Does Earth's Movement Affect the Twin Paradox in Space Travel?

[Tea Jay]

Think of the rod being made of jello. You can move one end of the rod fairly independently of the motion of the other end. At the time, length, and force scales where relativistic effects are important even the hardest structural steel is like jello.

Hmmm, ok, so we push one end of our jello rod, and the rod gets fatter as the jello is compressed on the pushed end, but the far end is intact, and not moving, as all the propulsive forces have been dispersed.

I'll buy that.

Does that count as accelerating the rod? Or just crushing one end of it? Would there be a difference between doing the above, and firing a speed of light piston into a bowl of jello? Would the bowl of jello undergo time travel where it was impacted, but not at the unperturbed end? Would the contraction of spacetime at the impact prevent the transmitted forces from being transmitted to the rest of the jello?

If I did have a rod of jello, I'm not sure what means I'd use to get it to accelerate, given its lack of purchase so to speak. But let's say we have means to accelerate a jello rod instantaneously...and in a way that only accelerates one end of it...how do we get instantaneous acceleration without movement? If we just happened to have such a rod when at rest, and then, anytime later when it was traveling along at the desired speed...and just started the measurements before and in flight so to speak, wouldn't we get the same readings as what was desired to be obtained by the instantaneous acceleration example?

 

[ghwellsjr]

Although we have been talking about instantaneous acceleration all along the rod causing the rod to stretch, the same thing will happen with a reasonable amount of acceleration lasting over a reasonable period of time, that is, any time we accelerate all parts of a rigid body identically, it will stretch. If we want it to maintain its same proper length (the length in its rest frame before acceleration equal to the length in its rest frame after acceleration) then we have to accelerate one part of the rod and let the rod pass the forces along its length to allow the remainder of the rod to accelerate however it wants to. In the original rest frame, it will then be contracted which means the two ends must have accelerated differently.

 

[Snip3r]

i am not sure but i think even a single elementary particle like electron shrinks as it moves. how can you explain that?or do you think this is getting too much and stepping into quantum mechanics?

 

[ghwellsjr]

Everything shrinks along the direction of motion according to the Frame of Reference in which it is moving, but not in its own rest frame. Relativity is such a well established principle that any theory (like quantum mechanics) that does not remain invariant after undergoing Lorentz transformation has to be modified until it does.

 

[Snip3r]

Everything shrinks along the direction of motion according to the Frame of Reference in which it is moving, but not in its own rest frame. Relativity is such a well established principle that any theory (like quantum mechanics) that does not remain invariant after undergoing Lorentz transformation has to be modified until it does.

ok great. But you were explaining for a rod if instantaneous acceleration is applied to all the particles simultaneously it expands else shrinks(in rest frame)but when you consider something as electron the acceleration can only be instantaneous still it shrinks. how can this be explained?

 

[ghwellsjr]

The issue is not instantaneous acceleration but rather simultaneous acceleration along all parts of the object. You have no choice about how you accelerate an electron.

 

[Snip3r]

if an electron shrinks when accelerated then is it not right to say even if simultaneous acceleration is applied to all particles of the rod, every subatomic particle shrinks resulting in the net reduction of rod's length?

 

[ghwellsjr]

It was your idea to accelerate all the particles of a rod simultaneously. Maybe you're beginning to see that it might be easier said than done.

 

[Snip3r]

It was your idea to accelerate all the particles of a rod simultaneously. Maybe you're beginning to see that it might be easier said than done.

yes it was. But you said when something like that was done, rod will expand. I am now talking about that.

 

[ghwellsjr]

Do you understand what acceleration means? Do you understand that the integral of acceleration is speed and the integral of speed is position? Do you understand that if you apply the same acceleration to two items that are a certain distance apart, they will remain that same distance apart all during the acceleration and after it is all over, they will still be the same distance apart although moving at some speed relative to their starting condition?

 

[Dale]

Does that count as accelerating the rod? Or just crushing one end of it?

It is acceleration, just not rigid body acceleration.

Would there be a difference between doing the above, and firing a speed of light piston into a bowl of jello? Would the bowl of jello undergo time travel where it was impacted, but not at the unperturbed end? Would the contraction of spacetime at the impact prevent the transmitted forces from being transmitted to the rest of the jello?

There is no such thing as a speed of light piston, so no time travel to worry about. The forces are not prevented from being transmitted in any way, they are just transmitted at the speed of sound in the jello. For jello the speed of sound is low enough that we can easily visualize the transmission of the force, but compared to the speed of light, even the speed of sound in steel is jello slow. That is why the analogy is useful.

If I did have a rod of jello, I'm not sure what means I'd use to get it to accelerate, given its lack of purchase so to speak.

When I wish to accelerate jello I typically use a spoon

But let's say we have means to accelerate a jello rod instantaneously...and in a way that only accelerates one end of it...how do we get instantaneous acceleration without movement? If we just happened to have such a rod when at rest, and then, anytime later when it was traveling along at the desired speed...and just started the measurements before and in flight so to speak, wouldn't we get the same readings as what was desired to be obtained by the instantaneous acceleration example?

That is just a useful approximation, don't worry too much about it. Think about a constant force which accelerates from rest to a fixed speed. The distance traveled is a function of the force, and in the limit as the force goes to infinity the distance goes to zero.

 

[Dale]

if an electron shrinks when accelerated then is it not right to say even if simultaneous acceleration is applied to all particles of the rod, every subatomic particle shrinks resulting in the net reduction of rod's length?

You are Probably thinking of what is called Born-rigid acceleration.

http://www.mathpages.com/home/kmath422/kmath422.htm

 

[Snip3r]

@ghwellsjr and DaleSpam
thanks :)