# What speed shall I go to make my day longer?

I have many things to do during my day (work + study + projects + ... + ...)

and seriously 24 hours a day is not enough to finish my tasks.

I know that by Einstein's theories that time gets slower if travel fast.

So I decided to travel fast ( not to the speed of light, but a closer speed maybe)

All I want is 12 hours extra a day, so my day is 36 hours.

So at what speed I should travel to make my 24 hours day (travelling hours) equals 36 hours (normal earth hours)?

Edit

Reading comments and answers, I realised that I need to have 36 hours travelling while earth only made 24 hours, if that possible!

Which means I have to make earth goes close to the speed of light while I am still not moving!!

but if I travelled to the speed of light ( from my perspective i am still and the earth is moving)

I am confused now!.

• Surely this would make your problem worse - a due date 36 hours in the future would be upon you in only 24! Mar 16 '21 at 23:44
• @J.Murray Maybe they could be doing their HW in a stationary spaceship while they somehow accelerate the entire earth. Mar 17 '21 at 0:12
• Related: you can get a few extra nanoseconds per day, relative to sea-level-dwellers, if you spend your time on a mountaintop.
– rob
Mar 17 '21 at 1:21
• @rob How do you think those monks get all that time to work on enlightenment? 😏OP, you have to arrange high-speed/strong-gravity space travel for your professor as already suggested. For a heuristic check, remember who got old and who remained young in Interstellar. ;-) Mar 17 '21 at 1:47
• Head west at 1000 km/h. This will get you roughly one sunrise per 36 hours.
– Mark
Mar 17 '21 at 22:33

I'm afraid you have it backwards. A stationary (inertial) clock takes the longest possible path through spacetime, and accelerating the clock will reduce the length of its path (I.e. the elapsed time for it). If you travel very fast then only a little time passes for you, while years may pass on Earth. This would not help you get more done in an Earth day!

• However, if you go up into space you can get a little more time! (only a little) Mar 17 '21 at 13:26
• Just introduce a pluterday (a.k.a. pluterdag or framstag), an 8th day of the week than only exists for the rich and privileged ;-) Mar 17 '21 at 13:47
• An inertial clock takes the longest path through time, but not spacetime, surely? A moving clock travels less distance in time, but more distance in space. The spacetime interval is the same, though. All observers who measure the time and distance between any two events will end up computing the same spacetime interval. If you and your twin shake hands and the twin goes on a 24h journey at speed, meeting you back on earth 36 of your hours later, the spacetime interval you both traverse is the same because you both measure the same start and endpoint events.
– J...
Mar 18 '21 at 10:18
• So really what I'm reading from this is that you need to accelerate the Earth to relativistic speeds, while you stay still. Of course then you'll be left floating alone in empty space, unable to get much of anything done. Hope you brought a spacesuit. Mar 18 '21 at 13:30

If you want to experience 36hrs while 24 hrs elaspses in Earth, Earth should move and not you. Using the relation $$t'=\displaystyle{\frac{t}{\displaystyle{\sqrt{1-\Big[\frac{v}{c}\Big]^2}}}}$$, you can find out the velocity with which Earth should move. $$\displaystyle{\sqrt{1-\Big[\frac{v}{c}\Big]^2}}=\frac{t}{t'}$$ $$\Big[\frac{v}{c}\Big]^2=1-\Big[\frac{t}{t'}\Big]^2$$ $$v=c\sqrt{1-\Big[\frac{t}{t'}\Big]^2}$$ Substituting $$t=$$ 24hrs, $$t'=$$ 36hrs and $$c=3\times10^8ms^{-1}$$, you'll get $$v=\sqrt{5}\times10^{8}ms^{-1} \approx 0.75 c$$

• @EricSmith it's the Earth that should turn back, not you. Otherwise you'll get less time to do things than people on the Earth. Mar 17 '21 at 12:18
• How do I know if I'm moving away from Earth or if Earth is moving away from me? Does it require a 3rd body as a reference point? Does it matter if the 3rd body is moving? Mar 17 '21 at 14:02
• @DarrenH c.f. en.wikipedia.org/wiki/Twin_paradox Mar 17 '21 at 14:48
• @TobiasKienzler thanks, a lot of contemplating to do there! I must get my head around this Mar 17 '21 at 15:21
• @DarrenH: If I recall, the big TL:DR: is that the twin who feels the acceleration (up to light speed and then back to rest) is the one who experiences relativistic effects, like aging more slowly relative to the rest of the universe. Mar 18 '21 at 12:05

The layman's answer would be that for you it will be the same time. If you measure your pulse you will get 76 no matter your speed.

In other words, you will not feel the time passing slower when you travel fast.

What you will see, however, is that when you are back, the time of the others has gone faster (= you will be relatively younger)

• Wel, if I would travel at half the speed of light, my pulse would probably go up... Mar 18 '21 at 8:22
• @Toffomat: I thought about this as well but I wanted to keep the answer without any jokes because the concept is not obvious to understand in the first place.
– WoJ
Mar 18 '21 at 8:28
• Younger than your hypothetical identical twin who stayed on Earth, but not younger than your past self. Mar 18 '21 at 11:23
• @Neurotransmitter: yes, this is why I used relatively in the last sentence.
– WoJ
Mar 18 '21 at 11:35
• Relatively younger than your relatives? Mar 19 '21 at 6:10

You can't do more things simply by going fast. All the things you are doing have to go along with you and move through time at the same rate as you do.

Suppose you accelerate to close to the speed of light (as seen from Earth), together with all the necessary stuff for doing the things you want to do. From Earth, it appears as if your wristwatch has almost stopped. You and all the stuff that goes along with you seem to move real slow. But you don't experience anything strange. It would be strange if all the stuff you brought along would move slower according to you. In that case, you could manipulate even less stuff (in reality, this only occurs if the stuff is moving fast relative to you, so you can't actually manipulate it).
If the stuff moves faster in time relative to you (which in reality never occurs), you would have a chance. You could make a sandwich in a flash (but eat it in your own time), travel to the other side of the Earth in no time, or wrap a packet in a second. But it would be very difficult for your body to synchronize with the stuff surrounding you. This would be a nice idea for a sci-fi movie.

Suppose you move away from Earth at near light speed with a huge amount of stuff to do. If you return to Earth, then, according to the [twin paradox] 1 things on Earth will have aged much more than you (and the stuff you brought along). So in effect, you'll have done the things you wanted to do in more Earth time. I.e., you'll have the same things in more time and not in less.

You could do things on a high mountain. Up there time goes faster than at sea level. Or even better, hire a rocket and do your stuff on board when circling the Earth. If you come back things on Earth will be somewhat younger than you and you'll have done more things than you would have done if you'd stayed on Earth. The amount of gained time is such small though that you better could have stayed down. It takes a lot more time to climb a mountain or take off in a rocket.

So it's best to just do things faster (and getting tired).

As the others have answered moving fast will not help you. But if you move infinitely far away from the Earth (or just far enough) you will have gravitational time dilation on your side! Unfortunately you can only get limited time gains from this. To compute the gravitational time dilation experienced close to a massive object we can use the formula $$$$t_0=t_\infty\sqrt{1-\frac{2GM}{rc^2}},$$$$ where $$t_\infty$$ is the time you experience and $$t_0$$ is the time experienced on the surface of the planet. Inserting the Earths mass and radius into $$M$$ and $$r$$ we obtain that one second for a faraway observer is ~$$0.999999999305$$ seconds for an observer on the earth. This is far from your desired extra 12 hours per day, but it results in you gaining an extra $$0.02193$$ seconds per year!

Other answers have computed that with Earth moving at 75% lightspeed you would get your 12 extra hours. But time dilation is symmetric! So you can get the same effect if you move yourself at 75% lightspeed! As you very quickly leave it behind, Earth will appear slowed down to you.

How helpful this is for your practical purposes is limited, as you will also appear slowed down when observed from the Earth.