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.
This is not really an accurate analogy sorry.
What is really happening is that everything (atoms etc..) are made of fields in which disturbances/patterns travel at the speed of light. When an object is moving through space, the fields have to move extra far to cover the distance through space, as well as to do the usual oscillations/vibrations/movements that give timing effects. This is where time dilation comes from. It's best understood with the reflecting-mirror-as-clock thought experiment.
To add to my comment: If you really want to understand relativistic time dilation, you want to understand the bouncing-light mirror-clock experiment. It's even in the article. And it's not even an analogy, it's really why moving objects run slow. You can derive the exact special relativity time dilation factor from it.
The thing is, in this case, the actual cause of time dilation is reasonably understandable. There's no need to go off and invent some wild analogy. But apparently the average HN reader prefers a wildly inappropriate and ungrounded analogy to putting in a little time to understand the commonly accepted reasoning behind time dilation.
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.
> 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.
You should scale time proportionally to the scale of space. Let's call one complete orbital cycle of one thing around another thing a "year", and one spin a "day". For example, one orbital cycle of the Sun around the center of our galaxy is "galaxy year".
If we measure a human body at the scale of seconds, then we can measure position of the human with precision to single digit meters. It will behave like a particle.
If we measure it at the scale of days, then it will start to blur, like a quantum particle: 30% at home, 30% at work, 30% everywhere else, including the Moon. We can use probabilistic math at this scale, to describe this weird behavior.
If we measure human at the scale of years, then the human body will demonstrate dynamics and predictable trajectory: home -> school -> work -> home. We can even invent a math formula, which will correctly predicts trajectory for a human at average.
If we try to measure a human at the scale of galactic year, then our detector will fail completely, because humans are short living objects.
When you measure your particles, you measure it at particle seconds, particle days, particle years, or at much higher scale?
Thanks for this! Never thought about it this way, but it's a terrific perspective / way to frame and explain probabilistic measurements in an intuitive way.
The difference though is that for a quantum particle, there is no "particle second" in the sense that you can't measure exactly where it is however fast you try.
For example, it's impossible to measure distances shorter than photon wave length using photon stream, but it's easy to do using beam splitter and interference.
IMHO, you should look at this video, where water droplet at macro scale «exists in two places at once» (demonstrates self interference when passing two slits).
Our solar system is just a few galaxy years old. Our circles (I hope they will be circles) around Big Attractor and Shapley Cluster are just started, so we are at year one.
If we scale up infinitely, then we will see that our Universe is "forever young", frozen in time.
If we scale down, we will see more and more exceptionally stable "dead" objects, completely missing short living ones, so our Universe will look "forever dead" for us again. Anything interesting will happen at our own scale only.
ahh. let's call your spacetime water something that evokes these qualities...
"ether"!
(this is not meant to be substantive criticism of your idea; I just think it's funny how much this sounds like the 19th century concept of ether that was abandoned)
Do you see much difference between ether, which is presented everywhere in our Universe, and Higgs field, which is presented everywhere in our Universe? Quote from your link:
«To justify giving mass to a would-be massless particle, scientists were forced to do something out of the ordinary. They assumed that vacuums (empty space) actually had energy, and that way, if a particle that we think of as massless were to enter it, the energy from the vacuum would be transferred into that particle, giving it mass.»
I personally think of the water as space, rather than spacetime. I think time is a byproduct of space-mass interactions. I could of course be very wrong!
Space in [x,y,z], spacetime is [x,y,z;t]. It's math. Space represents the physical object, which is currently named as "physical vacuum" (literally "physical emptiness", where "physical" means that emptiness is not empty). It's hard to say what is represented by spacetime in math models.
> 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.
I find it much easier to picture in relation to the unit circle. We're always moving at the speed of light, it just depends on whether that's at 1 second per second, 300,000 km/sec, or somewhere in between.
I am not sure how accurate that analogy is, ( I guess most analogy are not made to be 100% accurate anyway ) but it explains the problem or help creating the image in my metal model far better than any thing else.
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.
"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_argume...
I don't think I understand what's shocking about this. It's like saying that for somebody who watches a taping of a soccer match the result is not yet known, yet for somebody who watched it live it's a foregone conclusion. I don't really get what's the paradox here.
Or maybe more to the point: if you were watching a soccer game Earth from Proxima Centauri, you could only get the result about 4 years after the game took place on earth, so for you the issue is uncertain while for somebody on Earth "at the same moment" the result has been known for years. But of course then the whole concept of "at the same moment" is pretty ambiguous and fuzzy.
I think it's still surprising, if not "paradoxical" (obviously it's not paradoxical if it's reality).
The difference is: in your two examples we know there's a delay, and all you did was say that some people will know the result before others who are receiving the delayed result.
What the original question is saying is that you can't ask "well, what is happening right now on Proxima Centauri?" since the very question of "now" is not specific. I think that's quite different.
On Earth, with Newtonian physics, we intuitively think that "now" is shared, so we really can say "I wonder whether someone has scored a goal now," and the answer shouldn't depend on whether you're in a car or not.
>On Earth, with Newtonian physics, we intuitively think that "now" is shared, so we really can say "I wonder whether someone has scored a goal now," and the answer shouldn't depend on whether you're in a car or not.
That's insightful, and actually it made me realize that it's probably true that nowadays we expect information to be available worldwide effectively instantly, but that obviously wasn't always the case. "Right now" we're having this discussion on Hacker News with people from around the world, but merely a few decades ago this type of simultaneity wouldn't have been possible. Nothing of what would could've done locally could've immediately influenced dozens of people around the globe.
This shared "now" is effectively a modern invention.
I think the unusual part is that it is not a limit of communication, it is time itself. With a tape, you know that it happened in the past, for this, both are experiencing their real present time, but they don't agree with each other.
The notion of “at the same moment” is not ambiguous and fuzzy. You use clocks and synchronize them. What relativity adds to the picture is the requirement for a common reference frame, which is surprising. It creates paradoxes because our intuitive notion of “at the same moment” does not include the reference frame, so there is a conflict between our intuitive understanding of past/future (which does not change whether you are moving) and the relativistic description of past/future (where two people can disagree about whether a particular event is int the past or the future).
Because of this disagreement, if you had FTL communication and wired it up so you could make a phone call to Andromeda, your phone call would arrive before or after the debate depending on your reference frame on Earth, and you could use it to send information backwards in time.
Synchronize the clocks how? Last I knew, this was still impossible, unless you employ hand-waving.
If I synchronize two clocks next to each other, and then move one away, they are no longer synchronized as one was moving. And we still don't have the speed of c one way, so you can't use that either.
> Last I knew, this was still impossible, unless you employ hand-waving.
I think you may be thinking of synchronization as perfect synchronization for ideal clocks. If you go down this route everything becomes impossible. Instead, think of synchronization as assurance that the maximum error is below some known bound. In general, the bounds can be made quite low.
This is not intended as sarcastic, but you solve the theoretical problem by making it a practical problem?
If 2 clocks are out synch, but only to a small amount that doesn't affect my ability to meet someone for dinner, that doesn't mean they are in sync.
I agree that if you go down this route everything becomes impossible, because at some point you're talking about Planck time, which thankfully we don't need to meetup for dinner.
> This is not intended as sarcastic, but you solve the theoretical problem by making it a practical problem?
I think this is based on some false idea that error is somehow “not theoretical” which makes no sense. There is a rich set of about error and even an entire field dedicated to its study (statistics). The only reason we are interested in theories in the first place is because the theories correspond to the real world. If you have some theory about time which cannot be measured, or cannot explain errors, then that theory belongs in the garbage. (Think about this: if your theory cannot explain errors, but any actual experiment produces errors, then any actual experiment will demonstrate that your theory is “wrong”.)
Or consider other concepts like “flat”. What does it mean for a surface to be “flat”? No matter how flat a real surface is, it will never be mathematically flat. So either we have to throw away the word “flat” and stop using it outside mathematics (which is a stupid idea), or we define “flat” to mean that a surface is within some deviation from mathematical flatness.
You can’t escape error, even in theory, unless you leave the world of physics and do pure mathematics.
Its not impossible. Civil time is just this, in fact.
Its true that if two observers use their own local atomic standard to precisely measure elapsed time then they would have difficulty agreeing on when something happened. However, that's not how civil timekeeping works. One clock declares itself to be a master clock and broadcasts a time+position standard to everyone else. Other observers then construct their own PLL to compute a running estimate of the total phase shift between their local time standard and the one that is broadcast.
In effect, received civil time has a velocity relative to your local atomic time. If every observer can label their observations with civil time then the paradox disappears and you are left with information flow that is bounded to the speed of light. A fast-moving observer has a local atomic standard of time that moves at one second per second, and a received civil time that appears to be running much faster.
A peer-to-peer version of this is how we define international atomic time. Subtle variations in local gravity conspire to actually give the different clocks in the network a different local speed of time. They steer a global PLL to minimize the total squared phase error in the network. Each node in the network can make observations on the TAI timebase by adding its own clock offset to their local clock.
But you can calculate the difference, which happens with GPS satellites all the time.
GPS is based on synced clocks. Problem is that the satellites suffer the rules of relativity. But the good news is that we know the rules of relativity, and therefore can compensate for them.
I always thought relativity was purely theoretical, but it is actually practically applied in GPS sattelites.
It turns out there's some circularity in your definitions of "Move clocks at the exact same speed and acceleration in opposite directions" and "synchronized"; that's basically the definition of "synchronized", which is fine from a certain point of view, but from the point of view of examining the nature of space and time themselves, not adequate.
Long time Veritasium subscriber here. He actually made a great video a while ago explaining why professional Youtubers don't have much of a choice when it comes to clickbaiting with titles and thumbnails, because it's the only way to reliably get lots of impressions and views and grow their channel: https://www.youtube.com/watch?v=fHsa9DqmId8
It made me gain a bit of empathy for creators using these tactics on Youtube and tolerate it as long as it's not being used to promote content that's devoid of any substance, which is pretty much never the case for Veritasium videos or any of the other educational channels I subscribe to.
Yes, I understand and agree. It makes me sad as well but I've made my peace with it.
Nevertheless, I commented about this one in particular because when I saw the title card, I legitimately thought, even having seen many of his videos, that he couldn't possibly deliver on that. He got me; he did. I was impressed.
I don’t think this works either because you can’t meaningfully agree on when light was emitted from one of the clocks. The only solution should involve a single clock but then you are always measuring 2 way and not 1 way speed.
> I don’t think this works either because you can’t meaningfully agree on when light was emitted from one of the clocks.
You can in fact meaningfully agree. You put the clocks in similar reference frames (like “standing on the surface of the Earth”), and accept some small but non-zero margin for error. The fact that a spaceship traveling around the earth does not measure light pulses emitted by these clocks as simultaneous is irrelevant—because we know that the notion of simultaneity relies on reference frame. What we do get is that anyone standing on the Earth’s surface can measure the pulses as simultaneous, within the specified margin of error. This error must necessarily account for the the fact that time progresses differently at different altitudes and latitudes, if your clocks are accurate enough. Because General Relativity is an extremely accurate theory and we have accurate measurements of the relevant physical constants & the mass of the Earth, we can account for the different reference frames and run the clocks at the correct rates so they continue to be synchronized even when they are free running (again, with the appropriate margin of error).
If you are using ordinary quartz clocks, then the clocks probably have enough error that you can ignore relativistic effects. I’m assuming we want atomic clocks if we’re series about chronometry, especially considering how cheap they are these days.
The idea that synchronizing clocks is somehow impossible stems from an unrealistic idea of how people measure time in the first place.
The consequence you refer to is not a logical necessity based on relativity. It's just a particular interpretation, the "block universe" interpretation, which is not accepted by all physicists.
See here for a refutation of the argument referred to:
> relativity does away with the alternative, that of a universally accessible “now”
Relativity does away with "now" period--"now" is a frame-dependent concept in relativity, and frame-dependent concepts, in relativity, have no physical meaning.
As I noted in the article I linked to upthread, the physically meaningful division of spacetime, at some particular event "here and now" (like you sitting in your chair reading this), is into three parts, not two: the past light cone, the future light cone, and the spacelike separated region (what Roger Penrose, in the very same book where he presents the Andromeda scenario, calls "elsewhere"). The past light cone behaves like our intuitive concept of "past", and the future light cone behaves like our intuitive concept of "future", but the spacelike separated region does not behave like anything our intuition is familiar with. The whole "Andromeda paradox" argument is based on failing to recognize that the spacelike separated region exists in relativity and doesn't match up with our intuitions about either "past" or "future".
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?
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."
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.
Which circles right back to the paradox. The moving persons reference frame has aliens still debating an invasion, and the stationary persons reference frame has the aliens already on their way. How can there be any room for free will in the deliberations of the alien government, if the timelines of both observers are equally valid? The article on relativity of simultaneity has much more detail on the subject https://en.wikipedia.org/wiki/Relativity_of_simultaneity
For there to be a paradox, the observers would have to find out about it sooner than it would take light to communicate the result.
Otherwise, the earliest time that the aliens can find out if they're going to invade or not is when they make the decision. Sure, the observers can find out, and try to tell each other and the aliens, but since it takes at least a round trip of light from the aliens to the observers, the observers always find out after the aliens have made up their minds.
If the aliens find out that they make the decision when they make the decision, it seems to me at least that they actually made the decision rather than having it be predestined
The two people would perceive the changing of a traffic light on the same street at almost the same time - why would it be different for the Andromedans?
Welcome to the ancient times. The speed of information travel has always been capped but now we know that there is absolute upper limit - c. It still works on earth, now is not shared, but for most practical purposes the synchronization delay does not matter, except when it does like stock and sport betting.
I think about this like this. The universe is always in exactly one state but for each inside observer the knowledge about this state depends on its location.
Is the person in the car moving away from or towards Andromeda?
The example you gave can be interpreted two ways and my intuition tells me that the example is only true in the case that the car is moving _away_ from Andromeda.
Is it also, weirdly, the case that if the car is travelling towards Andromeda that time slows down sufficiently that they perceive the outcome of the debate _after_ the person standing still?
I'm fairly convinced this is intellectual masturbation. I think two situations are being confused for one another:
a) If you travel close to the speed of light, causality goes more slowly (e.g. a clock ticks more slowly) than it does for someone who is stationary. So, two clocks will diverge. This is true, AFAIK.
b) If you travel close to the speed of light, and somebody else is stationary, they are traveling "into the future" relative to you, whereas you are "in the past" relative to them. I believe this is nonsense. But, I believe this is required for the "Andromeda Paradox" to hold. Thus, I don't think it holds. (BTW, we know that paradoxes never hold, so there must be something wrong with it.)
The solution to the Andromeda Paradox that I am proposing is to say that there is one universal ordering of events (among both observers and the Andromedans), but the two Earthling observers have different times on their clocks at the particular point in the sequence of events where the Andromedans decide to invade.
>The solution to the Andromeda Paradox that I am proposing is to say that there is one universal ordering of events
Proposing this is fine, but proving it is quite a matter altogether - you have to replace special relativity. Special relativity pretty much explicitly states this isn't the case, making an exception for events that are causally connected, but there's been a slew of experiments over the past several decades that call into question even that exception at long distances, and more recently, even ones for local observers, e.g. https://advances.sciencemag.org/content/5/9/eaaw9832
Personally, I'm in the Rovelli and loop quantum gravity camp - time probably isn't actually a real thing on its own, and what we perceive as time is just an emergent property of thermodynamics.
To be clear, my conception of a "universal ordering" doesn't mean we can always measure when things happen relative to one another. If two things are causally related, we know one happened first. If a tree falls on Andromeda "right now," I don't know if that happened before or after a particular timestamp here on Earth, but it either did or it didn't. (Same goes for all possible timestamps for all clocks going at whatever speed they are going; their timestamps will diverge, but they could still be ordered if we knew the speed they travel relative to light and the starting value and how often they tick, e.g. once per second nanosecond or whatever. So if we had an observer on Andromeda with such a clock, we could eventually order events there relative to events on Earth based on the timestamp they report, though it would take a very long time for their report to reach Earth).
Are you sure that's not compatible with special relativity? Genuinely asking. If not, is it possible to explain why it isn't? I'd like to know (but if I'm asking you to write a book, never mind).
When you say you're in the Rovelli and loop quantum gravity camp - is that compatible with special relativity? I'm guessing yes, but let me know.
I think time is an emergent property of causality. That sounds close to what you are saying (possibly a different way to say the same thing).
I agree! Time is emergent. It is only comparing one thing moving relative to another thing. Without anything moving relative to each other, time can't exist:
Yea, i think time is kind of used to define two different things and that seems to make these discussions confusing. I think if you are close to the speed of light, your atoms are moving slower than those of the stationary person and so your local clock time seems to stay constant while the stationary persons clock
time seems to speed up in relation. But it's all a matter of perception of clock time passing and now is the same everywhere.
I believe you are correct in that the closest you can get to change the order of two events is to make them simultaneous (in the case of photons, which do not experience time) but you cannot change one event ordering beyond that since that would violate causality.
You could change the event ordering by forcing some events to take a longer path through space?
For a real world example, we can predict supernovas because we've already seen them from another trajectory of light: https://youtu.be/ljoeOLuX6Z4 so we can both see the remote event before and after local events
Relative to a clock on earth, moving at a given speed relative to the speed of light, the supernova happened when it happened.
All that is changing with lensing is that you're seeing the light coming from it earlier looking in one direction than another. Either way, it happened in the past. The order of events is not changing.
It's like saying that a stock trader using a fiber connection figures out about a price movement more quickly than a stock trader using a dial-up connection.
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.
> There is a minus sign and the speed of light in front of time in the space-time metric.
Yes, that's called the Minkowski metric, and it's absolutely nothing new.
You can do the exact same physics with the opposite sign convention (called the signature of the metric), where time has a positive sign and all three spatial dimensions have negative signs; the only rule is that time has to be the odd one out, so rotations in a space-time plane obey hyperbolic geometry as opposed to Euclidean. You can get rid of the factor of c by moving to a different system of units, commonly called the natural units, where the speed of light is 1.
All of this is covered in any real introduction to Special Relativity, which, in turn, is at the beginning of any course on Modern Physics, as opposed to the Newtonian Physics.
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.
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.
"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.
> 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.
The math doesn't work unless time is different from the 3 spatial dimensions. In particular, distances in space-time can be negative, unlike distances in space.
Well, I'm just arguing that it isn't clear whether this prefactor (that shows up in the metric in front of time) is a property of time or a property of the metric. It is pretty clear that the math wouldn't work if the prefactor was different, though.
Given that there is a physical difference between events separated by positive and negative distances in spacetime, I think it's pretty clear that the prefactor is a property of spacetime.
Yes, it is mostly semantics but the question really is what you think the space-time metric is. In order to attribute the prefactor to time you would need to argue that the space-time metric really is Euclidean, but because time is different from space there is this negative prefactor showing up in the metric. But you can also claim that time and space are the same and the space time metric is hyperbolic. Since there is there is no good argument why metrics necessarily need to be Euclidean, I find the second option more convincing.
Not at all - spacetime is real, but it is not a 4-dimensional Cartesian coordinate system where all 4 dimensions are of the same kind. For example, for any two events that are time-like separated, any two observers will agree on the order in which they happen, whereas for two events that are space-like separated, there will be observers that see these two events happen in either order. Time is different from space, though they are related.
Note that if the space intervals are all zero and the time interval is unit time or 1, the spacetime displacement is equal to C. Thus when at rest physically we progress though the time dimension at the speed of light. Conversely if two points are separated by an interval equal to C, their distance in the time dimension is zero.
The latter result isn't really a surprise, we all know time doesn't pass if you're traveling at light speed, but IMHO it's interesting to see how it arises from the geometry.
> if two points are separated by an interval equal to C
If d = c, I don't think it determines the values of x, y, z, and t. What if x = 2c, y = z = 0, and t = 1? Unless I'm not following your logic correctly. In my recollection, for two given points in spacetime, d is invariant but the values of x, y, z, and t depend on the observer's frame of reference.
From the point of view of the photons, yes. From the point of view of everything else, no.
One of the bits of relativity that took me the longest to become aware of was that “right now” isn’t even meaningfully and universally defined within it.
What about my point of view? He said that if my eyes and the sun are separated by X light seconds, then X seconds later sun and my eyes are at time distance of zero
This is for an observer following a trajectory in space time. So for an observer covering a distance at light speed the time interval is zero. For other observers on different trajectories, such as stationary in the space coordinates, that will not be the case.
This seems odd because there clearly time dilation effects between two observers even when they are not accelerating but merely have a large difference in relative constant speed.
You seem to be saying that there has to be constant acceleration between observers for this effect to take place.
My apologies I really didn’t explain myself very well at all. That was quite confusing. This formula represents a trajectory in spacetime with respect to some frame of reference of an observer. As with any trajectory it has space and time components.
The x, y, z deltas are your displacement through space in those dimensions relative to some frame of reference (of an observer, presumably) and t is the time component. If the space deltas are all zero then you are at rest relative to that inertial frame. You are not accelerating or moving and your motion through the time dimension in unit time, according to this formula, is C. This is odd because C is normally thought of as a motion through space, but in this case your not moving through space (in the reference frame).
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. "
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.
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.
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.
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.
The last time someone brought this up I was surprised that I reacted to it. Knowing a thing and hearing it explained can be a different experience.
The presenter I’m thinking of offers us a self aware photon that is born in a star and then is immediately absorbed by a planet in the next galaxy. Or put another way, from the photon’s perspective it isn’t a vector so much as a line segment between two points.
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).
> 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.
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).
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.
Imagine one dimensional space. You are a point tracing some path in space over time. That’s how we experience it. But zooming out and looking at the path itself, you are not really a point (moving through space and time), you are a curve in space and time.
I’m not trying to talk about ideas of self or anything. Just that the same thing can be described in two ways: as a low dimensional thing changing with respect to another dimension, or a slightly higher dimensional object that just is.
Viewed as points changing over time, a solution to the grandfather paradox would be a remarkable coincidence, with everything happening to match up exactly as it had.
Viewed as curves in time, a loop is just a loop. There’s nothing remarkable about a circle. You don’t look at a circle and think “gee what a remarkable coincidence that this infinitely fine path crosses itself perfectly. You just go “yup, it’s a circle.”
Neither of these is a better picture than the other. Everything (things described as 3D things) does move in time. Everything (described as 4d things) just exists.
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.
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.
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.
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.
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.
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.
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.
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.
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?!
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.
Reading this entire thread (I didn't expect this many replies this detailed!), I think it finally clicked with me after all these years.
So, for me, in a vehicle moving at 90% of the speed of light, the time itself slows down such that I observe the photons coming out of my lightbulb still at the speed of light, right? Basically, it would adjust the t in v=s/t because the speed and the distance are to remain constant. And because me and my spaceship or whatever have mass, there will always be a bit of difference between my speed and the speed of light to accommodate this adjustment. That's just so weirdly backwards to think about.
Now, I wonder about redshift and universe expansion deduced from it. Wavelength is a frequency, right? And frequency, by definition, is how many times something (wave period) happens per unit of time. So maybe the universe isn't expanding after all, maybe it's just that time runs faster in the parts of the universe where this light comes from, and the photons just keep oscillating with the frequency that was "correct" in whichever reference frame they were emitted? Besides, the idea that universe expands seems silly tbh. There must be a more sensible explanation. Maybe time slows down over time (?!) and it just ran faster when the universe was younger?
If "time slows down over time" then we would still observe the light at its original frequency - why would the energies of the states of hydrogen atoms in distant stars change over time, but the energies of the photons emitted long ago not change?
How does this hypothesis account for the CMB?
Wikipedia has a nice summary of alternative cosmological theories (and why they are often dismissed by experts):
> Logically, it would be 190% of the speed of light.
The important point here is that this is is not "logically" but "intuitively", and it turns out our intuition is simply wrong. Historically, this was in fact the motivation for special relativity: we noticed that the speed of light does not obey Newton's relativity principle: if you fire two beams of light, one from the ground and one from a moving train, they will both arrive at a detector at the exact same time.
Having observed this concerning fact about the world, we now had to come up with a theory that explained it. The one we landed on was that speed is a number that goes not from 0 to infinity, but from 0 to c. This then must mean that accelerating an object from 0 to 1/3c is easier (requires less force) than accelerating that same object from 1/3c to 2/3*c, and that this difficulty increases the closer you get to c. The final theory in fact predicts that an object with mass can't even reach c, it's speed can only grow infinitely close to c. However, massless particles (such as the photon) do move with speed exactly c.
Note that we have since repeated this experiment with other particles of non-0 mass and confirmed that photons themselves are not special, c is indeed a limit. For example, electrons have some mass and don't move with speed c, and an electron fired from a moving train will arrive faster than an electron fired from the platform, but the speed of the speedier electron will NOT be V_e + V_train as Newton would predict, it will be (V_e + V_train)/sqrt(1-(V_e+V_train)^2/c^2) if I remember the Lorrentz transform correctly.
The other answers here attempt to "reason" it from the currently accepted formulas, but it's not how the humanity learned that there's no "190% of the speed of light."
The author of the article we all comment here wrote a book which, if I remember, covers that story in more detail (I linked to it in another post and I highly recommend it to anybody who wants to learn a bit more than when reading an article here or there or read some comments).
Just to give you some hints, the real story is not "reasoning" something but the experiments -- the experiments practically produced the results that, when analyzed, are still the best explainable by accepting that the speed of light doesn't change. See:
Michelson is such a genius, that even the most currently advanced experiments today use the same ideas that he used then -- LIGO is also an interferometer:
Learning from these experiments, even before Einstein, some important formulas we know today as related to special relativity were already developed by others:
In my mind, it simply can't go faster because you get fastest speed already, with light.
Just consider that you have this object, light, that will always travel at the fastest speed possible. You can approach that speed. But throwing light in front of you can not increase light's speed.
I'm not sure how right this is but I was told it's to do with time dilation. If you're moving close to the speed of light, stuff that isn't is experiencing way more time than you. As light isn't affected by time dilation it's still traveling at the same speed but now has much longer to do so. So from your perspective the speed of light seems to be 190% not because it's traveling faster than C but because it's traveling more C seconds per your second when your time is dilated.
Edit: on further reading perhaps I haven't even addressed your question...
If I had to hazard a guess I would say it's to do with light having no mass. Once it's emitted it's no longer in your frame of reference so your supposed speed is irrelevant to it.
I like to think that the universe is discrete, composed of "slots", like a big multidimensional array. If you imagine that the discrete universe has some kind of transition, where the properties of a given slot can be transferred to a neighbor slot, then the speed of light is the upper limit on the rate of change. Why does this upper limit exists? We don't know, maybe we live in a simulation, maybe the universe would no be stable enough without this limit.
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.
Part of your next conceptual step is realizing that the speed of the photons will measure the same to anyone, 100% of light speed.
In the vehicle, you'll measure the photons moving at 100% c.
Someone outside the vehicle as it speeds by will see the photons moving at 100% c - as you approach and as you move away. Other parts of spacetime change to accommodate this, effectively.
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.
(in case you didn't know - we're talking mainly about special relativity here, which applies in situations where things are not accelerating; general relativity is a broader theorem that also accounts for acceleration and gravity, and is much more involved)
In our daily life we have a handy stationary frame of reference - the Earth; it's therefore intuitive and normal for us to think about speed in an absolute sense. In reality though, speed can only ever be measured relative to some other point, so if you're an astronaut freely floating in space, you can't make any definitive statement about your absolute speed because there is no such thing.
Another thing that we are used to experiencing is a uniform flow of time - you and I can both synchronize our watches and believe that we're reading the same time even if we're on opposite sides of the globe. This is in fact only true in a very limited set of circumstances, and generally speaking not the case. Just as there is no such thing as absolute speed (or more properly, velocity), there is also no such thing as absolute time.
Special relativity stipulates that light always travels at c in every reference frame; this is not a discovery of relativity but a prerequisite of it, and a key insight that allowed Einstein and friends to explain things that had previously been inexplicable. The explanation for this, as others have commented, comes from general relativity, and is due to the interconnection between space and time - space-time - such that every non-accelerating thing is moving at the speed of light through time (whatever that means). The speed of light is therefore not so much the speed of photons, as it is that photons move at the speed of time. Something like that I think - this is beyond the scope of my brain to explain!
So why aren't your photons moving at "190% the speed of light"? In our normal life, we think of time as fixed, and velocity as variable; in reality, the speed of light is fixed, and time is the variable. What changes for a 'stationary' observer is not the speed of the incoming photons, but some time-related factor - their frequency. This is (a simplified explanation) of redshift, that led Hubble to theorise that the Universe is expanding. Everything is moving away from us emitting light, and since the velocity of light is fixed, it's the colour that appears to change.
A note about the notion of velocities adding up - in fact they don't ever, exactly. That they appear to is an approximation due to the enormous velocities needed before you would notice any difference. This is another consequence of relativity. Likewise synchronizing clocks - we can get so close that we couldn't measure any difference, but it would be insanely impractical to set and keep totally synchronous time.
(source: physics-related undergrad some years ago - I stand to be corrected on any of the above :-)
> 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.
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.
> 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.
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.
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.
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 :)
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).
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.
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.
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.
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 -
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
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.
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.
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.
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.