# Twin Paradox and Deceleration

#### muon

If velocity is relative to the observer, i.e. if there's no absolute velocity, then there's no difference between acceleration and deceleration. If you were in a cylindrical spaceship with no windows, and it suddenly accelerated, you'd be squashed against the back of the ship. If it suddenly decelerated instead, you'd be squashed against the front of the ship. If you didn't know which way was the front of the ship or the direction it was travelling, because it was cylindrical with no windows, you would have no way of knowing whether you were currently being squashed against the back because it was accelerating, or squashed against the front because it was decelerating. Is there a difference at all? To the observer, the current velocity is always rest velocity, and there's no way of telling whether you're experienced ACceleration or DEceleration, only CHANGE in velocity. Positive vs negative change is impossible to determine, and even meaningless.

This isn't just because in that example the ship had no windows. Suppose you somehow made a window in the ship. The next time you were squashed against one of the ship's ends, and you looked out the window at nearby planets / rocks etc, it appears to you that you're in fact accelerating this time, and being squashed against the back of the ship. But what if instead of an acceleration "north", those planets / rocks etc, and your spaceship, were all actually travelling together in the other direction ("south"), and your "northward acceleration" relative to them, is in fact a deceleration so that you're actually just decelerating your southward velocity?

In other words, since velocity is relative, acceleration and deceleration only make sense in the context of a given way you "want to go". They feel the same, and deceleration is literally just acceleration in the other direction.

Now put this perspective into the Twin Paradox. In the Twin Paradox, suppose Earth was travelling "left" (just to name the direction for simplicity) through the solar system at 100,000 mph, and the space twin's rocket blasts off "right", that is, against the current motion of earth, and travels at (according to its speedometer) 20,000 mph. In the normal telling of the twin paradox story, the twin who goes on the trip ends up being the one aging less because he "experienced acceleration" to begin the trip, etc and therefore was the one who "really ended up travelling closer to the speed of light". But from that perspective of earth traveling "left" and then the rocket taking off from the "back of earth" ("right") against earth's motion, the twin was decelerating, because his rocket's speed ends up being 80,000 "leftward" from that reference point (his speedometer wasn't taking into consideration that the earth itself was already going 100,000 mph left).

Since it now seems apparent that the twin can be equally validly said to have accelerated in his rocket takeoff, or decelerated in his rocket takeoff, and therefore to have ended up travelling closer to OR less closer to the speed of light while on his rocket than he was on earth, it doesn't seem possible to attribute any meaning to his "experiencing acceleration" because it can be equally validly said to have been "experiencing deceleration" and therefore for the space twin to have been travelling FURTHER FROM the speed of light while in his rocket ship (which would mean that his spaceship's clock ran faster than one on earth, not slower).

So I don't see how the twin paradox resolution (which experiments have supposedly proven as well) makes any sense. The spaceship twin experienced change in inertial frame, but there's no way of telling, or meaning of stating, whether it was positive or negative.

Am I wrong? Please help me understand it if I am, thanks

Last edited:

#### Woody

Firstly you are correct in saying that there is no difference between acceleration and deceleration.

The whole time verses relative velocity issue is difficult to get ones head around
because our brains are not suited to thinking in 4 dimensions!

If an observer in an inertial frame measures his velocity in 4 dimensions, he will find that he has zero velocity in space and a high velocity in time.
If he measures the 4Dimensional velocity of someone moving relative to him, but also in an inertial frame,
he will find that the second person is moving in space, but has lost a corresponding amount of velocity in the time component,
such that the total length of both their the 4 dimensional velocity vectors is actually the same!

Consider three observers, A,B and C
Observers A and B are travelling side by side at the same speed, in the same inertial frame of reference.
Observer C is coming up behind them travelling faster, in a different inertial frame.
Observer B starts accelerating, such that when Observer C catches up with observer B both B and C are now travelling at the same speed.
Observer B stops accelerating and is now in the same inertial frame as observer C (a faster one than observer A).

So we can see that acceleration is the act of moving from one inertial frame to a different one.

The time paradox arises when one twin accelerates into a different inertial frame, stays there a while and then accelerates back into the original inertial frame.

Last edited:
2 people

#### muon

When you say "when one twin accelerates into a different inertial frame", you're saying that that twin will always be the one who ages less no matter which direction they accelerate (meaning, it could be a deceleration to some observer, even themselves)? Then how are they any closer to the speed of light than before, if they themselves see it as a deceleration to a slower velocity?

#### Woody

There are two events in 4 dimensional space-time,
one with the two twins together just before twin B leaves
the second with the two twins together just after twin B returns.

Twin A travels between these two events by taking a short route through space, but a long route through time.
Twin B has taken a long route through space,
but remember that the 4 dimensional speed of both is the same,
so he must have taken a shorter route through time,
in order to arrive at the same second event in 4 dimensional space-time
as his stay at home twin.

(by 4 dimensional speed I mean the length of the 4 dimensional velocity vector)

Last edited:

#### muon

Ok, I think I understand, let me see:

* from the original perspective of both twins before the rocket takeoff, earth was at rest, because they were in an inertial frame
* from that original perspective, earth in fact never moves, so Spacetime Event 1 (the departure) and Spacetime Event 2 (the reunion) take place at the exact same x,y,z coordinates in space, but a different coordinate in time
* this means that, from that perspective, Twin B has moved through space, and Twin A has not
* finally that means that, since Twin B has MOVED, his velocity relative to his original velocity if his original velocity was taken as 0 (inertial), must have gotten higher for a while, so his time must have slowed

I think what I had wrong was that not every perspective matters. If his rocket trip was viewed as a deceleration from an original 100k mph "earth velocity", that perspective is irrelevant, it's the perspective *from the initial inertial frame* (in which earth's velocity is zero) is the one that matters. From that perspective, Twin B moved, and it was Twin B's own original perspective as well (prior to departure) as well as Twin A's

#### muon

How can it be a shorter route through just the space component, if they both start at point A in space, and both end at point B in space? (Regardless of whether A equals B)

But, I think what you're saying is, the perspective that Twin B decelerated and therefore slowed his speed, doesn't matter, because from Twin A AND B's initial inertial frame's perspective, earth is at rest, so from that perspective, Twin B accelerated and therefore increased his speed. And from their shared perspective upon arrival that was also the case. Because from those shared perspectives, both of which are on Earth, Earth is at rest. Is that right?

However what if there was an observer in a rocket parallel to Twin B's rocket, and travelling the same speed? And he watched the whole thing, while travelling at that same speed the whole time? From his perspective, he was at rest, and the earth was moving, then Twin B's rocket decelerated until it was at rest for a while next to his own rocket, then Twin B's rocket went incredibly fast in the other direction and "caught up to" Earth. Therefore to him, Twin B first went slower than Twin A, then went faster. If he looked through a telescope at earth upon Twin B's arrival, would he still see Twins A and B talking and saying to each other how much younger Twin B looked?

#### muon

I replied to this twice several days ago but it said it was waiting for a moderator. What can I do about getting my repli(es) to appear?

#### Woody

A while ago (about a year?) there was a spate of (annoying) spam messages getting through to this forum.
The spam filters were upgraded, and we have not (fingers crossed) had problems with spam since.
However I have noted a number of instances, like yours, where genuine posts have been blocked (particularly, it seems, for newer members).

It is another of those situations where the selfish behaviour of a few makes life more difficult for the many.

1 person

#### topsquark

Forum Staff
I replied to this twice several days ago but it said it was waiting for a moderator. What can I do about getting my repli(es) to appear?
You should be able to see them now. The spam filter kicks in with new members for their first and second posts but you are beyond that. I have no idea why.

In any event please let me know if this happens again.

-Dan

#### Woody

Did your 2 posts get reversed in the holdup...
Since the first indicates you have it,
then the second indicates confusion again.

Thinking in relative terms does become easier with some practice,
Thinking in 4 dimensions is always going to be difficult,
which is why we resort to trusting the mathematics.

Note that there is no absolute reference for position or velocity.

The key point is that one twin stays in the same inertial reference frame throughout,
while the other twin changes (accelerates) to a new reference frame
and then returns (accelerates {or if you prefer decelerates}) to the original reference frame.

Note that because he has changed his velocity (accelerated) Twin B must have moved further (through space)
But they both start at the same (initial) event in space time and end at same (second) event in space-time.

Last edited: