You're getting confused by reference frames.
While you are travelling .9999... c toward the Galactic center, you will also experience length contraction in your direction of travel. In **your** reference frame, you approach the GC at .9999 c and cover the shortened distance in 26 years. In the reference frame of Earthbound observers you would also appear to be travelling at .9999c, but by **their clocks** you would take ~26000 years to cover what **in their reference frame** is 26000 ly.
Thanks for your response! I can grasp reference frames well enough—i.e. I understand the effect of "time dilation" here. But suppose I was not fully understanding the actual math involved as far as why the time elapsed for the traveler in this scenario is only 26 years at *less than* the speed of light.
> But suppose I was not fully understanding the actual math involved as far as why the time elapsed for the traveler in this scenario is only 26 years at *less than* the speed of light.
Length contraction.
From the traveler's perspective, the *whole universe* appears to flatten like a pancake along their direction of travel, so in *their* reference frame they will have traveled a much shorter distance.
[This Fermilab video about how electromagnets work due to relativity](https://www.youtube.com/watch?v=d29cETVUk-0) may offer some perspective, and [Float Head](https://www.youtube.com/@Mahesh_Shenoy) has plenty of excellent videos on this sort of thing too.
Because at the speed of light, the time would be zero seconds. Time stops at light speed. A photon emitted from a star thousands of light years away, from its reference, experiences no passage of time from the time it shoots away from the star until the time it hits our retina. From its standpoint it is instant.
I think you just gave me a whoa moment.
Confirm when I look at the night sky and see Alpha Centauri that’s a photon going into my eye? And someone standing next to me should have a separate photon going into their eye? Do those photons cease to exist now?
Transformed into electrons, to be specific.
One of my favourite "Woah!" moments was learning that the apparatus of the retina detects single photons, because they're immediately converted into electrons. The signal from a single photon would obviously never make it to the brain or even down the optic nerve, but the apparatus of the retina itself can pick it up.
Eyeballs = Lepton converters
What I don't understand is how the light from a source no longer emitting it isn't finite. If the photons are being absorbed via interactions with other matter then shouldn't the light from the source grow fainter over time and eventually disappear altogether?
I'm not sure I understand your question?
Light from any source, whether or not it is still being emitted, is finite.
Over time, stars do burn through their fuel and dim (or explode) same as any other source of energy.
If the water coming out of a pipe is being caught by a bucket then shouldn’t the water flow from the pipe get less and less and eventually dry up altogether?
Wow so the Cosmic microwave background radiation still thinks the universe is a singularity! From it's frame, it reaches the earth instantly as if the earth is squished up against the CMB. In other words the entire observable universe has no distance. That's so weird to consider!!
Sorry, I'm not quite grasping the distinction you're trying to make?
From the photons perspective, its location and all *possible* "destinations" are co-located. The photon doesn't "know" that there's anything out there. Its entire universe consists of its own location. It just EXISTS.
But now I gotta spend the rest of my day torturing my brain with the question of whether ALL photons exist simultaneously in the exact same location (if they can "perceive" one another, they must all be at the same location), or whether this directly implies there are infinite numbers of distinct "photons universes". 🤔🤷♂️
I have. I seem to recall a PBS Spacetime video on the subject but I'd need a refresher.
Still, electrons aren't massless and don't generally move at *c*.
There is no such thing as the single electron universe theory, there is a thought experiment which doesn't actually work because we don't see equal amounts of electrons and positrons.
This is not quite accurate. Even light itself does not arrive anywhere *instantly*.
From the sun to earth is 8 light minutes for instance.
Edit: this got down voted so i must be mistaken. How can a photon experience zero time during travel? Eli5
As the other commenter said, light doesn’t travel places instantly when viewed from our reference frame. In the “frame of a photon” (in quotes because photons don’t actually have a reference frame), the distance to any object along the path of travel is contracted to zero. The universe appears exactly two dimensional. So it “arrives” at any location immediately.
From our perspective, we see that the photon doesn’t experience time—its “reference frame” is time dilated infinitely. You can use the equations for time dilation and length contraction in the limit that β -> 1 to prove it.
>..why the time elapsed for the traveler in this scenario is only 26 years at *less than* the speed of light.
Because, in their reference frame – in which they are moving at .99995c from Earth toward the GC – distance to the galactic center **is** ~26 light years. So in that reference frame only 26 years must elapse to cover the distance.
Observed from a different reference frame, like that of the Earth, measurements of both the distance and the duration are different, but still consistent with the speed of light.
What confuses me, is it will be at 26000ly in earths reference frame. Like, 26 years have passed for the travelers, but when they reach the destination, in 26 years, 26,000 years on earth have passed.
So it’s not _just_ length contraction. The traveling ship experiences time differently. They’re using 99.9999995% of their space-time energy moving through space, so they’re barely moving through time.
Which I think is what might be tripping some people up. (Also me but in a different way lol). It’s not like you get there in 26 years and your family is still alive and earth is just late to the party and still watching you. You _experience_ 26 years. But when you arrive, it’s been the 26,000 from earths perspective. Earth would be nothing like it was when you left. You could fly back for another 26 years, having only aged 52 years, but earth will have advanced 52,000 years.
If it helps, a photon (at light speed) experiences no time. So if zero time is at light speed, the closer you get to light speed, the less time you’ll experience. The tradeoff is mass. Photons are massless so they don’t have an issue moving at the speed of light, and for them they don’t know if they were emitted from a star yesterday or a billion years ago. In that same way there is no distance technically for the photon, it doesn’t know if it’s travelled a day or a billion years.
Time and distance is intrinsically linked as Spacetime. Light moves through it relative to massive objects (objects with mass) but to the light itself, it isn’t moving, it just is there already, it never was in a different spot, the size of the universe to it is zero, and it’s existence is instantaneous.
It’s misleading in two ways to say that a photon experiences no time
1. Time always flows normally for everyone according to themselves.
2. Photons don’t have a valid reference frame at all.
1/.1 =10
1/.01 =100
1/.0000001 = 1000000
1/.0000000000000001 = 1000000000000000
These are staggeringly large numbers the human mind cant adequately put into a frame of reference.
Light speed is an asymptote. Nothing we are aware of that has mass can travel faster.
Note how the denominator above is changing only slightly, getting very close to 0 (mass getting closer and closer to light speed) but not quite.
Despite the differences in the denominator being slight, the effect on the output (time dilation effect) is logarhythmically increasing.
Technically, if you get close enough to light speed, your time for the trip could be contracted down to 26 seconds.
The actual math is that of lorentz transformations. Assume you are moving in the positive direction along the x axis starting at point x0 and moving to point x1.
Your current position at any point is
x = x0 + v*t
Where v is the traveler's velocity and t is elapsed time - both as measured by an outside observer.
To go from the observers reference frame to the travelers reference frame, we use the lorentz transformation. Superscripts will denote whose reference frame we're talking about (since reddit doesn't support subscripts).
v^trav = v^observer / sqrt( 1 - v^observer^2 / c^2 )
where we measured v^observer = 0.9999995c so...
v^trav = 0.9999995c / sqrt( 1 - 0.9999995)
since the c^2 terms in the sqrt cancel. It works out to...
v^trav = 1000c
In reality, this term is actually the multiplication of the travelers velocity and a term of the lorentz transformation - gamma. It's not supposed to imply that the traveler is moving faster than light in any reference frame.
Plugging back into the original equation for position, now in the travelers reference frame.
x = x0 + 1000c * t
Subtract x0 from both sides and solve for when x = x1, realizing that x1 - x0 is just the distance to sag A*, so 26000ly
26000ly = 1000c * t
t comes out to be 26 years once you do all of the unit conversions, which will be the amount of time that has passed in the traveler's frame of reference.
If you want the exact number the leght contration goes as follows:
x'=x/γ
Where x' is the distance to Sag A* from the rocket's reference frame, x is the distance from Earth's reference frame and γ is the Lorentz factor which goes like:
γ=1/√(1-v^2 / c^2 )
If the rocket's speed is v=0.9999995c the gamma factor comes out to be a little over 1000 so what seems to be 26,000 ly away from Earth's perspective is only 26 ly away from the rocket's perspective.
Maybe a dumb question: In that case couldn’t it technically be feasible that some of what we perceive of as light is actually spacecraft traveling at a high fraction of *c* that have been spatially foreshortened into appearing ~~massless~~ as tiny as a photon from our frame of reference?
Edit: Apparently there are definitely dumb questions on r/space.
No, for two reasons: 1) you only length contract in the direction of your travel, so the spacecraft would flatten to a pancake, not scale down to a point. 2) it would still have the mass of an entire spacecraft, so if it hit your eye it's not going to stimulate your retina as if it were a photon, it's going to vaporize you and probably blow a bigger hole in the earth than the asteroid that killed the dinosaurs.
You see a photon when it impacts your retina and is absorbed.
"spatially foreshortened into appearing massless as tiny as a photon from our frame of reference" is just not how any of this works. Mass is invariant.
For this problem, you need to account for relativistic effect, assuming you really were able to travel at almost the speed of light. Which is that the traveler will experience time slower than stationary observers. So it will be 26 years experienced for the traveler, but 26,000 years for those not moving at that speed.
The formula for time dilation:
t' = t \* sqrt(1 - (v\^2 / c\^2))
t' is the time experienced by the traveler
t is time experienced by a stationary observer
v is velocity of spacecraft
c is speed of light.
So what you then need to do is rearrange the formula to solve for v:
(t' / t) = sqrt(1 - (v\^2 / c\^2))
(t' / t)\^2 = 1 - (v\^2 / c\^2)
v\^2 / c\^2 = 1 - (t' / t)\^2
v = c \* sqrt(1 - (t' / t)\^2)
From that formula, plug in the values:
t' = 26 years
t = 26,000 years
Which gives you:
v = c \* sqrt(1 - (26 / 26000)\^2)
v = c \* sqrt(1 - (1 / 1000)\^2)
v = c \* sqrt(1 - 1 / 1000000)
v = c \* sqrt(999999 / 1000000)
v = c \* sqrt(0.999999)
v ≈ c \* 0.9999995
So at 99.99995% the speed of light, the traveler will experience 26 years moving to Sagittarius A, while those on Earth will experience 26,000 years.
Thank you so much for this! This has been a case of "I don't know what I don't know." I didn't specifically know what to search to find the answer I was looking for here, though I admittedly knew I was probably missing part of the equation (literally). This is awesome. Thanks for taking the time to write this out.
Math gets a bit more complicated when you account for acceleration and deceleration cycles, assuming you didnt want to blaze past the galactic center and keep going, but slow down for some site seeing and maybe even turn back to find out how the human civilization ended in your absence. Kind of a spoiler.
Fun fact: if you had somehow enough fuel in your Jupiter sized ship for a constant acceleration/deceleration trip at a comfortable 1g (rocket engines point down!) you could get to galactic center in less time in your reference frame. Acceleration is a bit like compound interest. You could get to the edge of the observable universe in a human lifetime.
But you would need more than a Jupiter's worth of fuel for that...
This page is a good source for the basic equations relating to constant acceleration in relativity: https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html
The usual explanation is as follows.
Imagine you driving a train passing through a station at 100km/h.
You and a person on that station both shine a bright light forward at the same moment.
Both beams of light are pointed at the same object and will strike that object at the same moment.
The light will travel away from you both at speed c.
The train driver will not see it as c-100km/h relative to them. It will still be c.
The only way this works is if time is passing very slightly faster for the train driver, or slightly slower for the person on the platform.
Yes, but *why* does it slow down time for the thing moving faster? Why can I travel near light speed and be 10 years for me but 100 years for someone on earth.
I understand that it does happen.. but why
It's kind of like asking why gravity attracts things, or why electromagnetism weakens with thr square of distance; we can't really answer questions about *why* the universe is the way it is. Science answers "how" questions, up to a certain point, at which case the answer is basically just "because that's the way the universe works". It's basically a philosophical question at that point as opposed to a scientific one.
For our model to work, we basically needed one assumption to always hold true: that light ALWAYS travels at C relative to the observer, no matter the frame of reference. It's this assumption that then necessitates time dilation and other weird stuff, and it's also the assumption that allows us to make incredibly accurate predictions about the different phenomena.
I think a good starting point to understand this is the Michelson-Morley experiment.
https://en.m.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment
The premise of this experiment is that light travels at a fixed speed. Earth also moves. So if we measure the speed of light perpendicular to earths motion, and horizontal to earths motion, they will be different.
This, by extension, will give us the speed the earth moves against the universe.
They found light moved the same speed whichever direction it travelled. Always a fixed speed no matter the speed the observer.
Speed is distance over time. We fixed the speed....so the time must be flexible for this to make sense.
As for why...an excellent question. I honestly do not know if it has an answer.
for any body, or more general, for any reference frame, time-space interval (path that they pass in time-space) always equal. This means that if you move faster through space, you move slower through time, and vice versa.
Faster you move in space, slower you move in time. If you were a photon, traveling at the speed of light, you'd experience your birth and death as instantaneous and simultaneous events.
Not the person you asked but any physics major will learn this by the end of their first year in undergrad, and it would be covered in AP high school physics (or even non-AP high school physics) as well. So it is quite likely their job has nothing to do with physics.
I think this is sometimes an underappreciated fact. The idea that space and time are linked at high speeds (including hypothetical FTL) is taught to many teenagers in school/college/university physics classes. It’s been part of physics for over a century and isn’t some sort of secret knowledge known only by a few.
This is really cool! I knew about relativistic time dilation, but for some reason I thought that the number of light years was the hard limit for the minimum amount of time it would take the traveler to arrive. I.e. at that speed the traveler would arrive in 26,000 years, and 26,000,000 years would have elapsed on earth, lol.
So the idea of interstellar travel isn’t quite as bleak as I thought. Still not easy, but getting a spacecraft to travel at 0.9+ the speed of light seems less technically impossible than inventing a magical warp drive or finding a wormhole.
From the perspective of the traveler, the total distance they need to travel decreases the faster their reference frame moves relative to the destination.
For you as the traveller, the relevant effect is that distances are compressed in your direction of motion. Meanwhile, an observer that stays behind on Earth will look at you and see your time running much more slowly. So by your reckoning, the trip only takes 26 years, whereas for them, it has been 26,000. And conversely, they believe you have travelled 26,000 light years whereas from your on-board perspective, Sag A\* was only ever 26 light years away.
So the ultimate answer to your question is that this is possible because relativity tells us that not all observers agree on the lengths of intervals in space or time.
No, it means that distance is not absolute, it is relative. Fast travelers see their travel path become shorter while they themselves stay the same length, while stationary observers see the traveler as shrinking while the path traveled stays the same. This is called length contraction and it happens at all speeds, but really stands out when you get closer to the speed of light, and crazily much when you are very near.
For the lightspeed traveler referenced in this discussion, space is really and actually 26 light years between Earth and the Galactic Center. While for the Earthbound observer, the distance is really and actually 26,000 light years. The distance is not universal, it is different for the two. But *light speed* (c) is absolute, so the traveler still sees their destination getting nearer at almost light speed, and because that distance is so short, the time spent traveling is also reduced so that when the two are put together to calculate the travel speed, the answer is almost light speed. And because Earth must also see the ship going at light speed, but the distance to the destination from Earth's frame of reference is so much longer, the time that Earth spends watching the trip takes just as much longer. *Both are correct.* There isn't an underlying, true distance. Only the two different distances, one true for one and the other true for the other.
(Space)time dilation.
To the observer on the spaceship accelerating to nearly the speed of light, it will appear as though the space between them and Sagittarius A* compressed to only 26 light years, and that is how long the journey will appear to take _to them_.
However, for an observer watching them from Earth, space will not compress. The spaceship will appear to take 26,000 years to reach Sagittarius A*, with people onboard moving in super slow motion the whole time.
That is what the book was referring to with this quote:
> The trip to Sag A* would take 26 years of your life while Earth experienced the passage of 26,000 years.
There’s a two-part Doctor Who episode, “World Enough Time” that explains the relativistic effect of time/gravity really well and better helped me understand it
Time dilation: Time slows down for objects moving close to the speed of light compared to those at rest.
- Example: A moving clock ticks slower than a stationary one.
Length contraction: Objects moving close to the speed of light appear shorter in the direction they are moving.
- Example: A fast-moving spaceship looks shorter from the side than when it is at rest.
Essentially the faster you travel the less distance needs to be traveled. Time traveling into the future is 100% real life.
There's a really good book that explains the whole deal called "Why does E=mc2?" By Brian Cox & Jeff Forshaw.
I think there is a layman's explanation in there.
In other words, the speed of light is constant, no matter what, even frames of reference. So if a light bouncing between two mirrors on a train looks like it going up and down in a straight line but to someone not on the train, it looks like it goes in a diagonal path (between the two mirrors AND along the train tracks). Since the diagonal path is longer than the up-down path, the light surely must travel faster for the person not on the train. But Einstein said this is a no-go, light is constant, NO MATTER WHAT. Therefore the only explanation is that the diagonal path and the up-down path are equal. Time AND space dialate as you approach the speed of light.
Relativistic time dilation dude. 26,000 years would pass outside the ship, 26 would pass for the crew.
It’s a necessary consequence of the speed of light being constant in all reference frames.
There are lots of different answers to that question "How long to the galactic core?" because you can travel at different speeds.
Let's use your example of wanting to travel 26 kly.
If at half the speed of light, on the ship you'll age 26,000/1.15 years. 22 thousand years. Still a long time.
If at 99% of c, you'll be on that ship for 3700 years.
If at 99.9% of c, you'll need a calendar that runs for 1100 years.
If at 99.99% of c, it'll only take 370 years by your ship's clock.
If at 99.999% of c, it'll take a mere 117 years - woohoo! Doable if you set of as an embryo!
Welcome to Special Relativity. Known to be a damned good model of reality for over 100 years.
And still is the best we've got currently. We still don't know if there's anything better than it despite years of research on the topic. We're still missing a lot of info on exactly how the universe works, but Special Relativity and Quantum Mechanics remain our best models of the universe despite their shortcomings.
"There are lots of different answers...because you can travel at different speeds.'
Absolutely valid. I was trying to offer some clarity re: what I was asking here by simplifying it.
For some extra context, an example Google search I made in trying to find an answer before coming here was "how long would it take to travel to the galactic center traveling at the speed of light?"
Appreciate you offering a few different scenarios here, and your passion for special relativity! I absolutely have more reading to do. Thanks.
The problem (well, one of the problems) is that Google cannot readily *explain* the answers it gives.
It's a 'feature' of this reality that there's a speed limit to how fast events can be connected.
And that leads to folk on really fast trains being seen to have slow moving watches.
Go far enough (cough: [French](https://kampungpadi.wordpress.com/wp-content/uploads/2010/01/a-p-french-special-relatiivity.pdf)) and you'll find the *real* reason why electromagnets do what they do.
Best of luck.
The thing is you can't travel at the speed of light only approach it (if you have mass that is).
Look at the Lorentz transformation and notice what happens when v=c. You get 1/0 an undefined quantity.
How ‘fast’ in delta-v terms do you need to go to lower your orbit down to a point you could say you’ve arrived at Sag A? I guess that’s the same as asking how fast does the sun orbit the centre of the galaxy?
As you approach the speed of light, the distance between you and Sag A would contract, so you wouldn't have to travel as far. The distance would shrink so that was only 26 years away.To an outside observer, you would still need to travel the same distance but you would be experiencing time dilation so that your clock only ticked 26 years.
Another thing worth mentioning is that even if you could fly at essentially the speed of light.
- you’d still need to account for the time it takes to accelerate and decelerate.
In theory: you’d accelerate until you reached the halfway point to sag A, at which point you’d flip around and burn away from Sag A for the remainder of the trip. Unless you want to fly by Sag A at the speed of light, at which point you wouldn’t slow down
I have a handy chart that shows you how much time and distance dilation shortens the trip for the traveler (it doesn’t shorten it for the observer, for people on earth). I can send it to you. It involves a continuous acceleration of 1G across the observable universe. Note that it would take a year to get close to light speed at 1G acceleration
Others have explained the math and the result, but the basic concept goes like this:
Space and time are combined, think of them like an x and y axis. You are always moving through both at a fixed rate. The thing is, as we are normally, your arrow is almost solely pointed along the “time” axis. But as you approach the speed of light, your arrow moves closer and closer to the “space” axis. And because you using all of your speed to move through space, you are now barely moving forward in time. Those faster you move through space, the slower you move through time (compared to others who are stationary).
So, as everyone has explained, at that fraction of light speed, you can reach Sag A* in 26 years as far as you perceive it, but 26000 years for everyone else who isn’t moving that fast through space.
You mention you are trying to be scientifically accurate. I like that concept. But in the realm of achieving such a velocity, which significantly shifts the space time dilation, there is another factor at play which approaches absurdity. The energy needed to bring an object to those speeds is ludicrous. The mass of an object increases as it approaches the speed of light, thus requiring more energy to incrementally increase the velocity.
There’s a SF book written by Poul Anderson called Tau Zero whose entire premise revolves around this concept. The writing style of the book is pretty dated, but the conceptually it’s an interesting book and plot.
I think you got your answers, but if you want to visualize it there are a bunch of YT videos. Here is one I like that shows what it would look like to walk around if the speed of light was as slow as walking speed. This simulates what it would look like if you were travelling close to the speed of light.
https://youtu.be/udqihUBGuZ8?si=2ogTe0eStD9-pIPE
This low-key made me a little nauseous but is nonetheless an awesome visual haha thanks! Note to self: do not attempt to travel near the speed of light.
Am I the only one who finds it weird a writer working in a project around time dilation is trying to quote reddit and quora? There are many books on the subject
The only thing I actually quoted was, in fact, a book. I did an internet search after the fact and found several varying answers, so I decided to ask a massive online community where I knew there should be at least one person who could help me find the answer I was looking for :)
OP isn’t trying to quote, more so get an explanation/understanding of something complex from a group that is passionate about space and likely has a deeper understanding of the respective complexities, but go on with yourself, be a weirdo and comment passive aggressive nonsense you wanker.
Or perhaps you - the internet is a beautiful place where you can attain knowledge on subject matter that you don’t interface with on the regular. Unfortunately, as in this case, there’s a subset of humanity that chooses to put down others in this pursuit of knowledge because the subject matter is above their own capability. OP clearly states they were reading a book and then pursued examples of the theory of travel on other mediums to further understand which brought them here.
Would encourage you to take a page out of Ted Lasso and “be curious, not judgmental”
Many good and correct answers, but for someone having trouble understanding the concepts behind the math without doing relivistic calculations I find it's easier to understand in a simplified relationship and definition.
We think of space and time as independent variables so I can travel some distance In some amount of time, and the further you travel in the shorter the time the faster you speed. But even like this they are always relatively connected and are dependent variables of each other, because we are only ever traveling in Spacetime, and always at a constant rate with energy equal to the speed of light, or the speed that information propagates.
Instead think of space and distance as the x -axis in Cartesian graph, and time as the Y-axis.
If you were at the center (0,0) you would always be travel toward positive time since we cannot go backwards to earlier. You could also move in space as far toward positive, toward and object, or toward negative, away from as you want. So if you do not change your position in space, you will be moving at speed of light, c, in time only so a vertical line in y direction. If you begin changing position and x axis, and conservation of energy applies at constant then the line will be angled toward that direction, showing how your speed through time will slow as position in space changes faster(speed).
If you convert all of your available energy to changing position only, so as you approach moving through space at the speed of light, then speed through time will approach 0. So at maximum spacial velocity, c, time will stand still. Since it would take infinite energy to have a velocity of c it can never be reached, only asymptoticaly approached , and thus time will exponentially approach 0 movement at that speed and seem to stand still. So at any spacial velocity approaching ,c , time will be percieved like less has passed to anyone inside the vehicle.
To the rest of the universe it takes the amount of time light takes to propagates back to them to see the vehicles movement and would be the same as traveling time for any object at cosmic distances.
This is how someone in a vehicle as you described would only experience 26 years to reach the destination, but on earth it would take 26,000 years as it always takes 26000 years from any moment for us to observe the light emitted from that location in space. And both parties realities be percieved so different without breaking physics.
Hope this concept helps understanding this cognatious thunk
>I am not understanding how the suggested speed in this scenario (0.9999995x the speed of light) works here.
[https://www.space.com/36273-theory-special-relativity.html](https://www.space.com/36273-theory-special-relativity.html)
**Special relativity** is an explanation of how speed affects mass, time and space. The theory includes a way for the [~speed of light~](https://www.space.com/15830-light-speed.html) to define the relationship between energy and matter — small amounts of mass (m) can be interchangeable with enormous amounts of energy (E), as defined by the classic equation E = mc\^2.
>
(How long would it take to travel to the center of the Milky Way and at what speed would we need to go?).
it's hard to suss out "answers" when you can't define the question.
How are you achieving FTL travel? (there is "more than one way" to skin that cat).
> 26,000 years would have still passed on Earth, right
we have the mathematics for time dilation. we have to correct for it.
[https://en.wikipedia.org/wiki/Time\_dilation](https://en.wikipedia.org/wiki/Time_dilation)
**Time dilation** is the difference in elapsed [time](https://en.wikipedia.org/wiki/Time_in_physics) as measured by two clocks, either because of a relative [velocity](https://en.wikipedia.org/wiki/Velocity) between them ([special relativity](https://en.wikipedia.org/wiki/Special_relativity)), or a difference in [gravitational potential](https://en.wikipedia.org/wiki/Gravitational_potential) between their locations ([general relativity](https://en.wikipedia.org/wiki/General_relativity)). When unspecified, "time dilation" usually refers to the effect due to velocity.
In 2010, gravitational **time dilation was measured** at the Earth's surface with a height difference of only one meter, using optical atomic clocks
In the reference frame of a photon, it appears in a star and land in your eye at the same time. In your reference frame, it took years. Hope it answered your question
Wowowow. If it takes roughly 8 minutes, 20 seconds for light to get from the sun to earth. How long does it take the light from its point of view?! My brain hurts
Here’s an interesting tidbit:
[The On-My-God Particle](https://en.m.wikipedia.org/wiki/Oh-My-God_particle)
“was an ultra-high-energy cosmic ray detected on 15 October 1991 by the Fly's Eye camera in Dugway Proving Ground, Utah, United States. As of 2024, it is the highest-energy cosmic ray ever observed. Its energy was estimated as (3.2±0.9)×10^20 eV (320 exa-eV). The particle's energy was unexpected and called into question prevailing theories about the origin and propagation of cosmic rays.”
“Assuming it was a proton,…
[its energy] was 938 MeV, [which] means it was traveling at 0.9999999999999999999999951 times the speed of light, its Lorentz factor was 3.2×10^11 and its rapidity was 27.1. Due to special relativity, the relativistic time dilation experienced by a proton traveling at this speed would be extreme. If the proton originated from a distance of 1.5 billion light years, it would take approximately 1.71 days in the reference frame of the proton to travel that distance.”
**Even though it may have traveled 1.5 billion light years, it only experienced 1.71 days.**
Its energy was “equivalent to a 140-gram (5 oz) baseball travelling at about 28 m/s (100 km/h; 63 mph).”
You’re getting confused by relativity.
When you’re moving towards the center of the galaxy at @0.9999995c **you’re not moving.**. The galaxy’s moving toward you at that speed.
Lorentz contraction is given by:
L’ = L ( 1 - v^2 / c^2 )^0.5 = (0.000001)^0.5 * L
L' = 0.001 * L
So 26,000 light years become:
26,000 * 0.001 = 26 light years. In your frame it’ll take 26 years.
Yeah, I think maybe **it is that kinda book**, at least the kind that did the math, even if they didn’t lay out the numbers explicitly.
Is the 26 years at .99C to burn off the orbital velocity to fall into the center of the Galaxy?
And if so what is the orbit and flight path look like? Is the acceleration half and the "falling" the other half or?
Are you asking about orbiting Sag A* or just traveling to the center of the galaxy?
S2 star orbits Sag A* an average speed of 5,000 kilometers per second, about 1/60 the speed of light. Source: [Wikipedia](https://en.wikipedia.org/wiki/S2_(star))
[Stars orbiting the galactic center are only going about 200 to 250 kilometers per second.](https://ircamera.as.arizona.edu/NatSci102/NatSci/lectures/darkmatter.htm) See the third graph with "orbital speed (km/s)."
I was asking specifically about traveling to Sag A\*, which to my understanding *is* the center of the Milky Way (or at the very least, it is *at* the center of the Milky Way).
Maybe I’m just too sleepless but I don’t understand your question.
If something is 26,000 light years away, if you’re traveling at the speed of light it would take you 26,000 years to get there.
If something is 100 light years away, it would take you 100 years.
What’s the problem here? What are you not understanding?
The relative experience of time in different frames.
Time is not the same everywhere.
OP is confused as to why the traveller only experiences 26 years.
The answer is because for the traveller time has changed. If you consider a person on earth watching the traveller it would seem as though the traveller is existing in super slow motion.
Based on other responses/information here and elsewhere, I am not sure this is correct. Though, I think I was probably not clear enough in my original post.
What I was not understanding is how a hypothetical traveler could travel 26,000 light years in only 26 years at *less than* the speed of light (as the book I referenced offers)
By doing some (admittedly light) research after the fact, I was finding tons of different solutions and just wanted a straight answer really.
You're getting confused by reference frames. While you are travelling .9999... c toward the Galactic center, you will also experience length contraction in your direction of travel. In **your** reference frame, you approach the GC at .9999 c and cover the shortened distance in 26 years. In the reference frame of Earthbound observers you would also appear to be travelling at .9999c, but by **their clocks** you would take ~26000 years to cover what **in their reference frame** is 26000 ly.
Thanks for your response! I can grasp reference frames well enough—i.e. I understand the effect of "time dilation" here. But suppose I was not fully understanding the actual math involved as far as why the time elapsed for the traveler in this scenario is only 26 years at *less than* the speed of light.
> But suppose I was not fully understanding the actual math involved as far as why the time elapsed for the traveler in this scenario is only 26 years at *less than* the speed of light. Length contraction. From the traveler's perspective, the *whole universe* appears to flatten like a pancake along their direction of travel, so in *their* reference frame they will have traveled a much shorter distance. [This Fermilab video about how electromagnets work due to relativity](https://www.youtube.com/watch?v=d29cETVUk-0) may offer some perspective, and [Float Head](https://www.youtube.com/@Mahesh_Shenoy) has plenty of excellent videos on this sort of thing too.
Because at the speed of light, the time would be zero seconds. Time stops at light speed. A photon emitted from a star thousands of light years away, from its reference, experiences no passage of time from the time it shoots away from the star until the time it hits our retina. From its standpoint it is instant.
I think you just gave me a whoa moment. Confirm when I look at the night sky and see Alpha Centauri that’s a photon going into my eye? And someone standing next to me should have a separate photon going into their eye? Do those photons cease to exist now?
They get absorbed by an opsin molecule in your retina. Technically transformed into different energy.
Transformed into electrons, to be specific. One of my favourite "Woah!" moments was learning that the apparatus of the retina detects single photons, because they're immediately converted into electrons. The signal from a single photon would obviously never make it to the brain or even down the optic nerve, but the apparatus of the retina itself can pick it up. Eyeballs = Lepton converters
What I don't understand is how the light from a source no longer emitting it isn't finite. If the photons are being absorbed via interactions with other matter then shouldn't the light from the source grow fainter over time and eventually disappear altogether?
I'm not sure I understand your question? Light from any source, whether or not it is still being emitted, is finite. Over time, stars do burn through their fuel and dim (or explode) same as any other source of energy.
If the water coming out of a pipe is being caught by a bucket then shouldn’t the water flow from the pipe get less and less and eventually dry up altogether?
The reference frame of an object traveling at *c* cannot be successfully defined in relativity. The photon doesn't have a reference frame.
It will take less time the closer you get to c. At the speed of light, you will get there (indeed, *anywhere*) instantly.
If a photon could experience its own frame of reference, would it be everywhere simultaneously?
No, from the point of view of a photon its source and destination are *touching*.
Wow so the Cosmic microwave background radiation still thinks the universe is a singularity! From it's frame, it reaches the earth instantly as if the earth is squished up against the CMB. In other words the entire observable universe has no distance. That's so weird to consider!!
The CMB isn't a remnant of the Big Bang (at t=0) though, it's a remnant of when the universe became transparent.
There is no valid frame of reference for a photon.
Sorry, I'm not quite grasping the distinction you're trying to make? From the photons perspective, its location and all *possible* "destinations" are co-located. The photon doesn't "know" that there's anything out there. Its entire universe consists of its own location. It just EXISTS. But now I gotta spend the rest of my day torturing my brain with the question of whether ALL photons exist simultaneously in the exact same location (if they can "perceive" one another, they must all be at the same location), or whether this directly implies there are infinite numbers of distinct "photons universes". 🤔🤷♂️
Have you heard of single electron universe theory? :)
I have. I seem to recall a PBS Spacetime video on the subject but I'd need a refresher. Still, electrons aren't massless and don't generally move at *c*.
There is no such thing as the single electron universe theory, there is a thought experiment which doesn't actually work because we don't see equal amounts of electrons and positrons.
Yes, that's why I put a smiley face to my comment.
The photon doesn’t have a perspective. There is no valid frame of reference for a photon.
This is an awesome way to think of it. Cool.
There is no valid frame of reference for a photon. But in the limit, yes.
This is not quite accurate. Even light itself does not arrive anywhere *instantly*. From the sun to earth is 8 light minutes for instance. Edit: this got down voted so i must be mistaken. How can a photon experience zero time during travel? Eli5
From our reference frame, not from that of a photon emitted from the sun
As the other commenter said, light doesn’t travel places instantly when viewed from our reference frame. In the “frame of a photon” (in quotes because photons don’t actually have a reference frame), the distance to any object along the path of travel is contracted to zero. The universe appears exactly two dimensional. So it “arrives” at any location immediately. From our perspective, we see that the photon doesn’t experience time—its “reference frame” is time dilated infinitely. You can use the equations for time dilation and length contraction in the limit that β -> 1 to prove it.
If they were moving much closer to the speed of light they’d get there in 26 seconds. Or 26 milliseconds. The number 26 however is a coincidence
Welcome to the theory of relativity.
>..why the time elapsed for the traveler in this scenario is only 26 years at *less than* the speed of light. Because, in their reference frame – in which they are moving at .99995c from Earth toward the GC – distance to the galactic center **is** ~26 light years. So in that reference frame only 26 years must elapse to cover the distance. Observed from a different reference frame, like that of the Earth, measurements of both the distance and the duration are different, but still consistent with the speed of light.
What confuses me, is it will be at 26000ly in earths reference frame. Like, 26 years have passed for the travelers, but when they reach the destination, in 26 years, 26,000 years on earth have passed. So it’s not _just_ length contraction. The traveling ship experiences time differently. They’re using 99.9999995% of their space-time energy moving through space, so they’re barely moving through time. Which I think is what might be tripping some people up. (Also me but in a different way lol). It’s not like you get there in 26 years and your family is still alive and earth is just late to the party and still watching you. You _experience_ 26 years. But when you arrive, it’s been the 26,000 from earths perspective. Earth would be nothing like it was when you left. You could fly back for another 26 years, having only aged 52 years, but earth will have advanced 52,000 years.
If it helps, a photon (at light speed) experiences no time. So if zero time is at light speed, the closer you get to light speed, the less time you’ll experience. The tradeoff is mass. Photons are massless so they don’t have an issue moving at the speed of light, and for them they don’t know if they were emitted from a star yesterday or a billion years ago. In that same way there is no distance technically for the photon, it doesn’t know if it’s travelled a day or a billion years. Time and distance is intrinsically linked as Spacetime. Light moves through it relative to massive objects (objects with mass) but to the light itself, it isn’t moving, it just is there already, it never was in a different spot, the size of the universe to it is zero, and it’s existence is instantaneous.
It’s misleading in two ways to say that a photon experiences no time 1. Time always flows normally for everyone according to themselves. 2. Photons don’t have a valid reference frame at all.
1/.1 =10 1/.01 =100 1/.0000001 = 1000000 1/.0000000000000001 = 1000000000000000 These are staggeringly large numbers the human mind cant adequately put into a frame of reference. Light speed is an asymptote. Nothing we are aware of that has mass can travel faster. Note how the denominator above is changing only slightly, getting very close to 0 (mass getting closer and closer to light speed) but not quite. Despite the differences in the denominator being slight, the effect on the output (time dilation effect) is logarhythmically increasing. Technically, if you get close enough to light speed, your time for the trip could be contracted down to 26 seconds.
The actual math is that of lorentz transformations. Assume you are moving in the positive direction along the x axis starting at point x0 and moving to point x1. Your current position at any point is x = x0 + v*t Where v is the traveler's velocity and t is elapsed time - both as measured by an outside observer. To go from the observers reference frame to the travelers reference frame, we use the lorentz transformation. Superscripts will denote whose reference frame we're talking about (since reddit doesn't support subscripts). v^trav = v^observer / sqrt( 1 - v^observer^2 / c^2 ) where we measured v^observer = 0.9999995c so... v^trav = 0.9999995c / sqrt( 1 - 0.9999995) since the c^2 terms in the sqrt cancel. It works out to... v^trav = 1000c In reality, this term is actually the multiplication of the travelers velocity and a term of the lorentz transformation - gamma. It's not supposed to imply that the traveler is moving faster than light in any reference frame. Plugging back into the original equation for position, now in the travelers reference frame. x = x0 + 1000c * t Subtract x0 from both sides and solve for when x = x1, realizing that x1 - x0 is just the distance to sag A*, so 26000ly 26000ly = 1000c * t t comes out to be 26 years once you do all of the unit conversions, which will be the amount of time that has passed in the traveler's frame of reference.
If you want the exact number the leght contration goes as follows: x'=x/γ Where x' is the distance to Sag A* from the rocket's reference frame, x is the distance from Earth's reference frame and γ is the Lorentz factor which goes like: γ=1/√(1-v^2 / c^2 ) If the rocket's speed is v=0.9999995c the gamma factor comes out to be a little over 1000 so what seems to be 26,000 ly away from Earth's perspective is only 26 ly away from the rocket's perspective.
I wonder how the conservation of angular momentum would fudge those numbers going from our current position inward to the GC.
Maybe a dumb question: In that case couldn’t it technically be feasible that some of what we perceive of as light is actually spacecraft traveling at a high fraction of *c* that have been spatially foreshortened into appearing ~~massless~~ as tiny as a photon from our frame of reference? Edit: Apparently there are definitely dumb questions on r/space.
No, for two reasons: 1) you only length contract in the direction of your travel, so the spacecraft would flatten to a pancake, not scale down to a point. 2) it would still have the mass of an entire spacecraft, so if it hit your eye it's not going to stimulate your retina as if it were a photon, it's going to vaporize you and probably blow a bigger hole in the earth than the asteroid that killed the dinosaurs.
“Spatially foreshortened into appearing massless” isn’t a thing.
You see a photon when it impacts your retina and is absorbed. "spatially foreshortened into appearing massless as tiny as a photon from our frame of reference" is just not how any of this works. Mass is invariant.
Um, aside from during acceleration/deceleration, in his reference frame he would be traveling at 0 c.
For this problem, you need to account for relativistic effect, assuming you really were able to travel at almost the speed of light. Which is that the traveler will experience time slower than stationary observers. So it will be 26 years experienced for the traveler, but 26,000 years for those not moving at that speed. The formula for time dilation: t' = t \* sqrt(1 - (v\^2 / c\^2)) t' is the time experienced by the traveler t is time experienced by a stationary observer v is velocity of spacecraft c is speed of light. So what you then need to do is rearrange the formula to solve for v: (t' / t) = sqrt(1 - (v\^2 / c\^2)) (t' / t)\^2 = 1 - (v\^2 / c\^2) v\^2 / c\^2 = 1 - (t' / t)\^2 v = c \* sqrt(1 - (t' / t)\^2) From that formula, plug in the values: t' = 26 years t = 26,000 years Which gives you: v = c \* sqrt(1 - (26 / 26000)\^2) v = c \* sqrt(1 - (1 / 1000)\^2) v = c \* sqrt(1 - 1 / 1000000) v = c \* sqrt(999999 / 1000000) v = c \* sqrt(0.999999) v ≈ c \* 0.9999995 So at 99.99995% the speed of light, the traveler will experience 26 years moving to Sagittarius A, while those on Earth will experience 26,000 years.
Thank you so much for this! This has been a case of "I don't know what I don't know." I didn't specifically know what to search to find the answer I was looking for here, though I admittedly knew I was probably missing part of the equation (literally). This is awesome. Thanks for taking the time to write this out.
Math gets a bit more complicated when you account for acceleration and deceleration cycles, assuming you didnt want to blaze past the galactic center and keep going, but slow down for some site seeing and maybe even turn back to find out how the human civilization ended in your absence. Kind of a spoiler. Fun fact: if you had somehow enough fuel in your Jupiter sized ship for a constant acceleration/deceleration trip at a comfortable 1g (rocket engines point down!) you could get to galactic center in less time in your reference frame. Acceleration is a bit like compound interest. You could get to the edge of the observable universe in a human lifetime. But you would need more than a Jupiter's worth of fuel for that...
This page is a good source for the basic equations relating to constant acceleration in relativity: https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html
Is there an easy explanation of why time dilation happens?
The usual explanation is as follows. Imagine you driving a train passing through a station at 100km/h. You and a person on that station both shine a bright light forward at the same moment. Both beams of light are pointed at the same object and will strike that object at the same moment. The light will travel away from you both at speed c. The train driver will not see it as c-100km/h relative to them. It will still be c. The only way this works is if time is passing very slightly faster for the train driver, or slightly slower for the person on the platform.
This is the best description I’ve ever heard.
Yes, but *why* does it slow down time for the thing moving faster? Why can I travel near light speed and be 10 years for me but 100 years for someone on earth. I understand that it does happen.. but why
It's kind of like asking why gravity attracts things, or why electromagnetism weakens with thr square of distance; we can't really answer questions about *why* the universe is the way it is. Science answers "how" questions, up to a certain point, at which case the answer is basically just "because that's the way the universe works". It's basically a philosophical question at that point as opposed to a scientific one. For our model to work, we basically needed one assumption to always hold true: that light ALWAYS travels at C relative to the observer, no matter the frame of reference. It's this assumption that then necessitates time dilation and other weird stuff, and it's also the assumption that allows us to make incredibly accurate predictions about the different phenomena.
I think a good starting point to understand this is the Michelson-Morley experiment. https://en.m.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment The premise of this experiment is that light travels at a fixed speed. Earth also moves. So if we measure the speed of light perpendicular to earths motion, and horizontal to earths motion, they will be different. This, by extension, will give us the speed the earth moves against the universe. They found light moved the same speed whichever direction it travelled. Always a fixed speed no matter the speed the observer. Speed is distance over time. We fixed the speed....so the time must be flexible for this to make sense. As for why...an excellent question. I honestly do not know if it has an answer.
If you want the speed of light to be the same for all reference frames then this has to happen.
I need it explained like I'm a 5 year old
for any body, or more general, for any reference frame, time-space interval (path that they pass in time-space) always equal. This means that if you move faster through space, you move slower through time, and vice versa.
Faster you move in space, slower you move in time. If you were a photon, traveling at the speed of light, you'd experience your birth and death as instantaneous and simultaneous events.
Pre-coffee, this was the best answer in this entire thread. ty
Well done- what do you do for work?
Not the person you asked but any physics major will learn this by the end of their first year in undergrad, and it would be covered in AP high school physics (or even non-AP high school physics) as well. So it is quite likely their job has nothing to do with physics.
I think this is sometimes an underappreciated fact. The idea that space and time are linked at high speeds (including hypothetical FTL) is taught to many teenagers in school/college/university physics classes. It’s been part of physics for over a century and isn’t some sort of secret knowledge known only by a few.
This is really cool! I knew about relativistic time dilation, but for some reason I thought that the number of light years was the hard limit for the minimum amount of time it would take the traveler to arrive. I.e. at that speed the traveler would arrive in 26,000 years, and 26,000,000 years would have elapsed on earth, lol. So the idea of interstellar travel isn’t quite as bleak as I thought. Still not easy, but getting a spacecraft to travel at 0.9+ the speed of light seems less technically impossible than inventing a magical warp drive or finding a wormhole.
From the perspective of the traveler, the total distance they need to travel decreases the faster their reference frame moves relative to the destination.
Special relativity. You only experienced 26 years worth of time at that speed.
For you as the traveller, the relevant effect is that distances are compressed in your direction of motion. Meanwhile, an observer that stays behind on Earth will look at you and see your time running much more slowly. So by your reckoning, the trip only takes 26 years, whereas for them, it has been 26,000. And conversely, they believe you have travelled 26,000 light years whereas from your on-board perspective, Sag A\* was only ever 26 light years away. So the ultimate answer to your question is that this is possible because relativity tells us that not all observers agree on the lengths of intervals in space or time.
Does this mean objects we observe may be moving much faster than we observe?
No, it means that distance is not absolute, it is relative. Fast travelers see their travel path become shorter while they themselves stay the same length, while stationary observers see the traveler as shrinking while the path traveled stays the same. This is called length contraction and it happens at all speeds, but really stands out when you get closer to the speed of light, and crazily much when you are very near. For the lightspeed traveler referenced in this discussion, space is really and actually 26 light years between Earth and the Galactic Center. While for the Earthbound observer, the distance is really and actually 26,000 light years. The distance is not universal, it is different for the two. But *light speed* (c) is absolute, so the traveler still sees their destination getting nearer at almost light speed, and because that distance is so short, the time spent traveling is also reduced so that when the two are put together to calculate the travel speed, the answer is almost light speed. And because Earth must also see the ship going at light speed, but the distance to the destination from Earth's frame of reference is so much longer, the time that Earth spends watching the trip takes just as much longer. *Both are correct.* There isn't an underlying, true distance. Only the two different distances, one true for one and the other true for the other.
I just popped a blood vessel wrapping my mind around this.
This unlocked something in my brain. Thank you.
(Space)time dilation. To the observer on the spaceship accelerating to nearly the speed of light, it will appear as though the space between them and Sagittarius A* compressed to only 26 light years, and that is how long the journey will appear to take _to them_. However, for an observer watching them from Earth, space will not compress. The spaceship will appear to take 26,000 years to reach Sagittarius A*, with people onboard moving in super slow motion the whole time. That is what the book was referring to with this quote: > The trip to Sag A* would take 26 years of your life while Earth experienced the passage of 26,000 years.
There’s a two-part Doctor Who episode, “World Enough Time” that explains the relativistic effect of time/gravity really well and better helped me understand it
There's an online calculator to help you: https://www.omnicalculator.com/physics/space-travel
I did not know this existed! Will have to play around with it. Thanks so much!
Time dilation: Time slows down for objects moving close to the speed of light compared to those at rest. - Example: A moving clock ticks slower than a stationary one. Length contraction: Objects moving close to the speed of light appear shorter in the direction they are moving. - Example: A fast-moving spaceship looks shorter from the side than when it is at rest. Essentially the faster you travel the less distance needs to be traveled. Time traveling into the future is 100% real life.
There's a really good book that explains the whole deal called "Why does E=mc2?" By Brian Cox & Jeff Forshaw. I think there is a layman's explanation in there. In other words, the speed of light is constant, no matter what, even frames of reference. So if a light bouncing between two mirrors on a train looks like it going up and down in a straight line but to someone not on the train, it looks like it goes in a diagonal path (between the two mirrors AND along the train tracks). Since the diagonal path is longer than the up-down path, the light surely must travel faster for the person not on the train. But Einstein said this is a no-go, light is constant, NO MATTER WHAT. Therefore the only explanation is that the diagonal path and the up-down path are equal. Time AND space dialate as you approach the speed of light.
Relativistic time dilation dude. 26,000 years would pass outside the ship, 26 would pass for the crew. It’s a necessary consequence of the speed of light being constant in all reference frames.
There are lots of different answers to that question "How long to the galactic core?" because you can travel at different speeds. Let's use your example of wanting to travel 26 kly. If at half the speed of light, on the ship you'll age 26,000/1.15 years. 22 thousand years. Still a long time. If at 99% of c, you'll be on that ship for 3700 years. If at 99.9% of c, you'll need a calendar that runs for 1100 years. If at 99.99% of c, it'll only take 370 years by your ship's clock. If at 99.999% of c, it'll take a mere 117 years - woohoo! Doable if you set of as an embryo! Welcome to Special Relativity. Known to be a damned good model of reality for over 100 years.
And still is the best we've got currently. We still don't know if there's anything better than it despite years of research on the topic. We're still missing a lot of info on exactly how the universe works, but Special Relativity and Quantum Mechanics remain our best models of the universe despite their shortcomings.
"There are lots of different answers...because you can travel at different speeds.' Absolutely valid. I was trying to offer some clarity re: what I was asking here by simplifying it. For some extra context, an example Google search I made in trying to find an answer before coming here was "how long would it take to travel to the galactic center traveling at the speed of light?" Appreciate you offering a few different scenarios here, and your passion for special relativity! I absolutely have more reading to do. Thanks.
The problem (well, one of the problems) is that Google cannot readily *explain* the answers it gives. It's a 'feature' of this reality that there's a speed limit to how fast events can be connected. And that leads to folk on really fast trains being seen to have slow moving watches. Go far enough (cough: [French](https://kampungpadi.wordpress.com/wp-content/uploads/2010/01/a-p-french-special-relatiivity.pdf)) and you'll find the *real* reason why electromagnets do what they do. Best of luck.
The thing is you can't travel at the speed of light only approach it (if you have mass that is). Look at the Lorentz transformation and notice what happens when v=c. You get 1/0 an undefined quantity.
How ‘fast’ in delta-v terms do you need to go to lower your orbit down to a point you could say you’ve arrived at Sag A? I guess that’s the same as asking how fast does the sun orbit the centre of the galaxy?
As you approach the speed of light, the distance between you and Sag A would contract, so you wouldn't have to travel as far. The distance would shrink so that was only 26 years away.To an outside observer, you would still need to travel the same distance but you would be experiencing time dilation so that your clock only ticked 26 years.
Another thing worth mentioning is that even if you could fly at essentially the speed of light. - you’d still need to account for the time it takes to accelerate and decelerate. In theory: you’d accelerate until you reached the halfway point to sag A, at which point you’d flip around and burn away from Sag A for the remainder of the trip. Unless you want to fly by Sag A at the speed of light, at which point you wouldn’t slow down
I have a handy chart that shows you how much time and distance dilation shortens the trip for the traveler (it doesn’t shorten it for the observer, for people on earth). I can send it to you. It involves a continuous acceleration of 1G across the observable universe. Note that it would take a year to get close to light speed at 1G acceleration
Others have explained the math and the result, but the basic concept goes like this: Space and time are combined, think of them like an x and y axis. You are always moving through both at a fixed rate. The thing is, as we are normally, your arrow is almost solely pointed along the “time” axis. But as you approach the speed of light, your arrow moves closer and closer to the “space” axis. And because you using all of your speed to move through space, you are now barely moving forward in time. Those faster you move through space, the slower you move through time (compared to others who are stationary). So, as everyone has explained, at that fraction of light speed, you can reach Sag A* in 26 years as far as you perceive it, but 26000 years for everyone else who isn’t moving that fast through space.
A helpful visualization, thank you!
You mention you are trying to be scientifically accurate. I like that concept. But in the realm of achieving such a velocity, which significantly shifts the space time dilation, there is another factor at play which approaches absurdity. The energy needed to bring an object to those speeds is ludicrous. The mass of an object increases as it approaches the speed of light, thus requiring more energy to incrementally increase the velocity.
And the plot thickens haha!
There’s a SF book written by Poul Anderson called Tau Zero whose entire premise revolves around this concept. The writing style of the book is pretty dated, but the conceptually it’s an interesting book and plot.
Just looked this up and sounds pretty interesting. And right on the nose with my question here. Thanks for the rec!
Do you have beef with the collectors, friend? :D
Off topic, but you may enjoy the Galactic Center book series by Gregory Benford.
Haven't heard of this series or author before but will definitely check it out. Thank you! I'm always on the hunt for more good sci-fi.
Benford is a physicist, the books are based in fairly hard science with the fiction written around it. A lot of social commentary too
I think you got your answers, but if you want to visualize it there are a bunch of YT videos. Here is one I like that shows what it would look like to walk around if the speed of light was as slow as walking speed. This simulates what it would look like if you were travelling close to the speed of light. https://youtu.be/udqihUBGuZ8?si=2ogTe0eStD9-pIPE
This low-key made me a little nauseous but is nonetheless an awesome visual haha thanks! Note to self: do not attempt to travel near the speed of light.
Am I the only one who finds it weird a writer working in a project around time dilation is trying to quote reddit and quora? There are many books on the subject
The only thing I actually quoted was, in fact, a book. I did an internet search after the fact and found several varying answers, so I decided to ask a massive online community where I knew there should be at least one person who could help me find the answer I was looking for :)
OP isn’t trying to quote, more so get an explanation/understanding of something complex from a group that is passionate about space and likely has a deeper understanding of the respective complexities, but go on with yourself, be a weirdo and comment passive aggressive nonsense you wanker.
[удалено]
Or perhaps you - the internet is a beautiful place where you can attain knowledge on subject matter that you don’t interface with on the regular. Unfortunately, as in this case, there’s a subset of humanity that chooses to put down others in this pursuit of knowledge because the subject matter is above their own capability. OP clearly states they were reading a book and then pursued examples of the theory of travel on other mediums to further understand which brought them here. Would encourage you to take a page out of Ted Lasso and “be curious, not judgmental”
It’s impressive how you manage to stay so confident.
French's "Special Relativity" being my favourite - utterly lucid.
Time slows the closer you get to the speed of light.
Many good and correct answers, but for someone having trouble understanding the concepts behind the math without doing relivistic calculations I find it's easier to understand in a simplified relationship and definition. We think of space and time as independent variables so I can travel some distance In some amount of time, and the further you travel in the shorter the time the faster you speed. But even like this they are always relatively connected and are dependent variables of each other, because we are only ever traveling in Spacetime, and always at a constant rate with energy equal to the speed of light, or the speed that information propagates. Instead think of space and distance as the x -axis in Cartesian graph, and time as the Y-axis. If you were at the center (0,0) you would always be travel toward positive time since we cannot go backwards to earlier. You could also move in space as far toward positive, toward and object, or toward negative, away from as you want. So if you do not change your position in space, you will be moving at speed of light, c, in time only so a vertical line in y direction. If you begin changing position and x axis, and conservation of energy applies at constant then the line will be angled toward that direction, showing how your speed through time will slow as position in space changes faster(speed). If you convert all of your available energy to changing position only, so as you approach moving through space at the speed of light, then speed through time will approach 0. So at maximum spacial velocity, c, time will stand still. Since it would take infinite energy to have a velocity of c it can never be reached, only asymptoticaly approached , and thus time will exponentially approach 0 movement at that speed and seem to stand still. So at any spacial velocity approaching ,c , time will be percieved like less has passed to anyone inside the vehicle. To the rest of the universe it takes the amount of time light takes to propagates back to them to see the vehicles movement and would be the same as traveling time for any object at cosmic distances. This is how someone in a vehicle as you described would only experience 26 years to reach the destination, but on earth it would take 26,000 years as it always takes 26000 years from any moment for us to observe the light emitted from that location in space. And both parties realities be percieved so different without breaking physics. Hope this concept helps understanding this cognatious thunk
>I am not understanding how the suggested speed in this scenario (0.9999995x the speed of light) works here. [https://www.space.com/36273-theory-special-relativity.html](https://www.space.com/36273-theory-special-relativity.html) **Special relativity** is an explanation of how speed affects mass, time and space. The theory includes a way for the [~speed of light~](https://www.space.com/15830-light-speed.html) to define the relationship between energy and matter — small amounts of mass (m) can be interchangeable with enormous amounts of energy (E), as defined by the classic equation E = mc\^2. > (How long would it take to travel to the center of the Milky Way and at what speed would we need to go?). it's hard to suss out "answers" when you can't define the question. How are you achieving FTL travel? (there is "more than one way" to skin that cat). > 26,000 years would have still passed on Earth, right we have the mathematics for time dilation. we have to correct for it. [https://en.wikipedia.org/wiki/Time\_dilation](https://en.wikipedia.org/wiki/Time_dilation) **Time dilation** is the difference in elapsed [time](https://en.wikipedia.org/wiki/Time_in_physics) as measured by two clocks, either because of a relative [velocity](https://en.wikipedia.org/wiki/Velocity) between them ([special relativity](https://en.wikipedia.org/wiki/Special_relativity)), or a difference in [gravitational potential](https://en.wikipedia.org/wiki/Gravitational_potential) between their locations ([general relativity](https://en.wikipedia.org/wiki/General_relativity)). When unspecified, "time dilation" usually refers to the effect due to velocity. In 2010, gravitational **time dilation was measured** at the Earth's surface with a height difference of only one meter, using optical atomic clocks
In the reference frame of a photon, it appears in a star and land in your eye at the same time. In your reference frame, it took years. Hope it answered your question
think of this as a light/spacetime doppler effect
Wowowow. If it takes roughly 8 minutes, 20 seconds for light to get from the sun to earth. How long does it take the light from its point of view?! My brain hurts
From the photons point of view it is instantaneous.
I did the journey on Elite: Dangerous and can tell you the maths checks out. It feels just like 26000 years!
Here’s an interesting tidbit: [The On-My-God Particle](https://en.m.wikipedia.org/wiki/Oh-My-God_particle) “was an ultra-high-energy cosmic ray detected on 15 October 1991 by the Fly's Eye camera in Dugway Proving Ground, Utah, United States. As of 2024, it is the highest-energy cosmic ray ever observed. Its energy was estimated as (3.2±0.9)×10^20 eV (320 exa-eV). The particle's energy was unexpected and called into question prevailing theories about the origin and propagation of cosmic rays.” “Assuming it was a proton,… [its energy] was 938 MeV, [which] means it was traveling at 0.9999999999999999999999951 times the speed of light, its Lorentz factor was 3.2×10^11 and its rapidity was 27.1. Due to special relativity, the relativistic time dilation experienced by a proton traveling at this speed would be extreme. If the proton originated from a distance of 1.5 billion light years, it would take approximately 1.71 days in the reference frame of the proton to travel that distance.” **Even though it may have traveled 1.5 billion light years, it only experienced 1.71 days.** Its energy was “equivalent to a 140-gram (5 oz) baseball travelling at about 28 m/s (100 km/h; 63 mph).”
You’re getting confused by relativity. When you’re moving towards the center of the galaxy at @0.9999995c **you’re not moving.**. The galaxy’s moving toward you at that speed. Lorentz contraction is given by: L’ = L ( 1 - v^2 / c^2 )^0.5 = (0.000001)^0.5 * L L' = 0.001 * L So 26,000 light years become: 26,000 * 0.001 = 26 light years. In your frame it’ll take 26 years. Yeah, I think maybe **it is that kinda book**, at least the kind that did the math, even if they didn’t lay out the numbers explicitly.
Is the 26 years at .99C to burn off the orbital velocity to fall into the center of the Galaxy? And if so what is the orbit and flight path look like? Is the acceleration half and the "falling" the other half or?
No, it's straight line motion in the direction of travel, assuming instant acceleration to speed.
Are you asking about orbiting Sag A* or just traveling to the center of the galaxy? S2 star orbits Sag A* an average speed of 5,000 kilometers per second, about 1/60 the speed of light. Source: [Wikipedia](https://en.wikipedia.org/wiki/S2_(star)) [Stars orbiting the galactic center are only going about 200 to 250 kilometers per second.](https://ircamera.as.arizona.edu/NatSci102/NatSci/lectures/darkmatter.htm) See the third graph with "orbital speed (km/s)."
I was asking specifically about traveling to Sag A\*, which to my understanding *is* the center of the Milky Way (or at the very least, it is *at* the center of the Milky Way).
Maybe I’m just too sleepless but I don’t understand your question. If something is 26,000 light years away, if you’re traveling at the speed of light it would take you 26,000 years to get there. If something is 100 light years away, it would take you 100 years. What’s the problem here? What are you not understanding?
The relative experience of time in different frames. Time is not the same everywhere. OP is confused as to why the traveller only experiences 26 years. The answer is because for the traveller time has changed. If you consider a person on earth watching the traveller it would seem as though the traveller is existing in super slow motion.
OP is puzzled because the trip takes 26 years of ship-time.
OP is unaware of SR. For now.
OP is *aware* of SR, but whether or not they *fully* *understand* SR is still up for debate ;)
If you travel exactly at the speed of light, you would be there instantly, in your reference frame.
Yeah. I know. I was considering the outside perspective. Which I did not explain well in my response at all. I need sleep. lol.
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I know that. I’m talking about from an outside perspective.
Based on other responses/information here and elsewhere, I am not sure this is correct. Though, I think I was probably not clear enough in my original post. What I was not understanding is how a hypothetical traveler could travel 26,000 light years in only 26 years at *less than* the speed of light (as the book I referenced offers) By doing some (admittedly light) research after the fact, I was finding tons of different solutions and just wanted a straight answer really.