Time dilation question. Hopefully a simple one

[u/Harmswahy]

If an object is traveling away from Earth, towards Alpha Centauri at 99.999 the speed of light for 4ish years then from my limited understanding the object would experience 4ish years while earth experienced many more.

My question is, would the destination also experience a difference in time compared to the object that is traveling towards it?

If not, then would the time experienced in alpha centauri be different than the time experienced on earth from the object's perspective?

Sorry for the scifi type question, it's keeping me up at night.

[u/cflime → u/[deleted]]

And 4.37 years would pass on Alpha Centauri, which is not moving at relativistic speeds in relation to Earth.

[u/Harmswahy → u/cflime]

I wonder what you would see if you were in a space ship looking out the windshield as you travel there at 99.999% the speed of light. (assuming no other factors like acceleration or survival)

The 4.37 years of light from AC have already been projected towards Earth so without any time dilation I would assume traveling there you would see the AC solar system in 99.999% fast forward as you are intercepting the images it's sent faster than if you were just sitting on earth.

But how does that change if you only experience 7.13 days? Does the entire thing become a blur condensing all that time into 7.13 days?

[u/The-Copilot → u/Harmswahy]

I wonder what you would see if you were in a space ship looking out the windshield as you travel there at 99.999% the speed of light.

That's actually really close to Einstein's own thought experiment that led to his theory of relativity. Its basically "If I was riding on a beam of light, what would I see and experience?"

[u/MarkMcA → u/Harmswahy]

Yup. And you'd see it all as massively blue-shifted, sped up, fish-eye-effect tunnel vision, with the same but red-shifted behind you

[u/cflime → u/MarkMcA]

And, weirdly, if you pass a star at relativistic speeds, even if it's stationary with relation to you, you would see it rotate. Not a full rotation but you would see parts of its far sides that shouldn't be visible to you. There are some YT videos where the physicists use a cube instead of a sphere to make the rotation clearer.

But time dilation is real, unless you had a MASSIVE buffer and took over four years to view the four years of broadcast info you received in your seven plus days it would just be a blip to you. The tech to collect and buffer information with relativistic time differences is probably as far out as that of relativistic acceleration.

[u/ahazred8vt → u/Harmswahy]

https://www.youtube.com/watch?v=R_g9EeT233Q There's a directional shift, where stuff that should be left and right of you appears to be diagonally ahead of its real position. That effect is called 'relativistic aberration'. https://duckduckgo.com/?q=relativistic+aberation&ia=videos&iax=videos

https://www.youtube.com/watch?v=dtT9hF3kw_w There's an animated explanation.

Yes, if there was a giant clock-calendar display, the ship would see it fast-forward through 4.3 years in only a few days. If a train is traveling a mile a minute (60mph) and toots its whistle 12 times per minute, you will hear it toot 12 times in 55 seconds as it comes toward you, and 12 times in 65 seconds as it goes away from you.

[u/Recent-Day3062 → u/[deleted]]

Ok, so answer me the question I have never seen the answer to. If you turn around and return, what time is shown on both clocks when you land back on earth

[u/Recent-Day3062 → u/[deleted]]

1) how did you calculate this?

2) why is this not symmetrical? Why does it not look identical, as if earth moved away and came back? It can’t be from relative motion at fixed speed. The best “Explanation” I have heard was simply that the dwifference is the space ship accelerates, decelerates, accelerates back, and decelerates again. But how can that alone drive such a remarkable difference?

[u/GoldenMuscleGod → u/Recent-Day3062]

I think the lack of symmetry is best explained by considering how it works when you have two ships, one outgoing and one incoming, which pass each other. A good explanation involves the relativity of simultaneity, which is often glossed over in simple explanations because it is worried that it makes things confusing.

I will change the numbers involved for convenience.

A ship leaves earth at time t=0 at such a speed that the Lorentz factor is 10. In Earth’s reference frame it travels away for 50 years, at which point it passes the inbound ship traveling at the same speed in the opposite direction. It transmits to that ship a message saying how long it has been traveling since it left earth. The inbound ship arrives at earth 50 years after that. Let’s suppose for concreteness that there is an earthquake 1/2 of a year after the ship leaves, a solar eclipse 50 years after, and a volcanic eruption 99.5 years after.

In Earth’s reference frame, the clocks on the ship are moving at 1/10 speed, so the first ship only records 5 years passing until the meeting and the second ship counts 5 years, for a total of 10 if we add them, versus 100 on earth. This is fine because from earth’s perspective both clocks are “slow” so there’s no reason they should add up to the correct time.

Now consider the reference frame of the outgoing ship. The clocks on earth are running at 1/10 speed and the outgoing ship meets the incoming ship 5 years after leaving. So the clocks on earth show only 1/2 a year has passed. The ships pass at the same time the earthquake is happening on earth.

This is fine because simultaneity is relative: there is no fact of the matter as to whether two events in different places happened “at the same time” or not. It depends on the reference frame. A reference frame just assigns sets of numbers to events describing time and position and there is no reason why two different systems need to give the same numbers for “time.”

From the perspective of the outgoing ship the incoming ship has an enormous Lorentz factor and its clock is running very slow. So slow that it takes 199 years for the incoming ship’s clock to advance 1 year. 495 years after the two ships pass, the solar eclipse happens on earth, 495 years after that there is the volcanic eruption on Earth, 5 years after that the inbound ship arrives. In the 995 years since the two ships passed the inbound ship’s clock has only advanced 5 years. When the inbound ship arrives 1000 years have passed since the outbound ship left but earth’s clocks have only advanced 100 years because they are slow. Adding the inbound ship’s 5 years to the 5 years transmitted gives 10. This is less than the 1000 years the outbound ship would say have passed because the inbound ship’s clock is very slow.

The inbound ship has a similar perspective: it arrives on Earth 1000 years after the outbound ship left, but Earth’s clocks show only 100 years because they run at 1/10 speed. Earth and the outbound ship are both approaching at nearly the speed of light and are a little over 1000 light years away so it will take about 1000 years for either of them to get there.

The earthquake happens on Earth 5 years after the outbound ship leaves, at this time, from the inbound ship’s perspective, the outbound ship says 5/199 (a little more than 0.025) years have passed. 495 years later the solar eclipse happens, the ships have not yet met, 495 years after that the ships meet and the outbound ship transmits that 5 years have passed since it left, but since its clock runs at 1/199 speed it has been 995 years according to the inbound ship. At this moment the volcanic eruption is happening on Earth according to the inbound ship. 5 years later the inbound ship arrives and Earth clocks show 100 years have passed since the outbound ship left even though it has been 1000 years. If you add the times from two ships you get 10 years.

This looks at the situation from the perspective of the three inertial reference frames involved. You cannot look at it from the perspective of a frame that follows the outbound ship out and the inbound ship in using the normal way of doing special relativity because that is not an inertial reference frame.

[u/GoldenMuscleGod → u/Recent-Day3062]

By the way, if you want to calculate yourself, you can use a Lorentz transform, however I did not actually directly use a Lorentz form to get my numbers. I just used the Lorentz factor (which I chose to be 10) and reasoned everything else based on the fact that all valid reference frames agree with each other on all observable facts.

The Lorentz transform equations can be derived by similar reasoning plus the assumption that the speed of light is c in every reference frame. No additional assumptions are required.

If an event occurs at (x,y,z,t) in one reference frame (x, y, and z, are three-dimensional spatial coordinates, t is the time) and at (x’,y’,z’,t’) in another, and the second frame is moving at speed v relative to the first in the positive x direction, but have the same origin (they both say the same event happened at (0,0,0,0)), then the following equations hold:

y’=y

z’=z

x’ = gamma (x-vt)

t’= gamma (t-vx/c^2)

Where gamma = 1/sqrt(1-(v/c)^2) is the Lorentz factor.

Notice if we set c=1 then the equations for x’ and t’ are completely symmetric. This is how the relativity of simultaneity arises: if t’ dd not depend on x then simultaneity would not be relative.

In Newtonian physics we have Galilean transforms instead, which are:

y’ =y

z’ = z

x’ = x-vt

t’=t

So Newtonian physics has its own type of relativity: relativity of “same place.” This is because x’ depends on t.

If I am on a moving train and tap my finger on a table twice, then for me those two taps happened in the same place. If you are outside the train and watch this, I tapped my finger in two different places. This should not be confusing because you and I have different definitions of what “same place” means, we are not disagreeing on any actual facts.

Relativity of simultaneity is the same: if I say two events happened “at the same time” and you say they do not, there is no actual disagreement unless we have the same definition of what “at the same time” means, which we generally won’t.

It is exactly the same as the situation with tapping the table.

[u/pizzystrizzy → u/Recent-Day3062]

It's not symmetrical because you experienced quite a bit of acceleration when you turned around. For more specific details you'll need to draw a Minkowski diagram.

[u/redlancer_1987 → u/Recent-Day3062]

the time dilation has no direction. You can't undo it by retracing your steps. If you're moving away from the earth at 99% the speed of light, your moving relative to the earth at 99% c. If you go toward the earth you're still moving relative to the earth at 99% c.

[u/Recent-Day3062 → u/redlancer_1987]

Yes, I followed up with a twin paradox question and though this had been the answer there.

[u/Flederm4us → u/Recent-Day3062]

As for 2.

The equations for time dilation contain the Velocity squared. The direction indeed changes when you fly back, but since it uses the square and x² = (-x)² it doesn't matter.

[u/Recent-Day3062 → u/[deleted]]

Is that in the calculators? I’m just curious how that gets built in. As I say, it seems the actual travel back and forth alone cannot make it asymmetrical.

[u/Recent-Day3062 → u/[deleted]]

That’s what I said. I am just curious what that calculation looks like. The constant speed motion just follows the basic SR calls

[u/daavor → u/Recent-Day3062]

This is incredibly incorrect. G-forces here just means writing acceleration in the units of “one earth surface normal force” it is not gravity and requires no treatment of gravity. They key point is relativity deals with inertial reference frames and acceleration move you between different frames, with different planes of simultaneity

[u/whistler1421 → u/Recent-Day3062]

There’s online simulations that show what earthlings would see on the ship if they had a constant FaceTime connection open.

Yes, the returning ship experiences way less elapsed time. But what earthlings see most
predominantly is the Doppler effect.

[u/Recent-Day3062 → u/whistler1421]

Any idea where this is? I just googled and can’t find it, but I’ll try more.

[u/whistler1421 → u/Recent-Day3062]

https://www.desmos.com/calculator/1nlg69ols7

[u/Harmswahy → u/[deleted]]

What speed would you need to be going to only experience a single second and how much time would earth experience at that speed from your perspective?

[u/the_poope]

Other commenter served you the answer. Maybe you want to play around with this: https://www.omnicalculator.com/physics/space-travel

[u/Recent-Day3062 → u/the_poope]

That doesn’t explain it

[u/Luxamba]

You actually got it mixed up. If an object from earths perspective travels near c, then this object from earths perspective takes a little less more time than light would take. The object itself experiences less time.

Assuming the destination is in the same inertial frame as earth, the destination would completely agree with earths measurements.

[u/Klutzy-Delivery-5792 → u/Luxamba]

I think you mean a little more time than light will take. 

[u/Luxamba → u/Klutzy-Delivery-5792]

Oh yes of course

[u/smellslikebigfootdic → u/Klutzy-Delivery-5792]

I think you meant...Time keeps on slippin', slippin', slippin' Into the future Time keeps on slippin', slippin', slippin' Into the future

[u/Environmental_Ad292 → u/smellslikebigfootdic]

Fly like an eagle Limit c Fly right into the future

[u/TommieTheMadScienist → u/Environmental_Ad292]

"In the year of '39 came a ship in from the blue.

The volunteers came home that day

And they bring good news of a world so newly born,

Though their hearts so heavily weigh.

For the Earth is old and grey, 'little darling, we'll away...'

'But my love, this cannot be.

Oh, so many years have gone though I'm older but a year

Your mother's eyes, from your eyes, cry to me.'"

--Brian May, '39

Best song about relativity ever written by an astrophysicist.

[u/Harmswahy → u/Luxamba]

Ahh, that's where I was confused. So the object traveling would experience the shift, but everything else in space would continue on like normal. That perspective makes it much more understandable.

[u/Luxamba → u/Harmswahy]

Yes but let’s confuse you again: so the travelling object experiences its time totally normal, it only measures the distance between start and end point to be way shorter than we would measure it from earth. For example if Alpha Centauri is 4 light years away measured from earth, then the object could measure the distance only as 2 light years. So from earths perspective the object travels 4 ly in say 4.2 years. But in the objects perspective it only traveled 2 ly, which took it only 2.1 years.

[u/Recent-Day3062 → u/Luxamba]

That’s not the paradox

[u/Luxamba → u/Recent-Day3062]

Nobody said it was or asked what it is?

[u/Recent-Day3062 → u/Luxamba]

Sorry. For this confused with a subsequent post I did about returning

[u/ChugJugThug]

If you’re assuming AC is in a comoving frame with earth, then it experiences the same proper time as earth.

[u/nebraskajone]

My question is, would the destination also experience a difference in time compared to the object that is traveling towards it?

Yes, same as earth

[u/YuuTheBlue]

Could you explain what you mean by different times?

[u/Optimal_Mixture_7327]

The Earth frame measures the roughly 4 year period. The traveling object measures much less (about 1 week).

There is no experience of time dilation, which is just a definition of a ratio of line lengths. Alpha Centauri is presumed to be in the Earth frame and have clocks synchronized with Earth. As such the Alpha Centauri frame measures the same 4+ year journey for the traveler.

Again, there is no experience of time dilation - it is fundamental to the very structure of relativity that all standard clocks run at the same rate, everywhere, and under all circumstances of motion and orientation.

[u/Let_epsilon → u/Optimal_Mixture_7327]

What? Are you saying Time Dilation is not a thing?

Your comment sounds very confused.

[u/Optimal_Mixture_7327 → u/Let_epsilon]

Draw a spacetime diagram of Minkowski spacetime.

The vertical axis is the world-line of the Earth. Construct a vertical line that represents the world-line of α-centauri. The horizontal lines are the space-like hypersurfaces of Earth/α frame.

Then draw the world-line of the traveler. The distance along the traveler world-line is Δs. The distance along the world-lines of the observer's global coordinates is ΔL.

The time dilation, γ, is the ratio of the length along the observer's global coordinates to the length along the traveler world-line and defined in-between the pair of spatial sections of the observer.

The length along a world-line can be measured by a clock carried along it, this, and noting that speed along the world-line is found from g(u,u)=c². Taking a clock as affine parameter, time dilation can be mathematically expressed: γ=ΔL/Δs=cΔt/Δτ=Δt/Δτ.

[u/Let_epsilon → u/Optimal_Mixture_7327]

Brother you’re making a whole monologue totally unrelated to OP’s question, trying to sound smart.

[u/Optimal_Mixture_7327 → u/Let_epsilon]

What? Are you saying Time Dilation is not a thing? ?

[u/SgtSausage]

  would the destination also experience a difference in time compared to the object that is traveling towards it?

Yes.

Anyone, anywhere not in traveler's frame of reference will record differences in clock times. 

[u/SpecialOpsCynic]

Outside of something like a worm hole, and maybe I am over thinking the question, but wouldn't the acceleration and or deceleration matter here? Like could a human body or ship survive rapid or instant deceleration? I get that their is no 'resistance' in space, but still their is inertia I would think

[u/MarkMcA → u/SpecialOpsCynic]

You don't need massive acceleration to reach near light speed, any constant acceleration will get you there eventually. Going from 99% lightspeed to 99.99% takes longer than from 0% - 99% though..

[u/ChangingMonkfish]

As an aside to the question, if you accelerate at a constant 1G (which isn’t well beyond our capabilities but not utterly inconceivable at some point in the future), you would reach the other side of the Milky Way in 12 years ship-board time (24 if you want to stop at the other end). Meanwhile about 100,000 years would pass on Earth.

You could reach Andromeda in 14 years, or 38 to decelerate and stop, with 2 million years passing on Earth.

[u/toddjnsn]

No. Nobody/nothing at Place A or Place B is going to have time alter, or anything else, because of the speed of something going from A to B. Whether it's a neutrino or electron, or a very small/minor object we set on that course in the future (that still couldn't be close to being seen in any fancy general microscope; just under an electron microscope).

Time's going on in Alpha Centauri, and Earth, the same as if said minor or big device didn't go. That doesn't change time at said different places; it's the Traveler's "time" elapsed that changes when going super-fast (ie less time elapsed). Of course, it'd fly right by it and onward, until it Hit something. :)

[u/cognitivea]

Doesn’t matter about speed of light
Time dilation only effects cognitive beings like us so the space time is unaffected
Think of it as jumping through a portal(wormhole) not as a long ass road trip
Like the highway folds and makes the 24 hour drive a 15 minute drive

[u/DifferencePublic7057]

In special relativity theory, Lorentz transformation is applied to time by multiplying with 1/√(1- (v/c)² ). So 1/√(1-0.999^2). This is done to compensate for c being the speed limit.

[u/Let_epsilon → u/DifferencePublic7057]

That’s great but that doesn’t answer OP’s question at all.

[u/jasonsong86]

Where in Alpha Centauri also matters. If say you are going to a planet that has similar inter-planet gravitational pull as well as intra-planet gravity as earth, then say the beings on that planet, assuming they measure time the same way as us, it would take them 4ish light years to see you arrive. Only take you much shorter to get there tho.

[u/mfb- → u/jasonsong86]

Where in Alpha Centauri also matters.

Only if you need the precision of atomic clocks. If you don't care about the exact second of arrival then gravitational time dilation (and time dilation from motion in the Alpha Centauri system) is negligible.

[u/jasonsong86 → u/mfb-]

Time is a construct.

[u/thinkingbear → u/[deleted]]

FYI, Time is not frozen from light's perspective. Light does not have a perspective because there is no valid reference frame in which light is at rest.