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A Spacetime Surprise: Time Isn’t Just Another Dimension

271 points by chris_overseas 6y ago

sriku 6y ago
I found the title a little bit misleading, especially given that quantum physics looks at time differently these days it seems .. with the Wheeler-DeWitt equation for the wave functional of the universe not featuring time .. and further talk that space and time themselves are born of the more fundamental process of entanglement. .. but it "just" ended up describing the regular Minkowski space-time.
bra-ket 6y ago
Great article, what intro books would you recommend on 1) special or general relativity for an advanced (engineering) undergrad and 2) books on spacetime math/geometry/tensor algebra and its applications beyond modern physics.
- d--b 6y ago
  Einstein’s relativity: the special and general theory is very readable and very insightful. Instead of explaining how the math works first he goes about explaining how he came to put these theories together, which makes the math come pretty naturally
- pieterk 6y ago
  The actual papers that Einstein wrote weren't that hard to read, that's why he got so successful after all. For a more recent treatment, the works of Carlo Rovelli are all about more human scale applications or implications of the theory.
- gumby 6y ago
  Taylor’s and Wheeler’s “Spacetime Physics” is quite approachable and easy to read introduction to Special Relativity that has hardly any math beyond basic algebra.
- maskedinvader 6y ago
  I would highly recommend reading this collection of essays compiled into a book titled "Einstein's Theories of Relativity and Gravitation" There was a competition for anyone to explain Einstein's work for the layman and a lot of people wrote essays to win the $5000 prize, this book has the top essays that were chosen and really helped me get a grip on the idea of relativity. https://www.google.com/books/edition/Einstein_s_Theories_of_Relativity_and_Gr/CyUQAAAAYAAJ?hl=en&gbpv=0 https://www.google.com/books/edition/Einstein_s_Theories_of_...
  - kranner 6y ago
    Thanks! As the book (from 1922) seems to be out of copyright, here's a link to the PDF copy I found on archive.org. https://archive.org/details/einsteinstheorie0000bird https://archive.org/details/einsteinstheorie0000bird
- sriku 6y ago
  Mr. Tomkins in Wonderland by George Gamow of Alpher, Bethe, Gamow fame - https://m.youtube.com/watch?v=WIKOFLRQuc8 https://m.youtube.com/watch?v=WIKOFLRQuc8 That's not advanced undergrad certainly :) .. but I found the following great to learn from. Especially the treatment of momentum and the stress energy tensor really worked for me - https://www.amazon.com/First-Course-General-Relativity/dp/0521277035
- acqq 6y ago
  If you liked the article, note that the author has the whole book: https://www.amazon.com/Beyond-Galaxy-Humanity-Discovered-Universe/dp/9814667161 https://www.amazon.com/Beyond-Galaxy-Humanity-Discovered-Uni... “Beyond The Galaxy: How Humanity Looked Beyond Our Milky Way And Discovered The Entire Universe”
galaxyLogic 6y ago
Key observation: Time is relative, distance is relative but: "No matter who is doing the observing or how quickly they’re moving, the combined motion of any object through spacetime is something all observers can agree on. "
- elb2020 6y ago
  Agree, that was my main takeway too. I found the animation with the two mirror systems especially illuminating. Without the theory of spacetime, it would seem that the two mirror systems would somehow get out of sync over time, since it appears, from the stationary system, as if the photons in the moving system are doing fewer rounds in the same amount of time. And from the moving system the photons in the stationary system appears, likewise, to be doing fewer rounds. The theory reconciles it by saying that time itself is not fixed, but dependent upon relative motion. And the relative motion is something that observers at both systems can agree upon. So, by accepting that time is dependent upon relative motion, they can agree upon the motion of photons in both systems.
dstick 6y ago
Very interesting article. Explains spacetime in a way non-physicist like me understands. Even better than Hawking’s book did. Or maybe those books built the base of understanding that this article now profits from ;-) Fascinating stuff. Always reminds me of the movie Interstellar and how they treated time. Getting back to earth to find out your young daughter is now in her 80’s :)
bArray 6y ago
The way I like to think of it is like moving your hand through water in a swimming pool; the faster you try to move, the more the water (time) pushes against you. If you don't try to move your hand at all, the water (time) has seemingly no affect on you. In this analogy the water itself is space and time is the measurement of movement resistance. Of course there are nice little things to explore with this, like moving through running water, currents (localized loops), deep water (dense space), resistance on small vs large things, etc. If we imagine on the small enough scale where we're looking at single water molecules, resistance (time) doesn't even mean too much. As long as your water is liquid, your little molecules are bouncing around in all directions, only tending towards a given direction with some probability. Otherwise each direction is near and damnit equally easy to travel in. That's my two cents anyway.
- marliechiller 6y ago
  that was a really cool explanation and helped me create a mental model much easier than typical analogies, thanks!
- CGamesPlay 6y ago
  This is an interesting analogy which might be helpful; but I don't think taking it down to an atomic level is useful, since it breaks the analogy. Time means just as much to a single atom as it does to your entire hand, the speed limit and "increase in drag" (in the context of this analogy) is the same. The hand takes more energy to accelerate than a single atom does, but that's not because of temporal dilation--it's just the normal old classical inertia.
  - bArray 6y ago
    > I don't think taking it down to an atomic level is useful, > since it breaks the analogy It was simply a suggestion as to why things might start behaving weirdly at the quantum level. My understanding is that very small things seem to act as if time doesn't really have any real favoured direction. Of course the analogy is not perfect and does not measure correctly the scale of forces involved, or even how they behave at different extremes. It's just a rough and ready mental model to begin to see things in this framing.
code-is-code 6y ago
Forbes is so broken on mobile
- helloworld 6y ago
  That's what I just discovered, too, using Android Chrome. So, out of curiosity, I switched over to Android Firefox and turned on "reader view." Much better! https://support.mozilla.org/en-US/kb/view-articles-reader-view-firefox-android https://support.mozilla.org/en-US/kb/view-articles-reader-vi...
  - kuu 6y ago
    "Reader view" on Firefox is one of the best inventions ever ;)
Ono-Sendai 6y ago
The whole concept of spacetime is a bit of a red herring that has confused generations of scientists and the public. Time is not a dimension like space - you can't move freely in it.
- sheerun 6y ago
  You can't move freely in time only in your frame of reference
edna314 6y ago
For those who wonder what the bottom line in the article is why time isn’t just another dimension: There is a minus sign and the speed of light in front of time in the space-time metric. It is argued that the minus sign comes about because time is imaginary (in complex number terms). I don’t find this convincing. One could still argue that time is just an ordinary dimension and the structure of the metric is just a property of how we measure distances.
- sriku 6y ago
  You're right in that the article doesn't quite "explain" it .. and it cannot be explained relative to normal newtonian "intuition". Working with Maxwell's equations to understand how electric fields can transform to magnetic fields and vice versa, working out the "wave equation" and seeing the speed of electromagnetic waves emerge from the equation independent of the reference frame was what nailed it for me.
  - antman 6y ago
    Let’s not forget that Maxwell equations are shaped as such due to the respective algebra. In clifford algebric spaces it is simply one equation. One idea is that not only it is important to conceptualize a complex phenomenon but to also whether we can formalize it in a simple way.
    - sriku 6y ago
      "simply one equation" that expands to the same set of vector equations which expands to the coordinate-system-specific equations. ∂F=J (barring constants) is a beautiful restatement, but I think it puts the cart before the horse to focus on it because that formulation is possible because of the invariances that hold and that comes from the raw Maxwell's equations .. at least historically. The abstract formalisation is even harder to convey (at least for me, and so far) since it takes away the familiar "electricity" and "magnetism" and you need to think about the more complex F that combines both. One way perhaps is to start with circuits - which are discrete and circuit laws can be expressed with the same equation and then argue for the continuous case .. but speed of light invariance would still be a long way from that compared to the raw Maxwell's equations route. Or maybe I misunderstood what you're suggesting.
magicalhippo 6y ago
> The other dimensions are not like this at all: your motion through the x dimension in space, for example, is completely independent of your motion through the y and z dimensions. This reminds me of Quake (and many other games), where moving diagonally is faster than moving either forwards, as the game simply adds the two vector components independently based on which keys are pressed. Of course we're very familiar with the motion through one dimension being dependent of the others. My car has a top speed, regardless if I'm driving north, northwest or whatever. The weird thing about spacetime thus does not seem to be that we're racing through it at top speed, but rather that we can't slow down.
l33tman 6y ago
Something that can help thinking about Euclidean and Minkowski metrics as a programmer, is thinking of how to write a low-level physics sim, and you have a 4D array of values describing some aspect of your simulated world corresponding to space and time and you want to "fill it in" according to some physical rules. Without any metric, your 4D array entries are conceptually independent and you can't make rules that depend on a neighbor entry (as you haven't defined what a neighbor is!). In the Euclidean metric, which certainly is the most intuitive, the entries with indices closer to each other in each dimension are also closer to each other physically. But in the Minkowski metric, the x=0,t+1 or x=0,t-1 entries are actually not closest to your x=0,t=0 entry for example! Instead, x=1,t=1 , or x=-1,t=1 are closer (indeed, with distance zero). Generalizing to more dimensions this maps out what is called the "lightcone" as it's a cone. So you can in some sense say that all points along the lightcone are "the same" or "on top" of the cone tip, at least as seen from your rules that depend on the distance. This difference in metric is what causes all the time dilations and other artifacts of Special Relativity. Light can be seen as a connection between points in the array that are already the "same" point. You can go one step further and say that the lightcone originating from each array entry can tilt in 4D differently in each point. This is General Relativity and causes all the effects within, if you also postulate that the tilts originate from mass-energy in the region.
- thingsgoup 6y ago
  How does special relativity fit into your explanation? What is it missing that special relativity is needed?
  - cellular 6y ago
    Personally, I think every object can move 1 quantum unit every tick of the universe. If all the motion of surrounding objects is in one direction only, then no time passes. https://youtu.be/A-2XQQDD6QQ https://youtu.be/A-2XQQDD6QQ
karmakaze 6y ago
An interesting journey describing spacetime. > you can’t put space (which is a measurement of distance) and time (which is a measurement of, well, time) on the same footing without some way to convert one to the other. This idea about 'equal footing' is really a hazy way of asking if these dimensions can be considered 'independent', which the article then describes as being interdependent. > The key idea is that we’re all moving through the Universe, through both space and time, simultaneously. If we’re simply sitting here, stationary, and not moving through space at all, then we move through time at a very specific rate at which we’re all familiar: one second per second. This second/second rate is 'c' the speed of light, but through the 'time' dimension of spacetime. > However — and this is the key point — the faster you move through space, the slower you move through time. The other dimensions are not like this at all: your motion through the x dimension in space, for example, is completely independent of your motion through the y and z dimensions. This point is misleading. These dimensions are like time in that if I was traveling at the speed 'c' in only the x direction, then to move in y or z directions, movement in the x direction would need to be reduced. The main difference is that we're observing these x, y, z motions in non-relativistic scales but since 1 sec/sec is already 'c', any observation of change in motion through time is relativistic. > But your total motion through space, and this is relative to any other observer, determines your motion through time. The more you move through one (space or time), the less you move through the other. Hopefully, now you can see that we're always moving at 'c' through spacetime. The only reason spatial dimensions seem qualitatively different is due to our observed motion through spacetime being timelike. A photon would have reversed qualitative characterizations of space vs time dimensions. This video[0] (at ~1:55) illustrates this pretty well. [0] https://youtu.be/au0QJYISe4c?t=115 https://youtu.be/au0QJYISe4c?t=115
- sheerun 6y ago
  It's also worth mentioning that relative to us we are always moving through time with speed of c (there's no spacial speed). It's only relative to some other observers we are moving through space (and vice versa).
nullc 6y ago
I'm surprised to not see this linked here: https://en.wikipedia.org/wiki/Orthogonal_(series) https://en.wikipedia.org/wiki/Orthogonal_(series) I thought this series by Greg Egan was really good by any metric.
- andrewflnr 6y ago
  To add some more enticing detail, the series takes place in a universe where time really is just another dimension, and there's no minus sign in the distance metric (hopefully I'm using that term correctly). Consequently, Egan has to re-invent biology from scratch, among other things. It's a wild trip. My favorite if the series is The Arrows of Time.
  - nullc 6y ago
    I like how Egan goes through a lot of history of scientific discovery-- with classical experiments that can easily be recognized, ... which get opposite results in this universe. Everything has to work differently-- not just biology. Thermodynamics, electromagnetism, etc. The speed of light depends on wavelength. Sometimes a fictional work is written as a "single point of departure" from another work or some real event and the author explores the consequences of this change. Orthogonal merely changes a minus to a plus but the consequences are extremely far reaching.
    - andrewflnr 6y ago
      > Everything has to work differently-- not just biology. Thermodynamics, electromagnetism, etc. The speed of light depends on wavelength Well yes, that's why biology has to work differently. Biology is just (close to) the end of the chain of consequences of the change. ;-)
      - nullc 6y ago
        Sorry, not trying to tell you or other people who've read the books. That was intended as a "yes, and" to emphasize your point.
grishka 6y ago
Here's one simple thing about relativity and speed of light I can't wrap my head around for the life of me. In classical physics, forces that act in the same direction, add up. If you forcefully throw an object out of the back of a moving car, its speed at the moment you throw it would be the speed of the car + the speed of the throw. Simple and intuitive enough. But when you involve near-light speeds... So, if you're moving at 90% of the speed of light, and you have a lightbulb in your vehicle, what would be the speed of the photons coming out of it? Logically, it would be 190% of the speed of light. But apparently that's not how it works. So how the hell does it work then?!
- DJBunnies 6y ago
  That's not logical.
- gpderetta 6y ago
  From your prospective, as you are sitting in the car, they come out at exactly C. Edit: from an external observer, the forces also do not add linearly becasue they are not acting on the same spacetime direction.
- pferde 6y ago
  A hand-wavy explanation would be that photons are both particles and waves, so different rules apply. When you create waves on a water surface with your hands, the speed in which they propagate along the surface is the same regardless of whether you just tap the water straight down, or make a sweep with your hand.
- sergj 6y ago
  Maybe thinking about lightspeed as the upper speed limit helps? You could also think about the clock experiment by Hafele and Keating where two synchronised clocks where flown all over the globe and after a while they disagreed with each other. Or the popsci answer: Things that move fast get more massiv and time gets slower for them, at the speed of light time stops. Without time no speed.
- dsr_ 6y ago
  Classical physics is based on observations that humans can make with very low technology: polished metals and glasses, relative velocities up to a few thousand meters per second, timekeeping accurate to milliseconds in one location. Those observations lead to approximations which "feel" correct because humans spend most of their lives in those circumstances. But at the edges of those circumstances, we see discrepancies not predicted by classical physics. That lets us know that classical physics is an approximation. The truth is that even in your car + thrown object example, the velocities do not actually add linearly -- it's just that the difference between the linear approximation and the reality is tiny. One analogy that might be helpful: consider every object in the universe to be moving at c, but for most objects that you encounter, the vast majority of that motion is forward in time rather than space. As you add energy to the object, it transfers that velocity from time-motion to space-motion. Because c is so large compared to our usual experience, we have to look really hard to discover the change in time-motion... but it's real. GPS uses satellites that are in a sufficiently different frame from the surface of the Earth, and requires sufficient time precision, that relativistic time difference calculations are required.
johndoe42377 6y ago
Dimension of what? In where? There is no dimensions outside your head in the first place. It is a superimposed abstraction, like a coordinate system.
- herodoturtle 6y ago
  Well said. And the best part of your phrasing is its consistency with simulation theory.
irthomasthomas 6y ago
"The more you move in space, the less you move in time" The consequences of this simple rule are rather shocking, as the recent nobel winner Roger Penrose pointed out. Take the case of two people on Earth, one stationary and one travelling past in a car. They each have different events which they consider the present. Now imagine that there is an alien government in Andromeda debating a possible invasion of Earth. To the person on Earth who is moving, the debate still going on, but in the reference frame of the stationary person, it's a day or so later in Andromeda and the invasion fleet is already on it's way. If there is no absolute reference frame, and both observers reference frames are equally valid, then the outcome of the invasion debate is a foregone conclusion. This is the crux of the Andromeda Paradox and the Reitdijk-Putnam-Penrose argument. https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argume...
- sudhirj 6y ago
  Is this actually a problem? By the time the person travelling in the car and the stationary person synchronise their information enough to communicate won’t their frames of reference also sync up? Like if I’m moving and I see something before you, won’t you see it as well before or at the same time I can tell you I saw it?
  - irthomasthomas 6y ago
    From the wiki... "Notice that neither observer can actually "see" what is happening in Andromeda, because light from Andromeda (and the hypothetical alien fleet) will take 2.5 million years to reach Earth. The argument is not about what can be "seen"; it is purely about what events different observers consider to occur in the present moment."
    - sudhirj 6y ago
      But the entire point of relativity is that there’s no such thing as a joint “present moment” between more than observer. The only meaningful construct is your own present moment, about which information radiates outward at the maximum speed of information transfer in space-time (speed of light/gravity). Information reaches other observers based on their trajectory and position in space time. No such thing as the universal now.
sudhirj 6y ago
Didn’t see if this was mentioned in the article, but it was interesting to find out somewhere that for a photon time doesn’t pass even as it travels across the universe. Basically the time component is 0 so the space speed is 100%. That’s why I find it easier to stop thinking of the speed of light, and thinking of it as percentage of speed of information transfer in the space-time medium. Light (or rather electromagnetic waves) travels at 100% the speed of space, but it has no special treatment in the medium, and does so by travelling at 0% the speed of time.
- slfnflctd 6y ago
  I'm not sure if it's exactly the same thing, but I've heard the phrase, "From the perspective of light, everything happens at once". It's a bit unclear to me how light or a photon could have a perspective, but I guess it's not really relevant? This kind of thing is part of why I haven't taken a deeper dive into physics. The metaphors and allegories always break down if you look at them too hard, you really need to wade into the underlying math to get a real understanding I think.
  - sudhirj 6y ago
    Yeah, that's really everything with all caps EVERYTHING, isn't it? From the beginning to the end of the universe, it would all happen in an instant.
  - cellular 6y ago
    This perspective you mention is exactly why I made a video on the subject: https://youtu.be/A-2XQQDD6QQ https://youtu.be/A-2XQQDD6QQ It seems so simple to me now!
- sheerun 6y ago
  For photon time passes only for itself (because relative to itself it is not moving). Any interaction with photon (i.e. what we call "observing"), happens with t=0 from perspective of something that collided with photon, and normal time from the perspective of photon (which happens to be spatial distance from perspective of something that collided with photon).
jcims 6y ago
Here's a game that tweaks the speed of light to help make it more tangible - http://gamelab.mit.edu/games/a-slower-speed-of-light/ http://gamelab.mit.edu/games/a-slower-speed-of-light/
- mikewarot 6y ago
  I found the game quite interesting, and unfortunately nausea inducing.. 8:30 to get all the orbs.
Geee 6y ago
Does everything really 'move' in time? I thought that time is like a film, where nothing moves except the observer. I'm not sure which way it is. If we travel back in time, the universe is still there, and not moved to the future. Also, I never understood the grandfather paradox. If I travel in the past and change something, wouldn't the change propagate in time at the speed of light? And it would take a long time before it overwrites the original time.
- yathern 6y ago
  I have a couple of things to say here that might clear things up! > I thought that time is like a film, where nothing moves except the observer. We are not merely observers of the universe - we are part of it. When we change where (or when) we are in the universe, we change the universe itself. > Also, I never understood the grandfather paradox. Instead of the "go back in time and kill your grandfather" idea, lets keep the scale smaller. Let's go back in time 1 minute, and then smash our time machine. Now, there are two "me"s in this timeline. But energy and matter can't be created out of thin air! Maybe it took a lot of energy to send me back, but that was in the future, and that future is gone, now that our time machine is smashed. We could very well send gold bars back a minute, and double our money! The way you typically resolve this paradox is through keeping infinite timelines. In our example, there's a timeline where we disappeared off the face of the earth, and a timeline where there are two "me"s. They each continue independently. But if there is only a single timeline, we can do all sorts of paradoxical things. > If I travel in the past and change something, wouldn't the change propagate in time at the speed of light? The speed of light is measured in meters per second. Time is measured in seconds. I'm not sure I'm clear on what your suggested propagation looks like.
  - Geee 6y ago
    Well, I'm not sure actually. It seems to require more dimensions for causal events to 'propagate' in time. I was thinking that events can't change the future instantly, because information can't travel faster than speed of light (which is the normal passing of time). So if I travel from million years from the future, it should take million years for the change to propagate to my original future.
jl2718 6y ago
Let’s say we’re in the middle of a black hole. Some supernova event sends us toward the horizon with a bunch of mass, but it’s also getting sucked back in. Space-time starts out looking like a dish and then begins to form a vortex as mass gets sucked back in. It looks like we are accelerating away from other masses. The red shift keeps increasing. Then at some point we are back at the singularity orbiting at the speed of light and now the Schwarzchild metric gives a negative dt^2 due to the combined effects of gravity and velocity, so we can get rid of the negative sign in Minkowski space if we accept the singularity as the normal state of things.
hateful 6y ago
> your motion through the x dimension in space, for example, is completely independent of your motion through the y and z dimensions. But it does, if you're moving at a constant speed... just like you're moving through time in...
crazygringo 6y ago
Meta discussion -- and not a criticism, but why does Forbes publish something like this? It's not news, it's like a short physics chapter for motivated high school students. Not that I'm complaining at all, it's just a surprise. Is this part of a series of articles or something with a unique purpose? Curious if Forbes is on some kind of educational mission or something.
- Steuard 6y ago
  This is an entry from the "Starts With A Bang" blog. I think the author(s) (is it mostly just Siegel?) post regularly about physics/science topics, including newsworthy stuff, but clearly also sometimes just post about general cool ideas.
- humanistbot 6y ago
  A while ago, forbes.com went from being a digital version of their print publication to basically the same blogroll model as the Huffington Post. Thousands of "Forbes contributors" who are not on staff at Forbes get to have their blogs hosted on forbes.com/sites/username. Those articles never make it into Forbes magazine, but the authors get a pittance of revenue from ads and get to claim they write for Forbes.
  - solumos 6y ago
    Some contributors actually pay to publish.
pontus 6y ago
If you want to learn special relativity, I highly recommend this course from Brian Greene: https://worldscienceu.com/courses/special-relativity-world-science-u/ https://worldscienceu.com/courses/special-relativity-world-s...
- pontus 6y ago
  It has tons of great interactive widgets that you can play around with to gain some intuition around things like time dilation, length contraction, simultaneity etc.
tzs 6y ago
There are a few episodes covering similar material on PBS Space Time [1], if you want to go into a little more depth. Space Time episodes are short (typically 10 minutes or less), so this makes a great thing to watch when you have a little time to kill. If you want to play around with time dilation and length contraction in special relativity, I wrote a web-based calculator to help with that [2]. You can enter the relative velocity of two aligned frames that are moving along each other's x axis, and it gives you a series of rows representing events. The frames are called "your frame" and "their frame". Each row has 4 numbers, x and t of the event in your frame, and x and t of the same event in their frame. When you enter any two of those numbers, it updates the other two. For example, you could enter x = 3 in your frame, t = 5 in their frame, and it will update t in your frame and x in their frame so that x and t in your frame and x and t in their frame refer to the same event. The README gives an example of how you could use this to figure out the famous ladder paradox. [1] https://www.pbs.org/show/pbs-space-time/ https://www.pbs.org/show/pbs-space-time/ [2] https://github.com/tzs/Physics-special-relativity-calculator https://github.com/tzs/Physics-special-relativity-calculator
6gvONxR4sf7o 6y ago
I’m disappointed by this article. From the title, I expected it was a new development. Instead, it’s what you’d find on any discussion of space time. A Spacetime Surprise: Time Is The Easiest Dimension To Waste With Misleading Titles.
- kgwgk 6y ago
  I agree that the title is very strange. To the extent that anyone has ever said that time is "just another dimension" it won't be in conflict with what the article explains.
dfilppi 6y ago
The foundation of the article is false. There is no 'space'. There is only spacetime.
- sheerun 6y ago
  The same way X direction can can be arbitrarily defined in space, the time can be arbitrarily defined in spacetime (so called "frame of reference"). Other 3 directions parallel to time are called space.
justincredible 6y ago
It's left as an exercise for the reader to reconcile the headline and the initial premise.
SAI_Peregrinus 6y ago
> After all, the shortest distance between two spacetime events isn’t a straight line any longer. That's wrong. It's still a straight line, just along the geodesic of the local spacetime. It looks curvy if you bend and flatten spacetime into a Euclidean space, but that's because you bent it! Light in a vacuum always travels in straight lines. Gravitational lensing isn't gravity bending the light, it's the light traveling in straight lines through highly curved space.
mountainboy 6y ago
Time is simply a measure of matter in motion. Every clock ever invented measures... matter in motion. There are only 3 spatial dimensions. You're welcome.
danwills 6y ago
I reckon this phenomena could kinda be phrased like this: Moving through space takes up your turns, when you're moving really fast, most of your turns are taken up by moving (so there's less turns left for the operations of ordinary matter, which we use to measure the passage of time, so it seems slower).
- danwills 6y ago
  Time most certainly is not a dimension (or even very dimension-like, in general) in my opinion. It structures the orderings of events, more like some ultimate process that all other processes are hanging off (are a part of). The complexity in the ordering could be irreducible at any given point, depending what is happening there, and that includes fully non-reversible processes. To me, this is time's arrow.
xtiansimon 6y ago
I LOVE when science is explained as if you're talking to child. Or even a high school'r with algebra under their belt. And then this happens... > “...you can’t put space (which is a measurement of distance) and time (which is a measurement of, well, time) on the same footing...” ...two parentheticals followed by dippy do metaphor 'footing?' Feet? I’m only half kidding. The article's first 50% starts in the best of ways, ‘shortest distance between two points’. After ‘feet’ it’s all down hill-- > “the faster you move through space, the slower you move through time.” Well. Of course. Every school child knows this is true. When the kickball is heading for your face, time stands still. But slow down a minute, walk me through this as carefully as you did for the two-points... > "But as you approach the speed of light" Never going to happen > "— or rather, ..where the relative speed between you and it is close to the speed of light — you’ll observe that it’s contracted along its direction of relative motion..." It relative that it and it's--WHat? There was distance between two points and now I have 'relative speed'. What the heck is that that I should be able to call it an it so quick?? I could go on, but my point--Why, once the subject becomes actually difficult to understand, does the author's explanation becomes worse? More parenthetical. It and that. And tries to put me in a position to imagine moving at the speed of light or a clock "defined by light bouncing back and forth between two mirrors". Huh. What? Great start. Poor finish. Maybe if you thought less about name dropping Einstein, I could appreciate what is relative speed between two anything. I agree, this curious piece of math and science could use some popular updating. /END RANT

I found the title a little bit misleading, especially given that quantum physics looks at time differently these days it seems .. with the Wheeler-DeWitt equation for the wave functional of the universe not featuring time .. and further talk that space and time themselves are born of the more fundamental process of entanglement. .. but it "just" ended up describing the regular Minkowski space-time.

bra-ket 6y ago

Great article, what intro books would you recommend on 1) special or general relativity for an advanced (engineering) undergrad and 2) books on spacetime math/geometry/tensor algebra and its applications beyond modern physics.

d--b 6y ago
Einstein’s relativity: the special and general theory is very readable and very insightful. Instead of explaining how the math works first he goes about explaining how he came to put these theories together, which makes the math come pretty naturally
pieterk 6y ago
The actual papers that Einstein wrote weren't that hard to read, that's why he got so successful after all. For a more recent treatment, the works of Carlo Rovelli are all about more human scale applications or implications of the theory.
gumby 6y ago
Taylor’s and Wheeler’s “Spacetime Physics” is quite approachable and easy to read introduction to Special Relativity that has hardly any math beyond basic algebra.
maskedinvader 6y ago
I would highly recommend reading this collection of essays compiled into a book titled "Einstein's Theories of Relativity and Gravitation" There was a competition for anyone to explain Einstein's work for the layman and a lot of people wrote essays to win the $5000 prize, this book has the top essays that were chosen and really helped me get a grip on the idea of relativity. https://www.google.com/books/edition/Einstein_s_Theories_of_Relativity_and_Gr/CyUQAAAAYAAJ?hl=en&gbpv=0 https://www.google.com/books/edition/Einstein_s_Theories_of_...
- kranner 6y ago
  Thanks! As the book (from 1922) seems to be out of copyright, here's a link to the PDF copy I found on archive.org. https://archive.org/details/einsteinstheorie0000bird https://archive.org/details/einsteinstheorie0000bird
sriku 6y ago
Mr. Tomkins in Wonderland by George Gamow of Alpher, Bethe, Gamow fame - https://m.youtube.com/watch?v=WIKOFLRQuc8 https://m.youtube.com/watch?v=WIKOFLRQuc8 That's not advanced undergrad certainly :) .. but I found the following great to learn from. Especially the treatment of momentum and the stress energy tensor really worked for me - https://www.amazon.com/First-Course-General-Relativity/dp/0521277035
acqq 6y ago
If you liked the article, note that the author has the whole book: https://www.amazon.com/Beyond-Galaxy-Humanity-Discovered-Universe/dp/9814667161 https://www.amazon.com/Beyond-Galaxy-Humanity-Discovered-Uni... “Beyond The Galaxy: How Humanity Looked Beyond Our Milky Way And Discovered The Entire Universe”

galaxyLogic 6y ago

Key observation: Time is relative, distance is relative but: "No matter who is doing the observing or how quickly they’re moving, the combined motion of any object through spacetime is something all observers can agree on. "

elb2020 6y ago
Agree, that was my main takeway too. I found the animation with the two mirror systems especially illuminating. Without the theory of spacetime, it would seem that the two mirror systems would somehow get out of sync over time, since it appears, from the stationary system, as if the photons in the moving system are doing fewer rounds in the same amount of time. And from the moving system the photons in the stationary system appears, likewise, to be doing fewer rounds. The theory reconciles it by saying that time itself is not fixed, but dependent upon relative motion. And the relative motion is something that observers at both systems can agree upon. So, by accepting that time is dependent upon relative motion, they can agree upon the motion of photons in both systems.

dstick 6y ago

Very interesting article. Explains spacetime in a way non-physicist like me understands. Even better than Hawking’s book did. Or maybe those books built the base of understanding that this article now profits from ;-) Fascinating stuff. Always reminds me of the movie Interstellar and how they treated time. Getting back to earth to find out your young daughter is now in her 80’s :)

bArray 6y ago

The way I like to think of it is like moving your hand through water in a swimming pool; the faster you try to move, the more the water (time) pushes against you. If you don't try to move your hand at all, the water (time) has seemingly no affect on you. In this analogy the water itself is space and time is the measurement of movement resistance. Of course there are nice little things to explore with this, like moving through running water, currents (localized loops), deep water (dense space), resistance on small vs large things, etc. If we imagine on the small enough scale where we're looking at single water molecules, resistance (time) doesn't even mean too much. As long as your water is liquid, your little molecules are bouncing around in all directions, only tending towards a given direction with some probability. Otherwise each direction is near and damnit equally easy to travel in. That's my two cents anyway.

marliechiller 6y ago
that was a really cool explanation and helped me create a mental model much easier than typical analogies, thanks!
CGamesPlay 6y ago
This is an interesting analogy which might be helpful; but I don't think taking it down to an atomic level is useful, since it breaks the analogy. Time means just as much to a single atom as it does to your entire hand, the speed limit and "increase in drag" (in the context of this analogy) is the same. The hand takes more energy to accelerate than a single atom does, but that's not because of temporal dilation--it's just the normal old classical inertia.
- bArray 6y ago
  > I don't think taking it down to an atomic level is useful, > since it breaks the analogy It was simply a suggestion as to why things might start behaving weirdly at the quantum level. My understanding is that very small things seem to act as if time doesn't really have any real favoured direction. Of course the analogy is not perfect and does not measure correctly the scale of forces involved, or even how they behave at different extremes. It's just a rough and ready mental model to begin to see things in this framing.

code-is-code 6y ago

Forbes is so broken on mobile

helloworld 6y ago
That's what I just discovered, too, using Android Chrome. So, out of curiosity, I switched over to Android Firefox and turned on "reader view." Much better! https://support.mozilla.org/en-US/kb/view-articles-reader-view-firefox-android https://support.mozilla.org/en-US/kb/view-articles-reader-vi...
- kuu 6y ago
  "Reader view" on Firefox is one of the best inventions ever ;)

Ono-Sendai 6y ago

The whole concept of spacetime is a bit of a red herring that has confused generations of scientists and the public. Time is not a dimension like space - you can't move freely in it.

sheerun 6y ago
You can't move freely in time only in your frame of reference

edna314 6y ago

For those who wonder what the bottom line in the article is why time isn’t just another dimension: There is a minus sign and the speed of light in front of time in the space-time metric. It is argued that the minus sign comes about because time is imaginary (in complex number terms). I don’t find this convincing. One could still argue that time is just an ordinary dimension and the structure of the metric is just a property of how we measure distances.

sriku 6y ago
You're right in that the article doesn't quite "explain" it .. and it cannot be explained relative to normal newtonian "intuition". Working with Maxwell's equations to understand how electric fields can transform to magnetic fields and vice versa, working out the "wave equation" and seeing the speed of electromagnetic waves emerge from the equation independent of the reference frame was what nailed it for me.
- antman 6y ago
  Let’s not forget that Maxwell equations are shaped as such due to the respective algebra. In clifford algebric spaces it is simply one equation. One idea is that not only it is important to conceptualize a complex phenomenon but to also whether we can formalize it in a simple way.
  - sriku 6y ago
    "simply one equation" that expands to the same set of vector equations which expands to the coordinate-system-specific equations. ∂F=J (barring constants) is a beautiful restatement, but I think it puts the cart before the horse to focus on it because that formulation is possible because of the invariances that hold and that comes from the raw Maxwell's equations .. at least historically. The abstract formalisation is even harder to convey (at least for me, and so far) since it takes away the familiar "electricity" and "magnetism" and you need to think about the more complex F that combines both. One way perhaps is to start with circuits - which are discrete and circuit laws can be expressed with the same equation and then argue for the continuous case .. but speed of light invariance would still be a long way from that compared to the raw Maxwell's equations route. Or maybe I misunderstood what you're suggesting.

magicalhippo 6y ago

> The other dimensions are not like this at all: your motion through the x dimension in space, for example, is completely independent of your motion through the y and z dimensions. This reminds me of Quake (and many other games), where moving diagonally is faster than moving either forwards, as the game simply adds the two vector components independently based on which keys are pressed. Of course we're very familiar with the motion through one dimension being dependent of the others. My car has a top speed, regardless if I'm driving north, northwest or whatever. The weird thing about spacetime thus does not seem to be that we're racing through it at top speed, but rather that we can't slow down.

l33tman 6y ago

Something that can help thinking about Euclidean and Minkowski metrics as a programmer, is thinking of how to write a low-level physics sim, and you have a 4D array of values describing some aspect of your simulated world corresponding to space and time and you want to "fill it in" according to some physical rules. Without any metric, your 4D array entries are conceptually independent and you can't make rules that depend on a neighbor entry (as you haven't defined what a neighbor is!). In the Euclidean metric, which certainly is the most intuitive, the entries with indices closer to each other in each dimension are also closer to each other physically. But in the Minkowski metric, the x=0,t+1 or x=0,t-1 entries are actually not closest to your x=0,t=0 entry for example! Instead, x=1,t=1 , or x=-1,t=1 are closer (indeed, with distance zero). Generalizing to more dimensions this maps out what is called the "lightcone" as it's a cone. So you can in some sense say that all points along the lightcone are "the same" or "on top" of the cone tip, at least as seen from your rules that depend on the distance. This difference in metric is what causes all the time dilations and other artifacts of Special Relativity. Light can be seen as a connection between points in the array that are already the "same" point. You can go one step further and say that the lightcone originating from each array entry can tilt in 4D differently in each point. This is General Relativity and causes all the effects within, if you also postulate that the tilts originate from mass-energy in the region.

thingsgoup 6y ago
How does special relativity fit into your explanation? What is it missing that special relativity is needed?
- cellular 6y ago
  Personally, I think every object can move 1 quantum unit every tick of the universe. If all the motion of surrounding objects is in one direction only, then no time passes. https://youtu.be/A-2XQQDD6QQ https://youtu.be/A-2XQQDD6QQ

karmakaze 6y ago

An interesting journey describing spacetime. > you can’t put space (which is a measurement of distance) and time (which is a measurement of, well, time) on the same footing without some way to convert one to the other. This idea about 'equal footing' is really a hazy way of asking if these dimensions can be considered 'independent', which the article then describes as being interdependent. > The key idea is that we’re all moving through the Universe, through both space and time, simultaneously. If we’re simply sitting here, stationary, and not moving through space at all, then we move through time at a very specific rate at which we’re all familiar: one second per second. This second/second rate is 'c' the speed of light, but through the 'time' dimension of spacetime. > However — and this is the key point — the faster you move through space, the slower you move through time. The other dimensions are not like this at all: your motion through the x dimension in space, for example, is completely independent of your motion through the y and z dimensions. This point is misleading. These dimensions are like time in that if I was traveling at the speed 'c' in only the x direction, then to move in y or z directions, movement in the x direction would need to be reduced. The main difference is that we're observing these x, y, z motions in non-relativistic scales but since 1 sec/sec is already 'c', any observation of change in motion through time is relativistic. > But your total motion through space, and this is relative to any other observer, determines your motion through time. The more you move through one (space or time), the less you move through the other. Hopefully, now you can see that we're always moving at 'c' through spacetime. The only reason spatial dimensions seem qualitatively different is due to our observed motion through spacetime being timelike. A photon would have reversed qualitative characterizations of space vs time dimensions. This video[0] (at ~1:55) illustrates this pretty well. [0] https://youtu.be/au0QJYISe4c?t=115 https://youtu.be/au0QJYISe4c?t=115

sheerun 6y ago
It's also worth mentioning that relative to us we are always moving through time with speed of c (there's no spacial speed). It's only relative to some other observers we are moving through space (and vice versa).

nullc 6y ago

I'm surprised to not see this linked here: https://en.wikipedia.org/wiki/Orthogonal_(series) https://en.wikipedia.org/wiki/Orthogonal_(series) I thought this series by Greg Egan was really good by any metric.

andrewflnr 6y ago
To add some more enticing detail, the series takes place in a universe where time really is just another dimension, and there's no minus sign in the distance metric (hopefully I'm using that term correctly). Consequently, Egan has to re-invent biology from scratch, among other things. It's a wild trip. My favorite if the series is The Arrows of Time.
- nullc 6y ago
  I like how Egan goes through a lot of history of scientific discovery-- with classical experiments that can easily be recognized, ... which get opposite results in this universe. Everything has to work differently-- not just biology. Thermodynamics, electromagnetism, etc. The speed of light depends on wavelength. Sometimes a fictional work is written as a "single point of departure" from another work or some real event and the author explores the consequences of this change. Orthogonal merely changes a minus to a plus but the consequences are extremely far reaching.
  - andrewflnr 6y ago
    > Everything has to work differently-- not just biology. Thermodynamics, electromagnetism, etc. The speed of light depends on wavelength Well yes, that's why biology has to work differently. Biology is just (close to) the end of the chain of consequences of the change. ;-)
    - nullc 6y ago
      Sorry, not trying to tell you or other people who've read the books. That was intended as a "yes, and" to emphasize your point.

grishka 6y ago

Here's one simple thing about relativity and speed of light I can't wrap my head around for the life of me. In classical physics, forces that act in the same direction, add up. If you forcefully throw an object out of the back of a moving car, its speed at the moment you throw it would be the speed of the car + the speed of the throw. Simple and intuitive enough. But when you involve near-light speeds... So, if you're moving at 90% of the speed of light, and you have a lightbulb in your vehicle, what would be the speed of the photons coming out of it? Logically, it would be 190% of the speed of light. But apparently that's not how it works. So how the hell does it work then?!

DJBunnies 6y ago
That's not logical.
gpderetta 6y ago
From your prospective, as you are sitting in the car, they come out at exactly C. Edit: from an external observer, the forces also do not add linearly becasue they are not acting on the same spacetime direction.
pferde 6y ago
A hand-wavy explanation would be that photons are both particles and waves, so different rules apply. When you create waves on a water surface with your hands, the speed in which they propagate along the surface is the same regardless of whether you just tap the water straight down, or make a sweep with your hand.
sergj 6y ago
Maybe thinking about lightspeed as the upper speed limit helps? You could also think about the clock experiment by Hafele and Keating where two synchronised clocks where flown all over the globe and after a while they disagreed with each other. Or the popsci answer: Things that move fast get more massiv and time gets slower for them, at the speed of light time stops. Without time no speed.
dsr_ 6y ago
Classical physics is based on observations that humans can make with very low technology: polished metals and glasses, relative velocities up to a few thousand meters per second, timekeeping accurate to milliseconds in one location. Those observations lead to approximations which "feel" correct because humans spend most of their lives in those circumstances. But at the edges of those circumstances, we see discrepancies not predicted by classical physics. That lets us know that classical physics is an approximation. The truth is that even in your car + thrown object example, the velocities do not actually add linearly -- it's just that the difference between the linear approximation and the reality is tiny. One analogy that might be helpful: consider every object in the universe to be moving at c, but for most objects that you encounter, the vast majority of that motion is forward in time rather than space. As you add energy to the object, it transfers that velocity from time-motion to space-motion. Because c is so large compared to our usual experience, we have to look really hard to discover the change in time-motion... but it's real. GPS uses satellites that are in a sufficiently different frame from the surface of the Earth, and requires sufficient time precision, that relativistic time difference calculations are required.

johndoe42377 6y ago

Dimension of what? In where? There is no dimensions outside your head in the first place. It is a superimposed abstraction, like a coordinate system.

herodoturtle 6y ago
Well said. And the best part of your phrasing is its consistency with simulation theory.

irthomasthomas 6y ago

"The more you move in space, the less you move in time" The consequences of this simple rule are rather shocking, as the recent nobel winner Roger Penrose pointed out. Take the case of two people on Earth, one stationary and one travelling past in a car. They each have different events which they consider the present. Now imagine that there is an alien government in Andromeda debating a possible invasion of Earth. To the person on Earth who is moving, the debate still going on, but in the reference frame of the stationary person, it's a day or so later in Andromeda and the invasion fleet is already on it's way. If there is no absolute reference frame, and both observers reference frames are equally valid, then the outcome of the invasion debate is a foregone conclusion. This is the crux of the Andromeda Paradox and the Reitdijk-Putnam-Penrose argument. https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argume...

sudhirj 6y ago
Is this actually a problem? By the time the person travelling in the car and the stationary person synchronise their information enough to communicate won’t their frames of reference also sync up? Like if I’m moving and I see something before you, won’t you see it as well before or at the same time I can tell you I saw it?
- irthomasthomas 6y ago
  From the wiki... "Notice that neither observer can actually "see" what is happening in Andromeda, because light from Andromeda (and the hypothetical alien fleet) will take 2.5 million years to reach Earth. The argument is not about what can be "seen"; it is purely about what events different observers consider to occur in the present moment."
  - sudhirj 6y ago
    But the entire point of relativity is that there’s no such thing as a joint “present moment” between more than observer. The only meaningful construct is your own present moment, about which information radiates outward at the maximum speed of information transfer in space-time (speed of light/gravity). Information reaches other observers based on their trajectory and position in space time. No such thing as the universal now.

sudhirj 6y ago

Didn’t see if this was mentioned in the article, but it was interesting to find out somewhere that for a photon time doesn’t pass even as it travels across the universe. Basically the time component is 0 so the space speed is 100%. That’s why I find it easier to stop thinking of the speed of light, and thinking of it as percentage of speed of information transfer in the space-time medium. Light (or rather electromagnetic waves) travels at 100% the speed of space, but it has no special treatment in the medium, and does so by travelling at 0% the speed of time.

slfnflctd 6y ago
I'm not sure if it's exactly the same thing, but I've heard the phrase, "From the perspective of light, everything happens at once". It's a bit unclear to me how light or a photon could have a perspective, but I guess it's not really relevant? This kind of thing is part of why I haven't taken a deeper dive into physics. The metaphors and allegories always break down if you look at them too hard, you really need to wade into the underlying math to get a real understanding I think.
- sudhirj 6y ago
  Yeah, that's really everything with all caps EVERYTHING, isn't it? From the beginning to the end of the universe, it would all happen in an instant.
- cellular 6y ago
  This perspective you mention is exactly why I made a video on the subject: https://youtu.be/A-2XQQDD6QQ https://youtu.be/A-2XQQDD6QQ It seems so simple to me now!
sheerun 6y ago
For photon time passes only for itself (because relative to itself it is not moving). Any interaction with photon (i.e. what we call "observing"), happens with t=0 from perspective of something that collided with photon, and normal time from the perspective of photon (which happens to be spatial distance from perspective of something that collided with photon).

jcims 6y ago

Here's a game that tweaks the speed of light to help make it more tangible - http://gamelab.mit.edu/games/a-slower-speed-of-light/ http://gamelab.mit.edu/games/a-slower-speed-of-light/

mikewarot 6y ago
I found the game quite interesting, and unfortunately nausea inducing.. 8:30 to get all the orbs.

Geee 6y ago

Does everything really 'move' in time? I thought that time is like a film, where nothing moves except the observer. I'm not sure which way it is. If we travel back in time, the universe is still there, and not moved to the future. Also, I never understood the grandfather paradox. If I travel in the past and change something, wouldn't the change propagate in time at the speed of light? And it would take a long time before it overwrites the original time.

yathern 6y ago
I have a couple of things to say here that might clear things up! > I thought that time is like a film, where nothing moves except the observer. We are not merely observers of the universe - we are part of it. When we change where (or when) we are in the universe, we change the universe itself. > Also, I never understood the grandfather paradox. Instead of the "go back in time and kill your grandfather" idea, lets keep the scale smaller. Let's go back in time 1 minute, and then smash our time machine. Now, there are two "me"s in this timeline. But energy and matter can't be created out of thin air! Maybe it took a lot of energy to send me back, but that was in the future, and that future is gone, now that our time machine is smashed. We could very well send gold bars back a minute, and double our money! The way you typically resolve this paradox is through keeping infinite timelines. In our example, there's a timeline where we disappeared off the face of the earth, and a timeline where there are two "me"s. They each continue independently. But if there is only a single timeline, we can do all sorts of paradoxical things. > If I travel in the past and change something, wouldn't the change propagate in time at the speed of light? The speed of light is measured in meters per second. Time is measured in seconds. I'm not sure I'm clear on what your suggested propagation looks like.
- Geee 6y ago
  Well, I'm not sure actually. It seems to require more dimensions for causal events to 'propagate' in time. I was thinking that events can't change the future instantly, because information can't travel faster than speed of light (which is the normal passing of time). So if I travel from million years from the future, it should take million years for the change to propagate to my original future.

jl2718 6y ago

Let’s say we’re in the middle of a black hole. Some supernova event sends us toward the horizon with a bunch of mass, but it’s also getting sucked back in. Space-time starts out looking like a dish and then begins to form a vortex as mass gets sucked back in. It looks like we are accelerating away from other masses. The red shift keeps increasing. Then at some point we are back at the singularity orbiting at the speed of light and now the Schwarzchild metric gives a negative dt^2 due to the combined effects of gravity and velocity, so we can get rid of the negative sign in Minkowski space if we accept the singularity as the normal state of things.

hateful 6y ago

> your motion through the x dimension in space, for example, is completely independent of your motion through the y and z dimensions. But it does, if you're moving at a constant speed... just like you're moving through time in...

crazygringo 6y ago

Meta discussion -- and not a criticism, but why does Forbes publish something like this? It's not news, it's like a short physics chapter for motivated high school students. Not that I'm complaining at all, it's just a surprise. Is this part of a series of articles or something with a unique purpose? Curious if Forbes is on some kind of educational mission or something.

Steuard 6y ago
This is an entry from the "Starts With A Bang" blog. I think the author(s) (is it mostly just Siegel?) post regularly about physics/science topics, including newsworthy stuff, but clearly also sometimes just post about general cool ideas.
humanistbot 6y ago
A while ago, forbes.com went from being a digital version of their print publication to basically the same blogroll model as the Huffington Post. Thousands of "Forbes contributors" who are not on staff at Forbes get to have their blogs hosted on forbes.com/sites/username. Those articles never make it into Forbes magazine, but the authors get a pittance of revenue from ads and get to claim they write for Forbes.
- solumos 6y ago
  Some contributors actually pay to publish.

pontus 6y ago

If you want to learn special relativity, I highly recommend this course from Brian Greene: https://worldscienceu.com/courses/special-relativity-world-science-u/ https://worldscienceu.com/courses/special-relativity-world-s...

pontus 6y ago
It has tons of great interactive widgets that you can play around with to gain some intuition around things like time dilation, length contraction, simultaneity etc.

tzs 6y ago

There are a few episodes covering similar material on PBS Space Time [1], if you want to go into a little more depth. Space Time episodes are short (typically 10 minutes or less), so this makes a great thing to watch when you have a little time to kill. If you want to play around with time dilation and length contraction in special relativity, I wrote a web-based calculator to help with that [2]. You can enter the relative velocity of two aligned frames that are moving along each other's x axis, and it gives you a series of rows representing events. The frames are called "your frame" and "their frame". Each row has 4 numbers, x and t of the event in your frame, and x and t of the same event in their frame. When you enter any two of those numbers, it updates the other two. For example, you could enter x = 3 in your frame, t = 5 in their frame, and it will update t in your frame and x in their frame so that x and t in your frame and x and t in their frame refer to the same event. The README gives an example of how you could use this to figure out the famous ladder paradox. [1] https://www.pbs.org/show/pbs-space-time/ https://www.pbs.org/show/pbs-space-time/ [2] https://github.com/tzs/Physics-special-relativity-calculator https://github.com/tzs/Physics-special-relativity-calculator

6gvONxR4sf7o 6y ago

I’m disappointed by this article. From the title, I expected it was a new development. Instead, it’s what you’d find on any discussion of space time. A Spacetime Surprise: Time Is The Easiest Dimension To Waste With Misleading Titles.

kgwgk 6y ago
I agree that the title is very strange. To the extent that anyone has ever said that time is "just another dimension" it won't be in conflict with what the article explains.

dfilppi 6y ago

The foundation of the article is false. There is no 'space'. There is only spacetime.

sheerun 6y ago
The same way X direction can can be arbitrarily defined in space, the time can be arbitrarily defined in spacetime (so called "frame of reference"). Other 3 directions parallel to time are called space.

justincredible 6y ago

It's left as an exercise for the reader to reconcile the headline and the initial premise.

SAI_Peregrinus 6y ago

> After all, the shortest distance between two spacetime events isn’t a straight line any longer. That's wrong. It's still a straight line, just along the geodesic of the local spacetime. It looks curvy if you bend and flatten spacetime into a Euclidean space, but that's because you bent it! Light in a vacuum always travels in straight lines. Gravitational lensing isn't gravity bending the light, it's the light traveling in straight lines through highly curved space.

mountainboy 6y ago

Time is simply a measure of matter in motion. Every clock ever invented measures... matter in motion. There are only 3 spatial dimensions. You're welcome.

danwills 6y ago

I reckon this phenomena could kinda be phrased like this: Moving through space takes up your turns, when you're moving really fast, most of your turns are taken up by moving (so there's less turns left for the operations of ordinary matter, which we use to measure the passage of time, so it seems slower).

danwills 6y ago
Time most certainly is not a dimension (or even very dimension-like, in general) in my opinion. It structures the orderings of events, more like some ultimate process that all other processes are hanging off (are a part of). The complexity in the ordering could be irreducible at any given point, depending what is happening there, and that includes fully non-reversible processes. To me, this is time's arrow.

xtiansimon 6y ago

I LOVE when science is explained as if you're talking to child. Or even a high school'r with algebra under their belt. And then this happens... > “...you can’t put space (which is a measurement of distance) and time (which is a measurement of, well, time) on the same footing...” ...two parentheticals followed by dippy do metaphor 'footing?' Feet? I’m only half kidding. The article's first 50% starts in the best of ways, ‘shortest distance between two points’. After ‘feet’ it’s all down hill-- > “the faster you move through space, the slower you move through time.” Well. Of course. Every school child knows this is true. When the kickball is heading for your face, time stands still. But slow down a minute, walk me through this as carefully as you did for the two-points... > "But as you approach the speed of light" Never going to happen > "— or rather, ..where the relative speed between you and it is close to the speed of light — you’ll observe that it’s contracted along its direction of relative motion..." It relative that it and it's--WHat? There was distance between two points and now I have 'relative speed'. What the heck is that that I should be able to call it an it so quick?? I could go on, but my point--Why, once the subject becomes actually difficult to understand, does the author's explanation becomes worse? More parenthetical. It and that. And tries to put me in a position to imagine moving at the speed of light or a clock "defined by light bouncing back and forth between two mirrors". Huh. What? Great start. Poor finish. Maybe if you thought less about name dropping Einstein, I could appreciate what is relative speed between two anything. I agree, this curious piece of math and science could use some popular updating. /END RANT