# Black Holes time slows down

russ_watters
Mentor
So time dilation like this could be possible without a black hole? What did you mean by "c"?
C is the speed of light and time dilation also occurs at high speed. So rather than trying to go around the nearest black hole, you could just accelerate to close to the speed of light, then turn around and come back. When you got back, more time would have passed on earth than for you on your ship.

Whats the closest a spaceship can get to traveling at the speed of light?

Chris Hillman
Whats the closest a spaceship can get to traveling at the speed of light?
Arbitrarily close, as several posters have already pointed out. I stress again (sigh...) that velocity is always relative to another observer, usually an inertial observer. Did you yet look at the web page I cited above? All your questions are answered there.

DaveC426913
Gold Member
All you have to do to experience time dilation is have a rocketship with a nigh-bottomless fuel supply ... and a lot of patience.

You could fly the shuttle out from the solar system for a few months. After a few months of contstant accelreation (even the low acceleration of the shuttle's retros), you'll be travelling near the speed of light. Turn around and fly home. You will have expereinced less time than those on Earth. How much less time is dependent on how close you got to the speed of light and how long you were there.

There are calculators that will tell you how long a dilation will be exprienced for given input values. Google "relativistic calculator".

Chris Hillman
All you have to do to experience time dilation is have a rocketship with a nigh-bottomless fuel supply
I forgot to mention that the bottomless fuel supply is an extremely dubious aspect regarding any proposal to accelerate a spaceprobe to near the speed of light using a conventional rocket engine. Right now the best way to achieve reasonably large velocities relative to the solar system seems to be to use the major planets to achieve a "velocity boost", carefully aim at the nearest black hole, wait a few million years, and do the same thing upon arrival. (No, not a serious proposal with current technology!).

C'mon, this is supposed to be the best theoretical physics forum on the entire internet. "Google relativistic calculator" :yuck:

Let's work out the case of the photon rocket. Suppose in some frame the rocket is initially at rest in space. The four momentum is P1 = (M1,0). Then it burns anti-matter fuel and it's four momentum becomes P2= (M2 gamma, M2 gamma v). Conservation of four momentum:

P1 = P2 + Pf

where Pf is the total four momentum of the emitted photons and is thus of the form (E, -E). This means that:

Pf = P1 - P2

Square both sides and use that

Pf^2 = 0,

P1^2 = M1^2

P2^2 = M2^2

P1 dot P2 = gamma M1*M2

So we have:

0 = M1^2 + M2^2 - 2 gamma M1 M2 ----->

gamma = 1/2 [X + X^(-1)]

where X is the ratio of the final and initial mass

Note that if we use massive particles instead of photons Pf^2 would be strictly larger than zero and you would get a smaller gamma factor for the same initial/final mass ratio. So, the photon rocket is the best we can get.

Now, if we want to return to Earth we must put X= (M1/M2)^(1/4), where M1 is the initial mass of the rocket (which includes the fuel) and M2 the final mass. This is because we must accelerate to the gamma factor, and then change the direction of the velocity, which is equivalent to changing the velocity to zero and then back to the sama gamma factor but with the velocity in the opposite direction.

Then, when we reach Earth we must reduce the velocity to zero. If we want to travel at the same gamma factor during the trip, then the mass ratio's before and after the boosts must be the same each time, so X^4 = M1/M2

Now, we can play the following game. Suppose we have an anti-matter factory that produces anti-matter at a constant rate. We want to travel to some far away place, so we need a lot of antimatter. But, unfortunately, that takes a long time. An obvious strategy is to use some of the produced anti-matter to make small excursions. When we return form an excursion more time has passed in the frame of the factory, so we have a lot of anti-matter. If we do this right, we have more anti-matter than we would have had, had we stayed home despite using some for the excursion.

Now, if I remember correctly, it turns out that you can reduce the proper time you need to wait before you have the desired amnount of anti-matter be a factor of order Log(T/t), where T is the time needed to produce the anti-matter in the rest frame of the factory and t is the time needed to produce an amount of anti-matter equal to the mass of the rocket.

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DaveC426913
Gold Member
I forgot to mention that the bottomless fuel supply is an extremely dubious aspect regarding any proposal to accelerate a spaceprobe to near the speed of light using a conventional rocket engine.
No, but planetary lasers are the next best thing.

DaveC426913
Gold Member
C'mon, this is supposed to be the best theoretical physics forum on the entire internet. "Google relativistic calculator" :yuck:
You think the OP would rather have a half screen of calculation that leads to a single answer than be shown a tool where he can play to his heart's content?

You think the OP would rather have a half screen of calculation that leads to a single answer than be shown a tool where he can play to his heart's content?

The relativistic calculators only give the formulae for the gamma factor as a function of velocity. Trivial stuff. And without knowledge of relativity you wouldn't be able to see that the gamma factor is simply 1/2 [X + X^(-1)] where X is the mass ratio before and after the burning of the anti-matter fuel. So, a 10^6 kg spacecraft carrying 10^6 kg antimatter fuel can reach a gamma factor of
(1/2)(2 + 1/2) = 1.25. And note that this formula was derived above in 13 (small) lines. The derivation was so simple that you can imagine doing it in your head without paper and pencil.

So, who needs the "relativistic calculator" :rofl:

I heard a theory that black holes exist on Earth, like really really tiny ones I read something about it being someone's theory when I read something about people contemplating making really really tiny black holes in a collider

ZapperZ
Staff Emeritus