A thing that confuses me (quasi-paradox)

[The_AC]

Hello.

Last semester in PHYS151, our instructor said that if a rocket is traveling at .90c relative to the Earth, then time will flow slower for it. That's fine, but there's one thing that annoys me.
1. The Earth is standing still, and a rocket is traveling at 0.9c away from it.
2. A rocket is standing still, and the Earth is traveling at 0.9c away from it.

So in situation (1), time flows slower on the rocket than on the Earth, and in situation (2), time flows slower on Earth than on the rocket. A dude on Earth should think that (1) is true, but wouldn't a dude on the rocket think that (2) is true (or at least, "might as well be true")?

Is time traveling slower for the rocket just because it went through acceleration for a period of time, meaning that acceleration is what causes contraction?

 

[JesseM]

As long as the rocket doesn't turn around once it's far from the Earth, your argument is right--there is an inertial frame where the rocket is at rest ever since it left Earth, and in this frame it's clocks on Earth that are running slower than the rocket's clocks, and no inertial frame is judged to be "more correct" in any objective sense than another. The fact that two frames can disagree about which of two clocks is running slower has to do with the relativity of simultaneity, which says that different frames disagree about whether two events happened at the same time (same t-coordinate in that frame). For example, if you have twins on the rocket and on Earth who were both 20 when the rocket departed, and the rocket moves at constant velocity 0.6c relative to the Earth, then in the rocket's rest frame the event of the rocket twin turning 30 is simultaneous with the event of the Earth twin turning 28, but in the Earth's frame the event of the Earth twin turning 28 is simultaneous with the event of the rocket twin turning 26.4, so in each one's own rest frame the other one's aging is slowed by a factor of 0.8.

 

[feynmann]

Hello.

Last semester in PHYS151, our instructor said that if a rocket is traveling at .90c relative to the Earth, then time will flow slower for it. That's fine, but there's one thing that annoys me.
1. The Earth is standing still, and a rocket is traveling at 0.9c away from it.
2. A rocket is standing still, and the Earth is traveling at 0.9c away from it.

So in situation (1), time flows slower on the rocket than on the Earth, and in situation (2), time flows slower on Earth than on the rocket. A dude on Earth should think that (1) is true, but wouldn't a dude on the rocket think that (2) is true (or at least, "might as well be true")?

Is time traveling slower for the rocket just because it went through acceleration for a period of time, meaning that acceleration is what causes contraction?

It has nothing to do with the acceleration since it happened in the past. The equation in relativity has v in it, that's the speed. It does not matter how you reach that speed

 

[JesseM]

It has nothing to do with the acceleration since it happened in the past. The equation in relativity has v in it, that's the speed. It does not matter how you reach that speed

But speed is not absolute, it's relative to your frame of reference--that rocket has a speed of zero in its own frame, and comparing the perspectives of different frames was what The_AC's question was about.

 

[nealh149]

This is a question that often comes up when someone is new to Special Relativity, but it's fairly easily addressed. First consider the Rocket as the inertial frame. It has a single clock that it does all its time measurements with. Now the Earth is moving at constant v with respect to the Rocket, and it has a one clock in China and one clock in Boston, say. Now as Earth passes the Rocket clock, a man on the rocket synchs his clock with the China clock, and then measures how slow the clock moves by seeing how off the Boston clock is from his clock. This is how time dilation is measured for the rocket frame considered inertial.

Now you can imagine the Earth inertial frame can use a similar measurement for time dilation, EXCEPT that the Earth frame uses a single clock and the rocket frame has two clocks (one at the front and one at the back). So when considering time dilation, the two frames in question measure fundamentally different things about the system. They're not measuring the same thing. Thus, all paradoxes are eliminated.

I hope I was clear. By the way this argument comes mainly from Griffiths' Electrodynamics text.

 

[Naty1]

So in situation (1), time flows slower on the rocket than on the Earth, and in situation (2), time flows slower on Earth than on the rocket. A dude on Earth should think that (1) is true, but wouldn't a dude on the rocket think that (2) is true (or at least, "might as well be true")?

correct...
neither one is an absolute reference, each reference frame is equally valid, each observers viewpoint is equally valid, each observer sees the other clock as slower.

Just like sitting in a train stopped at a station as another train passes...without the platform as a reference point you can't tell who's moving...

 

[GiftOfPlasma]

This reminds me of the time my friend and I were flying in our rockets deep in intergalactic space. Now his rocket broke down and because we were in a part of intergalactic space we were not familiar with, I was going to fly off in search of a repair shop. Now because its kind of hard finding your way in intergalactic space, what with space expanding and all of these galaxies flying every which way. I was going to fly out on a laser from his position and then I could easily fly back and find him, we call it a Nav-beacon. The Nav-beacon is a two way device so it both sends and receives lasers in an omni directional manner. So before I leave him we calibrate the lasers to have the same frequency and synchronize our clocks, we agree to pulse our lasers at a 10 nanosecond interval with a 50% duty cycle. Now the Nav-beacon is a sensitive instrument, it's able to accurately measure the frequency, phase, and direction of the incoming laser signal it also times and counts the laser pulses. So I take off and I see his Nav-beacon red-shift, I start seeing a delay between when I send a pulse and receiving my friends, the pulse repetition interval of his laser gets longer and longer, and the Nav-beacon counts more pulses sent than received. Eventually I get into Comm range of a repair shop. I order the parts and setup the meeting place and I start decelerating. So the red-shift gets smaller and smaller until there is no red-shift at all, and his PRI gets closer to my PRI until they are equal, we will call this “at rest” with respect to my friend. My Nav-beacon still has counted more pulses sent than received. I pick up the parts and start back. This time his laser blue-shifts and his pulses start coming in faster than my pulses are going out and I eventually get to a point in flight when the Nav-computer says that I need to start decelerating. So I start decelerating and blue-shift gets smaller and smaller and his pulse repetition intervals get closer to mine and when the number of pulses counted are equal and there is no delay between sending a pulse and receiving a pulse, I know to engage the parking brake. And sure enough my friend is right there. You see light is the one constant, in space its the only meter stick and clock we got. It doesn't matter how much space is expanding or which way its bending as long as I stay right on laser our clocks will agree in the end.

 

[poopcaboose]

Does mass also have an effect on time? can't gravity warp the reference of time? If this is true the rest reference of the rocket will be insignificant compared to the rest reference of the earth.

 

[GiftOfPlasma]

It's more of a question about what mass does to light. Time, Space, and mass are not really good references.