, i.e. NOT sqrt((ct)^2 + x^2 + y^2 + z^2)
The article does mention this, although with slightly confusing wording, but it should be emphasized that Lorentz invariant quantities need to be computed with the Minkowski metric.
Now, the same path is described by many different parameterizations. For example, if we pick q(r) = p(2r) that's the same path. The point varies twice as fast with r, but that has no physical meaning. The total path that is traced out in spacetime is still the same path. That is, the set {p(r) | r in [-∞,∞]} is the same as the set {q(r) | r in [-∞,∞]}, and it is only this set that has physical meaning.
In fact, we can also pick q(r) = p(r^3 + r) or some other parameter transformation.
We might look at the vector p'(r) tangent to the path. The length of this vector depends on the parameterization, but its direction doesn't. So p'(r)/|p'(r)| is a true physical property of the path, but the length |p'(r)| is just an artefact of the parameterization that we chose to describe the path.
In order to make the parameterization somewhat more canonical, we usually pick a parameterization where |p'(r)| = c. As it happens, the four velocity is defined to be p'(r) given this choice of parameterization.
So the length of the four velocity is c simply by definition. This statement has no physical meaning. The statement "we travel through time with the speed of light" is uninteresting. It tells you nothing about physics. It only tells you something about the conventions we use when we describe paths through spacetime. We could very well have picked the convention |p'(r)| = c/2, and then we'd have the statement "we travel through time with half the speed of light", or even |p'(r)| = 2c, and then we'd "travel through time with double the speed of light".
Given any path through spacetime whatsoever, we can pick a parameterization such that it travels through spacetime at the speed of light. So the condition that something travels through spacetime with the speed of light places no constraints on the path that it takes. The statement "we travel through spacetime with the speed of light" makes it sound like there are paths that do travel through spacetime with the speed of light, and there are paths that do not travel through spacetime with the speed of light, and physical particles go along paths of the first kind. This is wrong. There are no paths that do not travel through spacetime at the speed of light, because whether or not it does is a property of the parameterization that we choose to describe the path, not a property of the path itself.
Four-velocity is change of spatio-temporal position (Δx,Δt) in an inertial frame per unit of time Δτ measured by the object in motion. For a concrete example, think a race track with distance markers accompanied by (synchronized) stationary clocks, and a vehicle carrying its own clock. Three-velocity will be given by Δx/Δt (the distance along the track divided by the time on the stationary clock), whereas the spatial component of four-velocity will be given by Δx/Δτ (the distance along the track divided by the time on the vehicle's clock). The temporal component of four-velocity will be c·Δt/Δτ, ie proportional to the clock ratio.
Turns out no matter the speed of the vehicle, it will always hold that
(c·Δt/Δτ)² - (Δx/Δτ)² = c²
However, once we've baked this relation into the geometry of spacetime, we can of course take the more abstract perspective described above and think about reparametrization-invariant dynamics, with choice of eigentime as parameter an insignificant way to fix an arbitrary gauge.
If you have a clock moving through spacetime along some path p(r), put tickmarks at regular intervals [1] of its arc length ∫|p'(r)|dr. Those tickmarks indicate when the clock ticks.
[1] e.g. choosing the length of an interval by matching it to a one second tick of a stationary reference clock.
In differential geometry, we traditionally parametrize curves by a parameter "t" and think of it as "time", so the parametrization allows us to "walk along" a curve. This is very intuitive geometrically of course.
But in relativity, we also have a "time" coordinate (or at least a timelike unit-length tangent vectors), which then completely oposes this geometric intuition about curves.
Of course now physicists decide to rename well-established concepts and start calling "arc length parametrization" by "proper time parametrization", which makes it sound like it is something special, while it, as far as I can tell, has no actual physical meaning.
Some vectors can vary in magnitude with time, yes. But rotating your coordinate system does not change the magnitude of any vector in Euclidean space. A Lorentz transformation is the spacetime analogue of rotating your coordinate system, and similarly does not change the magnitude of any vector.
The weird part isn't that two observers agree on the vector magnitude. The weird part is that one observer calculates the same value for any two objects. Frame-invariance isn't the relevant property.
That's not weird either, because the value being calculated has all object-specific information removed. See my response to andi999 downthread regarding rest mass.
But moreover, the rest mass isn't the issue here. Momentum in classical mechanics also takes mass into account but doesn't have the "weird" property that two objects of the same rest mass always have the same momentum magnitude.
If you think for stationary examples it just means that the eigenzeit has a different pace, so two clocks next to each other going at a different pace. But this is ruled out by another definition, such that clocks are references by light clocks. And now it is also clear why this invariance is c.
It's a unit vector, and physicists working with relativity habitually set C=1 to make the equations simpler. That being said, it isn't really a vector -- it's just a direction. The "equal to C" bit is a mathematical artifact of both vectors being normalized.
Because this 4-vector removes the factor of rest mass, which distinguishes objects. Putting back the rest mass converts 4-velocity to 4-momentum, which does not have the same magnitude for all objects--the magnitude is the rest mass.
The interesting thing was that I had this feeling that the other elements of the vectors were all also conveyor belts, moving in a single direction. X, Y, Z(and an infinite of other more subtle scalars) were each their own belts, with entities of a very different hyperdimensional sort riding along them. Essentially, they were each moving at a constant non-changing rate along a single dimension(X, Y, or Z) and because of this, they used time as we do a spatial dimension.
Think about it like this.
Imagine that a trillion years ago you were stationary, and time didn't exist. SUDDENLY you and all the stuff nearby you got pushed in space along the X axis at a speed of 100000000000 km/hr.
You kept moving along the X axis at a relatively constant rate with the stuff around you, such that the X-axis became a constant for you, while the other spatial dimensions were your degrees of freedom.
In this scenario, time is the X axis for you.
I noticed that there were entities moving perpendicular to our concept of time, treating our X-axis as their conveyor belt moving them along at a constant rate.
All a drug trip of course, and I don't know much about physics, however, this experience has shaped how I concieve of time and space.
Those entities exist: We call them photons (and a few other things). Photons move through space at a constant rate, c, and their clocks never move. If a photon were conscious it might ask "What is this time you speak of?"
It gets weirder: Because photons don't experience time they can't "remember" being in Place A "before" they were in Place B, so they might also ask "What is this space you speak of?" Photons are always everywhere they need to be, from their point of view.
I recommend watching it!
For what it's worth, time is distinguished in physics. It isn't just "another dimension" that "happens" to be used as time, but if you could just twist correctly it would become a spatial dimension. It is truly a "time dimension". The simplest way of looking at it is in the Minkowski metric, where distance is SqRt(x^2 + y^2 + z^2 - t^2), note the minus sign on the "t" which distinguishes it.
If you're really up for a solid math-based mind-screw, Greg Egan worked out the shape of physics in a universe that works on essentially Einsteinian relativity, but with two spatial dimensions and two temporal dimensions: https://www.gregegan.net/DICHRONAUTS/DICHRONAUTS.html It turns out that A: sensible things can be said about this and B: it looks nothing like what I expected two temporal dimensions to look.
(And if that's not enough, he's also got a universe of four spatial dimensions: https://www.gregegan.net/ORTHOGONAL/ORTHOGONAL.html)
I am looking forward to this next Christopher Nolan movie.
That is, I can imagine time as a single axis so that you could go back and forth. (Ooops, about to be eaten by a ghost, let's rewind.) But I can't imagine what it means to go northwest in time.
Disclaimer: my ideas come before having done my homework on the link above, so I need to read Greg Egan's stuff really. He's such a wonderful person and I need to dedicate more brainpower to his work.
In Pacman terms, I guess you could program it so that going up or down with the second joystick changes the terms of the game slightly. Maybe the maze configuration changes or in one timeline the ghosts bounce off you when you run into them but the walls themselves zap you.
In a more nuanced conception of the timeline axis, I suppose y-points would have to be branched or braided off x-points. Maybe that's where the third dimension comes in.
I'm sure Egan has worked it out with more rigor. I checked out the link for one of his books above but I admit I blanched when I got to the synopsis:
Seth is a surveyor, along with his friend Theo, a leech-like creature running through his skull who tells Seth what lies to his left and right.
I've got enough on my plate at the moment with the dissolution of civil society. I'm not sure I'm ready to entertain leech-like symbionts confronting the disintegration of time itself.
Or be under gravity.
Saw this in a salvia trip once
Edit: Why the downvotes? This was clearly supposed to be a joke.
> One of the deep insights of special relativity is that these scalar and vector quantities are actually unified into a single, new entity called a "four-vector"
On which basis was this pairing between position and time "decided"?
> But the really weird thing about this particular four-vector is that it always has a magnitude of exactly the speed of light
Why is that? Is it by definition?
> it's actually the change in coordinate time per change in proper time
How does this translate to what we call "time" in our daily lives?
Hollywood movies are not how physics works. The plucky protagonist can never look down at their hand and see a stopwatch run slower or faster! There is no such thing. If some sort of science-fiction field existed that would affect a clock, it would affect the protagonist also.
If the clock runs at half speed, your brain runs at half speed, so you see it ticking forward at twice the rate, and 2.0 * 0.5 = 1.
Now, of course, I tell a small lie: There can be differences in the tick rate over some distance. But these differences are necessarily small. Big differences in the rate of temporal flow create gravity, as per Einstein's General Relativity. To get an observable difference in time flow over the space of, say, a meter would require a fantastically huge gravitational field that would instantly crush the poor scientists into a pancake.
Conversely, in the gentle field of Earth's gravitational field, if you hold an atomic clock in your hand a meter from you head, and an atomic clock in line with your head, then yes, you can see a tiny difference in the tick rates, on the order of nanoseconds per century or somesuch (I'm too lazy to work it out).
However, as the distance decreases between the clock and the observer, the difference gets smaller. Extrapolating down to atoms and the like the conclusion is inevitable: time locally always ticks forward at one second per second.
This is why GPS satellites need time correction. GPS satellites contain atomic clocks, and they are further from the center of the Earth than you are. Therefore they experience slightly less gravity than you do. Therefore their clocks run slightly faster than atomic clocks on Earth's surface. That's the General Relativity correction.
But GPS satellites also move a lot faster than you do, because they are in orbit. That makes their clocks run slower than clocks on the ground. That's the Special Relativity correction.
Both corrections have different signs but they do not cancel each other out.
Consider changes in gravity affect cognition.
Likewise, if the brain has any quantum mechanisms, then that 1.0 might not be exactly 1.0.
That is literally what it does. It slows down cognition. In the exact same way that it slows down clocks. The "clock in your brain" and the "watch in your hand" are all operating on the same physical and chemical principles. It's all just atoms and electromagnetic interactions at the lowest levels.
> Likewise, if the brain has any quantum mechanisms
Again, this is a pop-science misunderstanding of all of physics, not just Quantum Mechanics (QM).
The rules of QM either apply to everything or nothing. The laws of the universe do not begin or end at the edge of the laboratory bench top. Similarly, there are no special rules that apply to just the human brain.
The rules that govern galaxies, particle beams, atomic clocks, mechanical watches, and human observers are the same. They all tick along at the same rate. One second per second, locally at least.
Well, for now we don't really know how the rules of QM apply to macroscopic objects. The exact physical interpretation of wave-function collapse (if any) is still a matter of speculation, with all options still being on the table - maybe there is no collapse (e.g. many worlds theory), maybe there exists a collapse when interacting with large enough systems (measurement - the Copenhagen interpretation), maybe collapse is a physical process that happens at precise scales (Roger Penrose seems to believe something like this), maybe the wave function is a physical wave (pilot wave theory) and there is no collapse in another way.
Sure we do, "we" just refuse to acknowledge this, keeping a 100 year old debate alive for no good reason.
Macroscopic objects follow microscopic rules. That's that. There's no further debate. There can be none.
I can't even begin to describe how absurd it is to argue anything else. It's like... saying with a straight face that software doesn't "really" follow the rules of boolean algebra if it has enough lines of code. That somehow once a program gets "big enough", it can transcend truth tables and somehow go analog or something.
It's like a mathematician saying that really big equations, the kind that span several pages stop following the rules of algebra.
Get it? It's just... insane. The rules of the universe are the rules for all things in it. They apply to everything, at all scales, at all times.
If they don't, they're not the rules!
QM and GR are approximations. The real rules are unknown to us. It just happens that "in the small", QM seems to be a good approximation that is consistent with experimental results. And "in the large" the same holds for GR. Neither of them works for everything though.
That just means we need to find a better approximation. That's not insane.
Bits are not an approximation of software "in the small". They are the real building block. We know that because we made them. First made them, then observed how they behave. But QM is a theory created by first observing. Physics is a natural science trying to understand what we observe. Math and CS are not. The objects they care about are conceived by us and observed second.
This is nowhere near as certain as you make it out to be. Take Conway's Life. With 4 simple "rules of the universe", you can create a series which to the best of our knowledge cannot be predicted from those rules. Clearly this series is a "thing" within the simulated universe, and clearly it emerges from the universal rules, but the rules don't give us any insight about it! The only known way to "predict" it is to let it run: in other words, it's irreducibly complex.
Causality can look different at different scales. It's well established that simple low-level rules can generate extreme if not irreducible complexity. This doesn't mean the bottom-level rules don't apply everywhere; it just means their descriptive/predictive utility is not necessarily preserved when you zoom out. Is a prime-finding algorithm best described by the mechanism of the computational substrate? Any number of substrates could suffice. We can best predict its output by thinking at a higher level of abstraction.
You can absolutely reversibly compute conways game of life state, and you can compute it forward as well (after all, it is a game). That's prediction.
> It's well established that simple low-level rules can generate [...] irreducible complexity.
Simple rules can create a very complex emergent system, but that doesn't mean it cannot still be reduced to it's component rules. That's what makes them rules and not just guidelines.
Notice I said irreducible, not irreversible. Yes, you can reverse the computation; but there's no known way to "shortcut" the forward process to predict the outcome of the series I mentioned any faster than simply letting it run. Letting it run is not prediction in the sense I mean here. By "predict" I mean foretell in advance what the system will do without needing to let it run.
> Simple rules can create a very complex emergent system, but that doesn't mean it cannot still be reduced to it's component rules. That's what makes them rules and not just guidelines.
I agree, with a minor caveat about language: you can describe a system which may display complex emergent behavior in terms of its underlying rules, but doing so is not guaranteed to give you useful information about (i.e., allow you to "predict", in the sense described above) the emergent behaviors. In contexts like these, to "reduce" typically means to describe in terms of a lower-level formalism while preserving predictive ability, AFAIK. In other words, the low-level formalism provides full information about the behavior of the entire system, such that you don't need to observe the system to know what it will do. In the Life example this is not the case.
Incidentally, Greg Egan wrote 2 short stories on basically that premise: Luminous and Dark Integers.
Furthermore, leaving behind direct observations which could perhaps be waved away with discussions of probabilities, we have one big problem: there is no gravity in QM and we have no idea how to account for it or curved spacetime in QM.
So for now, we have one working model for the macroscopic world (general relativity) and one for the microscopic world (QM), but the two are mathematically incompatible, they can't be simultaneously true, and we have not yet found an experiment which contradicts either of them.
> there is no gravity in QM
The weakness(es) of any one particular theory doesn't in an way disprove that macroscopic objects follow the same rules that microscopic objects do.
Just because MySQL is bad doesn't mean that the relational model is false, or that databases are pointless.
Just because the current theories of GR and QM aren't easily extended to all regimes doesn't meant that there is some sort of hard boundary where the rules change. Our theories of the world don't affect how it works. The boundaries of our theories are not boundaries of the world.
You can't fall of the edge of the world because the maps only go so far...
Yes, absolutely agreed. My point was simply that we don't know how QM extends to macroscopic objects, not that there must be some hard boundary (though we can't exclude the possibility that there exists some hard boundary at some level of energy, just as we know that the Standard Model doesn't describe matter at certain high energies).
Until we have some unification of GR and QM, we can't say for sure that QM describes the macroscopic world, just as we can't say that GR describes the behaviors of particles. Most likely we will at some point find such a model, and find out exactly how QM applies to large systems - perhaps with some limits to uncertainty, similarly to how c acts as a limit to speeds.
Sure it does - gravitational lensing, etc.
As a programmer, I wholly endorse this notion.
It literally does sometimes, just ask anyone that's programmed software designed to be resistant to bit flips caused by cosmic radiation.
And we do not know what those rules are. We have 2 widely accepted guesses: quantum physics and general relativity that have each been incredibly succesful in their predictive power.
The problem is, we do not know how to make these theories consistent with each other. Either relativity is wrong on quantum scales, or QM is wrong on relatavistic scales. Probably both.
Yes, but I'm talking actual changes in the cognitive output. Look at all the physiological changes astronauts undergo. Those changes extend to their cognition, even if the effect of general relativity is small.
>Again, this is a pop-science misunderstanding of all of physics, not just Quantum Mechanics (QM).
There's an entire field called quantum biology. I'm not advocating the brain has quantum magic (in fact last I checked the theory was pretty much completely discounted). Rather, on the off-chance that it does, your example breaks down via way of the elements that comprise the brain's computation not being necessarily subject to the same relativistic effects due to potentially vast distances between some of those elements.
Or, without QM at all, consider that there's an extremely minute difference in relativistic effects even across the few inches that span your skull. By that alone, 1.0 is not 1.0.
Not trying to be pedantic here, merely food for thought.
The only really interesting QM "stuff" that seems to be going on is that some enzymes have incredibly high efficiencies, even when bathed in dilute reactants. There are hints that this may be some sort of inherently quantum mechanical process that cannot be understood classically. But this is a tenuous hypothesis at best, there's no hard evidence yet, let alone a good theory.
If you made the difference in gravity more extreme the difference in measurement would be trivial to notice, but we don't have a way to achieve that in practice.
[1] because light is massless, so in a vacuum there is nothing slowing it down
Three partially correct answers of the same question:
1) Nobody decided it. It is just how the universe is.
2) You have the formulas where the space-something appear, and you randomly try propose to replace something with things you know, like mass, time, color, ... It is actually more easy, because using the units you know that something must be measured in seconds, so it discards a lot of possibilities.
3) You have the "classic" formulas where space appears https://en.wikipedia.org/wiki/Lorentz_transformation that were actually discovered almost 20 years before the work of Einstein. And you rewrite them in the equivalent of the "vectorial" notation. In the usual space it is like replacing (x,y,z) with a big X and never looking inside X. If you try it, the only way you can success is if you group (ct,x,y,z).
The trick is to look carefully at the calculation and try to think what you can arrange it to be able to rewrite the calculation in the correct form.
For example with momentum, you look carefully and realize you must add energy as the fourth component.
If you choose to group space and time, and you choose to group momentum and energy, then you must use the same choose in all the formulas. You can not choose a different grouping for each formula.
But sometimes it is not so easy. With speed you realize that it is too bad to be fixed, and you must define another speed-like-thing and then give another formula that transform the "real speed that you measure in a lab" and the "abstract speed-like-thing that you use in the calculation".
With the electric field, ... well you can't put it in a 4-vector, you must use something more weird that is a 4x4-matrix.
It's also why I'm basically convinced that any sort of FTL (including wormholes and compressing space), time travel or cheating causality is essentially impossible, no matter what results you contrive by putting things like negative mass and/or energy into various equations.
How this all gets reconciled with quantum mechanics is another matter. Part of me wonders if the problem isn't just that space and time are ultimately discrete (at the Planck unit level) and our equations describing it are continuous. But again, I'm no physicist.
I now have this (probably wildly incorrect, total layman here) vision of the time dimension of velocity being "a normal" simultaneously to all the spatial dimensions and acceleration as rotation of the four-vector away from the time axis...
sorry for any terminology errors.
> But the really weird thing about this particular four-vector is that it always has a magnitude of exactly the speed of light. No matter how fast you go, the magnitude of your four-velocity does not actually get larger. All you do by going faster is just mix some of the time component of your four-velocity into the spatial components.
This seems strongly to be confusing the map and the territory. The maths is a model, the description of vectors has not link to reality but happens to model reality in some useful way (reality and the model correspond to some useful approximation), but it isn't reality.
so
> at rest your four-velocity points directly in the future with a magnitude equal to the speed of light
may just be an artefact of the maths. IDK though. (and no offence intended, just my POV)
It's magnitude is called 'mass' (or 'rest mass'/'invariant mass' if you want to differentiate it from the concept of 'relativistic mass', which probably should be retired).
This means we have
four-momentum = mass * four-velocity
three-momentum = gamma * mass * three-velocityMy layman's research suggest these are, respectively, "electric charge" and "current"?
This was a gigantic problem, an experiment contradicting one of the most fundamental laws of nature as we knew them at the time - Galileo Galilei's principle of relativity.
Note that this observation has nothing to do with our eyes's ability to perceive light. The same observation will not happen with sound waves; and it will hold even for frequencies of light that we can't directly observe with our bodies, such as radio waves.
As others note, it was later discovered that this is not a special property of light itself. It is in fact a special property of the universe, and it applies to any particle without mass; the photon happens to be the only massless particle that we can directly observe, so it was the one which gave the name to the physical quantity.
That's wrong. Simultaneity is ill-defined in relativity.
The correct example is, "if Alice fires a light beam at you from a moving train and Bob fires a light beam from you from the platform, you will measure the Alice photons as going equally fast as the Bob photons.
However, you're right, your formulation is more precise, and actually possible to measure.
Another way to put it is that when you’re in a moving bus and you throw a ball towards the front of the bus, the ball is moving the speed you threw it plus the speed of the bus, but, when you shine a light, the photons from the light are moving the same speed as someone off the bus! That seems super weird.
Every other massless particle moves at the same speed. “Sound” is not a massless particle, it’s propagation of the compression of matter, so therefore moves much, much slower and would not replace c. It has nothing to do with what we can observe and rather to do with its properties. Personally, I find referring it to as “the speed of light” is confusing since it rarely has anything to do with light/photons other than that light happens to move at that speed.
Said like that, it reeeeeaaallly makes you think "we live in a simulation", doesn't it ^^ ?
Hell, why not take it a step further and say that the simulation is relative to an observer (which can be an inanimate thing, of course) as an optimisation because why bother simulating what isn’t seen or interacted with by an observer?
Light (in a vacuum) goes as fast as the speed of cause and effect. And it just so happens that the speed of light is pretty easy to measure (as compared to other possible things).
So if we were all blind, we would still be affected by this speed.
The speed of sound is the speed of air-molecules bouncing into each other (~300m/s). Since air-molecules have matter, they dont travel at the speed of light.
At least this is what I was taught in school many years ago...
The experimental "proof" of the frame-independence comes from the michelson morley experiment. (Scare-quotes, because you can't prove things in physics, only disprove)
https://www.google.com/amp/s/www.sciencealert.com/faster-tha...
The speed of light is variable, the speed of causality isn't.
It's amazing to think how the universe is ruled by such minute details.
Pun unintended?
For me reading this book, the process of understanding what it is that they are understanding ends up conveying very little useful information of how humans understand physics -- a bizarre and thought-provoking experience.
Reading his books make me feel stupid and clever at the same time.
"Twice, I have read books on relativity by PhDs who said that we travel through time at the speed of light, but I can’t find those books, and I haven’t seen it written anywhere else. Can you let me know if this is right or if this is utter nonsense."
I wonder, was this question asked by the Ed Catmull (https://en.wikipedia.org/wiki/Edwin_Catmull)?
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Edit: to make this comment less useless, I'd like to point any laypeople like myself who are interested in the nature of the universe to the PBS Space Time show/YouTube channel: https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g
I'm pretty sure they have videos related to this question.
I'm in awe of his contributions to both computer graphics and Pixar, and I really liked his management book, even if he definitely did some sketchy stuff with wage fixing.
In case anyone was having trouble parsing this, that's:
√(-(∆x² + ∆y² + ∆z²) + c²∆t²)
Or:
√(c²∆t² - ∆x² - ∆y² - ∆z²)
To me time is the rate at which things change or its just a measure of change. Everything is changing state, electrons are moving, bodies are moving from one point to another and also the clock moves the same way.
The diagrams that explain gravity show 'space' as a 2d plane with planets weighing it down making other small objects come toward it. That's a misleading representation I think in a sense that it depends on weight/gravity. I understand space as a sponge. Heavy objects with huge mass are like a squeezed lump in that sponge effecting space around it. Larger the mass, more it squeezes, more it effects what's around it.
When an object moves through space, it effects time as well i.e. rate at which change happens within that object. At very fast speeds, speed of light, it's already moving through space changing space, change within that object is reduced to nothing making time move slow for it.
That all I think it is.
This example would never work in zero gravity.
Someone gave this sponge visual on stackexchange I think and since then it made so much sense. Also, this makes time travel totally senseless.
You can not travel back in time without reversing all input you ever received from external factors. Only thing we can probably do is stop or slow down time for something.
I ask because I cannot view the video for some reason. The embedded video errors, and so does the direct YouTube video. Which means this post cannot function as standalone content, by the author's own admission.
Cynical me things this is a ploy to drive traffic to a YouTube channel. Non-cynical me hopes the equations in the video include snazzy graphics and animations a la 3b1b. Either way it left me frustrated.
AIUI the equations describe a path through spacetime. There is no "speed" or "movement" along this path, or at least none with an actual physical interpretation. The path simply has a certain shape. The equations define the path as a parametric function, and you could in principle calculate the change in 4D spacetime coordinates with respect to the change in that parameter, but it would have no physical meaning. To keep things simple, in a canonical representation of the path this ratio (the "speed" through spacetime with respect to the arbitrary scalar parameter—though "speed" is not really the right term since the parameter does not represent time) is held constant and defined as the speed of light.
To put things in more familiar (or at least less spacetime-y) terms, these very different parametric equations both describe a 2D unit circle with respect to an arbitrary parameter r with range (-∞, ∞):
p(r) = [cos(r), sin(r)]
q(r) = [abs(2 - t) - 1, ((2 - t) / abs(2 - t)) * sqrt(1 - (abs(2 - t) - 1)**2)]
Especially when looking at them with the lens of General Relativity.
Which proves Einstein's predictions based on General Theory Of Relativity.
This is being considered when e.g. sending probes to Mars.
[0]: https://www.nist.gov/news-events/news/2010/09/nist-pair-alum...
https://en.m.wikipedia.org/wiki/Hafele–Keating_experiment
> The Hafele–Keating experiment was a test of the theory of relativity. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with the predictions of special and general relativity.
——
Also, GPS wouldn’t work without understanding relativity because the clocks in the satellites move faster (I think?) than the ones here on Earth.
Can't find the reference now but even moving the clock a few meters is a measurable drift.
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....
That always leads me to this (probably) crazy rabbit hole I can never quite articulate or resolve that no doubt countless others have wondered about - what if it's not moving at all? What if time is 'solid'?
I guess the best way to explain what I mean here is like a flip book. On each page there is a drawing, if you look at one page you just see a static drawing. If you look at the book, it's just a static book. But if you flip through the pages, it animates and appears to be moving.
What if our experience of time is just like this 'flip book' experience, where in actuality, our experience of time is that we are moving through it, but time is not moving at all?
I'd love to know if there have been any other studies or discussions about this? Because if time is a constant, it could also be 0, no?
If you switch to viewing the universe as purely a mathematical construct, all these questions will fall away. :) The notion of ontologically privileged time or even space is based on us elevating our model of the universe into objective fact for no reason. Anything that the brain would notice even in a timeless, purely mathematical universe is thus an unneeded addition purely on Occam grounds.
For instance, we may ask the question: "would my brain, if you computed its output given its inputs, output data like 'I exist, I am conscious, I notice the flow of time passing, the present moment is ontologically privileged to me'? It seems obvious that it would; that is, the mathematical answer to the question of "what does my brain output" is that sentence. But a mathematical question cannot be ontologically privileged. We see thus that these notions of ours are necessarily vacuous; any conception of 'time', 'now' and 'me' must be relative, depending purely on the surrounding mathematical/causal structure, or else not exist at all - since even if they did exist, our noticing them is not dependent on their existence, and thus Occam bids us to discard them.
The idea is, maybe everything in the universe is just 1 electron looping through 4D space over and over, interacting with itself at various points of the loop. Comes about from the observation that antimatter can be described perfectly as just regular matter moving backwards in time.
BTW, I think Vonnegut had this right in 1969:
"I am a Tralfamadorian, seeing all time as you might see a stretch of the Rocky Mountains. All time is all time. It does not change. It does not lend itself to warnings or explanations. It simply is. Take it moment by moment, and you will find that we are all, as I’ve said before, bugs in amber."
You can adopt a perspective where time is solid. But then the question is, why are particles arranged in this solid time exacly as if they were moving in a real time.
As a metaphor, imagine that you are a god, and you are trying to create a 4D universe with solid time, where the same laws of physics (rephrased in the solid-time language) apply. How would you do it? Ultimately, you would have to create the earlier parts of the solid time first, then the following parts of the solid time, etc, until the end of the universe. It wouldn't work any other way, essentially because of chaos theory; the state at T+1 depends on the details of state at T, so you would have to create the T slice of solid time first, and the T+1 slice later, depending on it.
If you remove the time from the universe naively, you are sweeping it under the rug... into the process that created the universe. But isn't this just adding an extra complexity? If the "process that created the universe" can have real time, why not the universe itself? Isn't this just an extra epicycle?
The only way out is if you used your godlike powers to create all possible states of universe simultaneously -- not just our universe, but literally every possible combination of particles -- and then connect them causally in a way that respects the laws of physics. You don't have to create time T first and time T+1 later, if you create all possible realities first, and then just draw an arrow from each T into the corresponding T+1.
So, instead of the frozen version of our universe (where time = linear movement from the beginning of the movie towards its end), you get a frozen version of everything possible (where time = tracing a path across the everything, following the local currents of causality).
The advantage of the latter model is that you get the parallel universe for free; it just means that local causality is not a single arrow pointing from the current place, but rather a collection of arrows.
But you still need to think (in both models) how to make them compatible with known quantum physics. How to model quantum interference, entanglement, etc.
Part of timless physics is that there is no privileged moment in time.
The laws of physics allow god to start at any point in the configuration space of the universe and evolve toward any direction.
This isn't prevented by chaos theory. Chaos theory happens regardless of where you start your t=0. The laws of physics are 100% symmetric (CPT symmetry).
This does not mean we will necessarily recurr either. The laws of physics are symmetric, but due to the Past Hypothesis (prior condition of the universe was very low entropy), we experience an emmergent direction in time, and if the universe is infinite and unbounded it seems like it wont recurr.
My standard model of “Thing going really fast” has been some nuclear powered craft that just shoots out into the abyss, but after a bit of googling apparently our fastest craft is/will be Juno, which is staying within the solar system. This will apparently go 250,000km/hr or 0.000232c partially based on Jupiter’s gravity.
It is interesting to think about just “living fast”, where our lives are still only ~80 years, but the time elapsed on earth is on the order of many multiples of that. We would exist in a way that we orbit the earth at a much larger fraction of light speed, while still allowing us to interact with the earth’s resources on normal time scales. Imagine taking a vacation back to earth for a year, but popping back to the space station where it has only been a few hours.
Maybe I’ll write a novel on that or find one already written, there seems to be a lot of depth in exploring that.
[0] https://www.missionjuno.swri.edu/earth-flyby/story/how-fast-...
Hmm, this hasn't really fully clicked with me yet (so take what I am saying with a grain of salt, I'd be glad if anyone could clarify/prove me wrong), but speed is relative.
If your station moves fast from the perspective of earth, earth moves fast from the perspective of the station. So, from the perspective of earth, time moves slower on the station, and from the perspective of the station, time moves slower on earth.
If you were to travel back and forth, that would even out (something about having to accelerate in one direction, then another). There is no absolute time reference in the universe.
That can work, however, if you spend some time inside a strong gravity field.
The time delta math (Sqrt(1-v^2/c^2)) puts us at 3 earth days per two space days.
The vacationing was more cheeky, in that in this case a 2 week vacation would appear 3 weeks on earth. If there would be some way to quickly switch between modes than 1 week, you would spend more self-referential time doing something than your home clock would count.
A couple of high school sweethearts promise they'll love each other forever, but there's a war on and the boy quickly gets recruited to fight at the edge of the solar system (I remember a scene where they stand at some railroad tracks and watch a monumental silver space craft fly overhead, one of the battle cruisers), but before he gets there the boy and girl continue their relationship as pen pals, at first sending messages back and forth from mars base (45 minute delay, but not aging any faster), but as the boy travels closer to the front of the war, his velocity increases and he ages less than the girl waiting for him back on earth, and of course more time passes by between messages.
Eventually it's the boys 20something birthday and he still has love for the girl, while the girl has already grown up and moved on with her life.
Edit: hah, figures my bias would mix the genders up, the girl went off to fight the war.
If you mean the actual Earth and a free-fall orbit, the orbital speed of something in low earth orbit, like the ISS, about 8 km/sec, is as fast as anything can orbit the earth.
To get really fast orbital speeds (as in, speeds that are any significant fraction of the speed of light), you need objects much, much more compact than the Earth, objects whose actual size is not that much larger than the size of a black hole with the same mass. The only non-black hole objects we know of that are anywhere close to that compact are neutron stars.
I was thinking about this last night. How does this fit into GR? I understand how it fits into SR, but in GR space is just curved. Unlike velocity time dilation, under Einstein space isn't moving. In GR it's the curve that's "equal" to gamma, the dilation factor in SR.
This is evident where escape velocity (root((2GM)/r)) replaces the (v^2) term in the Lorentz factor to give gravitational time dilation in the Schwarzschild solution (t' = t(root(1-(2GM)/(rc^2))).
Mind you, I've always thought everything is moving at c through spacetime, but I understood that from SR. I just don't see how it fits with GR.
Not really. The instant you move in space, you also move in time, and since everything is moving and there is no fixed frame of reference, technically you can never move back to the same spot where you started.
So even though it might appear to us, at our perception scale, that we can move back and forth in space, in reality whenever we move, space changes and so it's just like moving in time, there is no going back.
I would rather spend a bit of time formalizing that classical spacetime, and then get into how special relativity is different. Much more apples to apples.
But what if you fly against the turning of the earth. That way the clock on the earth goes slower, and so when arriving back, the clock on earth is behind?
Every time I look this up, I never seem to be able to wrap my head around that.
EDIT: Found the answer to my question: https://en.wikipedia.org/wiki/Time_dilation#Reciprocity . Basically when you accelerate and decelerate, your time gets influenced, and so the person experiencing the most acceleration will have the slower time.
I really dislike it when explanations about reality become explanations about a model of reality.
Can the original question be answered without assuming some model is the perfect reflection of reality, or just without using the model?
In a similar way, the ratio π is the mathematical description (or model, if you like) of a circle's circumference relative to its diameter. I'm not sure how to describe this relationship without invoking the mathematical description of said relationship.
No, not neccessarily. It's purpose is to make predictions. It need not be an accurate description of reality. We know this from our own internal model of reality and from classical mechanics, neither of which seem to be accurate descriptions of reality but both of which are very good models for predicting outcomes.
I happen to disagree with ta1234567890 too, and think the parent is correct, and ta1234567890's comment is non-sensical.
He says:
"I really dislike it when explanations about reality become explanations about a model of reality. Can the original question be answered without assuming some model is the perfect reflection of reality, or just without using the model?"
My point is, you cannot talk about reality without using a model, except in some obscure philosophical sense (like e.g. Kant's ding an sich).
Models are not some bizarro abstractions that have little to do with reality, they are exactly our way of talking about reality. Any talk about reality is about a model of reality.
So ta1234567890 inquiry is bogus, we can't have "explanations about reality [NOT] become explanations about a model of reality".
That models are abstractions, and that 'the map is not the territorry" (two ideas that might have informed ta123456... comment) is correct, but it just means that no model is perfect. Not that model-less talk about reality is possible...
Plus, the idea that no model is perfect, is problematic in itself, often usef for a tin-foil rejection of any model. Some models can be perfect for their domain, or perfect for up to some very small degree of measurement error...
They're tools to predict experience. Anything beyond that is philosophy, positive or negative (i.e. that they are only that or that they are more than that). Your philosophical position is that the reason that they are able to predict future experience is because they accurately describe reality to some degree. This is just the opposite position of Hume. If you think that the models give us knowledge of reality, then this is the opposite position of Kant.
Your position is held by only 57.1% of professional philosophers. The Humean position is held by 24.7%. [1] My point here is that Kant's position is hardly obscure being that one more extreme than it is held by a quarter of philosophers and it's not wise for you to take your position as being objectively correct and anything else a "misunderstanding." Even if you only mean that it is more common, it's firstly only barely so and secondly however reality is or is not is not going to be decided democratically.
I think additionally that your position is particularly naive considering that QM doesn't even pretend to tell us how reality actually is. That's what the various interpretations do. Or will you claim that QM is not a physical model?
Isn't that backwards? QM, without "interpretation" tells what outcomes of experiments should be. That's reality.
The interpretations are interchangeable, so even if there was some oracle to tell us one of them was better, it wouldn't tell us anything about reality.
If you stop believing in QM, everything happens just as before and if all knowledge was lost, the theory could be recreated.
But if you stop believing in the Copenhagen interpretation, and start believing in many-worlds, or you say "the hand of God directs things", nothing changes. If all knowledge of those ideas vanished, nothing would ensure it was recreated.
What people want to know is what doesn't go away when you stop believing in it. What you've claimed so far is that the results of experiments (i.e. effects) don't go away if you stop believing in them. This isn't controversial; however it is incomplete. It doesn't tell us what caused the effects. If many-worlds, for example, is true, then when you stop believing in it then its branching and branches will not go away. If pilot-wave theory is true, the pilot waves do not go away when you stop believing in them. If objective collapse theories are true, wave functions spontaneously collapse whether you believe so or not. You, on the other hand, are only accounting for effects and models, not causes and what is modeled.
If so, I don't know what.
Anyway, I think you're implicitly privileging one abstraction, called an "interpretation" over "just the plain math". But if they're equivalent, what is real about choosing one or the other, let alone between different "interpretations"?
Why is an "interpretation" a real thing and not the equations?
This seems structurally similar to a classic theological argument between theist and atheist; ok, you believe in a god, but why that particular god? And if there's no reason for a particular god, why bother with any?
Like the things I mentioned. Please read more carefully.
> Anyway, I think you're implicitly privileging one abstraction, called an "interpretation" over "just the plain math".
One doesn't need to privilege one over the other to ask what the math is about.
> Why is an "interpretation" a real thing and not the equations?
Nobody thinks the math is not "a real thing." They want to know what the math is about.
Movement through space (in any direction) is movement against time.
Is positive kinetic energy the direction opposite time?
That seems a tautology isn't? Perhaps you wanted to say something else?
Very nearly, but it is exactly what I wanted to say. Light travels at a fixed speed _through space_ which we happen to call "the speed of light". A physical object which is motionless in space travels at a fixed speed _in the time dimension_ which happens to have the same size as the speed of light.
This has consequences. A physical object which has some speed in space still has a 4-velocity vector whose length is the speed of light. That means the space velocity and time velocity must combine into a vector whose length is c. Naturally, if the space velocity is non-zero, the time velocity must be less than c. This is called time dilation.
> Therefore, if I got this right, for an external observer, light does not travel trough time, only space. However, in its own reference frame, light should travel trough time at the speed of light (and doesn't move in space in that reference frame).
Not quite.
Taken to the extreme, an object with a space velocity equal to the speed of light would have no velocity at all in the time direction. This can be a confusing statement, because we must make a distinction between times as measured by an observer and times measured by the moving object. If a photon could measure events (and most cannot), it would measure no time elapsing between it's own creation and it's own destruction. It will be emitted by an electron in one place (perhaps the coronasphere of the sun) and simultaneously absorbed by another electron in another place (perhaps a rhodopsin molecule in someone's retina). An observer, such as the owner of the retina, would of course still measure some time between the emission and the absorption; the events would not appear to be simultaneous. This is called relativity of simultaneity.
Imagine a photon that is emitted by the sun and travels through space bouncing off the moon and onto my retina. In my frame I can trace the path of that photon and see a sequence (sun->moon->eye). For the photon, all of that happened simultaneously, right? It would have no experience of having traveled from the sun to my eye because it was in both places at once. Is that right?
However, in its own reference frame, light should travel trough time at the speed of light (and doesn't move in space in that reference frame). I wonder what happens to the energy in that frame...
>physics is all about equations
No. Physics is about the nature of reality. Mathematics is a tool we use to describe the world.
Consider that the faster you travel, the more collisions (or potential collisions) between particles need to be decided.
Is the limiting factor of c directly related to the available computational power?
You can either simulate the entire universe in infinite detail taking infinite time, or you can optimize to focus on the more important bits in finite time.
For low energy an approximation might suffice, and that would go some ways to explain quantum effects.
Also, when we speak of traversal the implication is closing distance across a space. Space is also variable. According to the Special Theory of Relativity space is curved and that curvature varies according to the forces acting upon it. The general assumption is that such a curvature is uniform according to the force imposed upon at a given point relative to that force, but there is no reason to make such an assumption. More simply space is curved and that curvature may vary in unexpected ways regardless of whether an observer is outside or effected by the force imposing the curvature.
That said the safest prediction is to say we all travel at various speeds of light given enough space and duration compared to a competing observation.
The implication being suggested is - if I was trapped in a block of plastic or... underwater, I would experience time different compared to someone standing on land just because "c" is slower.
Clearly not the case.
To be specific, when "the speed of light" is discussed like this, it usually means the "speed of causality"[1] which is the underlying meaning of "c" in relativity.
The speed of causality through a medium (i.e. water) is the same as a vacuum if spacetime curvature is the same.
For example, if a powerful laser beam was shot off in a vacuum towards an observer who is far away, it's not the "speed of light in a vacuum" which dictates the time at which the observer detects that laser light, it's the speed of causality in that volume of spacetime which determines when that light beam reaches them/is detected.
The curvature of space is directly related to time travel. Strange how you completely ignored that much larger portion of my comment to punch a straw man.
> is the same as a vacuum if spacetime curvature is the same.
If that were true particle physics wouldn’t need dark matter/energy to balance conditions that are irregular upon observable matter alone.
https://en.m.wikipedia.org/wiki/Causality_(physics)
Causality, at least in physics, is an abstract notion and not an empirical notion. In causality effects occur in the same order as their respective causes which is substantive for logical consider, but is not necessarily measurably accurate or expected.
> If that were true particle physics wouldn’t need dark matter/energy to balance conditions that are irregular upon observable matter alone.
You responded to my vacuum statement as if we agree the vacuum is perfectly empty. In relativity, the vacuum is not considered empty[0]. Maybe I should have used "patch of space", but more importantly I said "if the spacetime curvature is the same". That literally defines how causality moves through it so that would be inclusive whatever was there including dark matter/energy, which brings us to...
> Causality, at least in physics, is an abstract notion and not an empirical notion... but is not necessarily measurably accurate or expected.
No it's not... From the wiki you quoted: "In Einstein's theory of special relativity, causality means that an effect can not occur from a cause that is not in the back (past) light cone of that event. Similarly, a cause cannot have an effect outside its front (future) light cone."
We're talking about relativity here, not philosophy or another topic where causality isn't well defined. It is not abstract. It is explicitly defined as "c" in Einstein's equations. I'm not sure what you're trying to prove/disprove here.
You can say I attacked a straw man, but the original comment was edited. So now, I don't know.
I recommend PBS SpaceTime[1] - I still don't understand a lot of things in this space even after watching many videos multiple times, but it really helped put pieces together.
[0] https://en.wikipedia.org/wiki/Vacuum_state#:~:text=According....
[1] https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g
> No it's not
Causality states that the order of effects must match the order of events. The Wikipedia articles states that almost verbatim. The mention of a light cone binds the general use of the word to its application of physics without changing the definition. No where does the article extend that definition to anything vaguely measurable.
> You can say I attacked a straw man, but the original comment was edited.
It was most likely edited hours before your reply. When I completed the edit there were no replies. I am living on the otherside of the world from the US in a far away timezone.
Ah, you're right, I didn't realize you dropped the "speed of" in the "speed of causality" (because the "speed of causality" can be measured and expected... what does "expected" even mean in this context?!). So going 2 replies up you linked to Causality and made a statement about causality but ignored the "speed of causality". So nothing was said?
So you agree with me!
> It was most likely edited hours before your reply. When I completed the edit there were no replies.
Ah! Don't worry, thankfully we know that I replied to you 35 minutes later thanks to Hackernew's API[0][1] and that I'm half a world closer in SGT, and that I was originally replying to something that was edited away.
[0] https://hacker-news.firebaseio.com/v0/item/24328890.json?pri... [1] https://hacker-news.firebaseio.com/v0/item/24329038.json?pri...
I don't find that as reassuring. Instead of an editing/time conflict the problem is just poor reading comprehension.
No, it's the General Theory of Relativity that says that spacetime is curved. Spacetime is flat in Special Relativity.
> curvature varies according to the forces acting upon it
No, in GR spacetime curvature varies according to the matter and energy that are present. Gravity is not a force at all in GR.
Rather, the gravitational force is a pseudo-force like the Coriolis force.