# Yet another one on the twin paradox/proper acceleration

#### fluidistic

Gold Member
I don't understand why/how for instance in the twin paradox the twin that comes back to Earth will feel a proper acceleration/deceleration when turning back to Earth. I do know that this twin will suffer an acceleration since an accelerometer will tell him he's not in an inertial frame.
If I am over the Earth I will "see him" turning back and it's accelerating with respect to the Earth, I understand this. However if I was this twin and I look at my accelerometer, I'd say "wow, I'm accelerating... but with respect to what?!!!!".
On one side, I know I'm obviously accelerating with respect to the Earth but the Earth isn't a "privileged reference frame" in special relativity. So it seems like there's an "ether", in other words, a privileged reference frame from which I'm accelerating... This is how I see it. I know that the ether doesn't exist but I still don't understand what's going on.

There's this accelerometer that tells me I'm not in an inertial reference frame and that I'm "accelerating". I have no idea with respect to what I'm accelerating. It seems like in the twin paradox the Earth is treated as an inertial reference frame and not the flying twin when he's turning back, I don't understand why either.

Another thing I don't understand is that if I was born on a constantly accelerating spaceship I'd feel a force in a certain direction. But I don't understand with respect to what I'm accelerating. Does it matter? I mean, I don't see why the existence of the stars/massive matter would influence noticeably my proper acceleration if I'm between 2 galaxies. And yet it seems that this "accelerometer" will tell me in what direction I'm accelerating. So eventually I could use an accelerometer as a compass if I don't see any stars in my spaceship.

I'd appreciate if someone could eradicate my doubts. Namely, when I'm accelerating it seems that there's somehow a privileged reference frame and I'm accelerating with respect to it. I know this is wrong, but where is it wrong?

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#### ghwellsjr

Gold Member
When we talk about the twin paradox and one of the twins remaining on earth and being in an inertial reference frame, we're just pretending because the earth is not really inertial--it's accelerating all the time, not to mention the gravity. We just pretend that both twins start out not accelerating at all. Then one twin, in order to start moving with respect to the other twin must fire some rockets. That takes energy. Lot's of energy. So much energy that we can't actually do the experiment. But there is no question about the fact that his acceleration would be very real. You could say that he is accelerating with respect to his other twin who is left behind. But even if there were no other twin, we could say that he's accelerating with respect to his exhaust gases which he is going to leave behind. He has to leave some matter behind in order to accelerate. Does that help you?

Same thing when he gets far away to his turn-around point. He's going to have to turn his spaceship around and accelerate back towards home. He could reference to his home twin if he can see him or a radio signal from him but even if we ignore that and assume that there is no planet or other matter for him to reference to in his vicinity, he will leave some matter behind which he could reference to. Does that sound good to you?

By the way, there are better answers to your question but I thought this one might make more sense to you.

#### Mentz114

Gold Member
Acceleration is not relative in the way uniform velocity is. It is easy to distinguish an accelerating state from a 'coasting' state because the acceleration can be felt as a force. When the rocket engines fire, the crew of the ship will feel it, instruments can measure it, and all observers will agree that the ship is accelerating.

So it's not necessary to say with respect to what you are accelerating. Acceleration is absolute in that sense.

[simultaneous with the post above ]

#### fluidistic

Gold Member
Thanks to both guys. To ghw: I'm not sure you need to leave matter behind you in order to accelerate. Photons from a close star (Sun for example) can transfer momentum to a hypothetical spaceship, hence an acceleration.
To Mentz: Ah now I understand a bit better. But if velocity is relative and acceleration is a change of velocity divided by an amount of time, I don't see how acceleration is absolute. I totally trust you on this but I don't understand it.
If acceleration is absolute, can't we set up a position for an "ether" or better said, we could determinate if any reference frame is inertial by looking at an accelerometer? And then some systems would be privileged as inertial versus others.

#### ghwellsjr

Gold Member
Thanks to both guys. To ghw: I'm not sure you need to leave matter behind you in order to accelerate. Photons from a close star (Sun for example) can transfer momentum to a hypothetical spaceship, hence an acceleration.
You're right, I forgot about that. But you won't get much acceleration from just light and no matter.
...
If acceleration is absolute, can't we set up a position for an "ether" or better said, we could determinate if any reference frame is inertial by looking at an accelerometer? And then some systems would be privileged as inertial versus others.
Yes, that is how we determine that a reference frame is inertial. But we can have two such frames with a relative motion between them so neither one of them is privileged.

#### Mentz114

Gold Member
fluidistic said:
But if velocity is relative and acceleration is a change of velocity divided by an amount of time, I don't see how acceleration is absolute. I totally trust you on this but I don't understand it.
'Absolute' is probably the wrong word. One of the key ideas of relativity is that 'it is not possible to distinguish a state of rest from a state of uniform motion' which was first said by Newton. But it is possible to tell if you're accelerating - even if you have no external reference, because you can use an accelerometer.
Any change of velocity of a mass ( including a change of direction) is caused by a force (I'm excluding gravity) .

$$F=ma=\frac{dP}{dt}$$
This force can be detected locally.

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#### fluidistic

Gold Member
Thank you very much to both.
This is getting clearer to me now.
But I still don't understand my main doubt.
Say observer O is inside an accelerating car and O' is inside another accelerating car in the same direction with same acceleration. Both observers will look at each other and say that they are in constant motion with respect to the other but they'd feel a force so they know that they aren't in an inertial frame.
Now say you have the same situation with the 2 cars aren't accelerating. Say P and P'. They don't feel any force (accelerometers shows 0m/s²) and so in a sense they are privileged compared to O' and O.
Also with respect to what are O and O' accelerating? Hmm.
I know how to solve introductory modern physics exercises but I don't understand well this stuff about acceleration and inertial reference frame.
Any more insight is welcome.

#### Dale

Mentor
Remember that relativity is a geometric theory. Geometrically, the statement that "velocity is relative" is equivalent to the fact that you cannot define the angle of a single line, but angles are always measured between a pair of lines. Geometrically, the statement that "acceleration is absolute" is equivalent to the fact that a single line can be curved.

#### Mentz114

Gold Member
But I still don't understand my main doubt.
Say observer O is inside an accelerating car and O' is inside another accelerating car in the same direction with same acceleration. Both observers will look at each other and say that they are in constant motion with respect to the other but they'd feel a force so they know that they aren't in an inertial frame.
Now say you have the same situation with the 2 cars aren't accelerating. Say P and P'. They don't feel any force (accelerometers shows 0m/s²) and so in a sense they are privileged compared to O' and O.
This is true, but I don't see the significance.
Also with respect to what are O and O' accelerating? Hmm.
Oh dear, you're not getting this. To paraphrase DaleSpam, an accelerating object has a curved worldline and so even if it were the only worldline it would still be curved. We can define the curvature of a line geometrically without referring to any other lines or points.

#### fluidistic

Gold Member
Ok thanks guys. I'm going to check out this worldline stuff.

#### ArthurB

the earth is not really inertial--it's accelerating all the time, not to mention the gravity
This really surprises me. I thought the Earth was inertial, because it moves on a geodesic around the sun. How can a planet, a body which undergoes only gravitational interaction, accelerate?

#### ghwellsjr

Gold Member
the earth is not really inertial--it's accelerating all the time, not to mention the gravity
This really surprises me. I thought the Earth was inertial, because it moves on a geodesic around the sun. How can a planet, a body which undergoes only gravitational interaction, accelerate?
I was talking about the surface of the earth where the two twins start out in the context of Special Relativity where we ignore the effects of gravity and the rotation of the earth. If we could only discuss our thought experiments in the context of real experiments, it would be very difficult to learn anything. Most people asking questions on this forum have no idea what a geodesic is and even your comment that the earth moves on a geodesic is also merely another simplification to what is really happening because you are leaving out the effect of the moon and the tidal forces and all kinds of things.

And note that I ended my post with:
By the way, there are better answers to your question but I thought this one might make more sense to you.
I always try to answer questions in a way that I think will make sense to the one asking the question, which is what I am now doing for you.

#### ArthurB

I was talking about the surface of the earth where the two twins start out in the context of Special Relativity where we ignore the effects of gravity and the rotation of the earth. If we could only discuss our thought experiments in the context of real experiments, it would be very difficult to learn anything. Most people asking questions on this forum have no idea what a geodesic is and even your comment that the earth moves on a geodesic is also merely another simplification to what is really happening because you are leaving out the effect of the moon and the tidal forces and all kinds of things.

I always try to answer questions in a way that I think will make sense to the one asking the question, which is what I am now doing for you.
Thanks, I am still studying, I was not sure of what I wrote. I am just trying to fix some concepts in my head, so when I read "earth-not-inertial" I was scared of not understanding once again.

#### ?????

I look at my accelerometer, I'd say "wow, I'm accelerating... but with respect to what?!!!!".
You are on a space station that is just floating in space. You jump on a shuttle and accelerate away from the space station. You are accelerating relative to the space station.

A different shuttle is approaching the space station with a speed v (completely different than your shuttle's speed). You are also accelerating relative to this shuttle.

A far off planet is circling around its sun, the sun traveling at high speed away from your space station. You are also accelerating relative to all these objects.

When you accelerate, you accelerate relative to everything. Don't be intimidated by the term "reference frame". It's much simpler than you are trying to define.

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