Both think the other's time is slower Paradox

[Odrabmug]

Now I know there's another thread like this, and I read through it but still don't understand... So I'll present my own 'case' here.

Two astronauts pass each other in space at speeds close to that of light (let's say one is at rest while the other one has a velocity greater than zero). As they pass each other they wave. To my understanding, both of them sees the other waving at a slower than normal rate (thus they both think that the others "clock" is ticking slower than theirs).

Now I get the point that you'd never know which is the one moving, but does that really matter? One of them IS traveling faster than the other, does it really matter that the minds of the humans don't know which one is moving faster, isn't it sufficient enough that the universe 'knows'? I mean, a tree falling with no one around to hear it still makes a sound...

Another question, why don't they both see each other waving exceptionally fast? How come the default position is that they each believe they're the ones traveling slower, why don't they each believe they're the ones traveling faster and thus see the other person moving faster than normal?

Thanks in advance.

 

[russ_watters]

Welcome to PF.

Now I get the point that you'd never know which is the one moving, but does that really matter? One of them IS traveling faster than the other, does it really matter that the minds of the humans don't know which one is moving faster, isn't it sufficient enough that the universe 'knows'?

You misunderstand: it isn't that we can't tell what something's absolute speed is, it's that absolute speed does not exist. One of them really isn't traveling faster than the other.

 

[Odrabmug]

Welcome to PF. You misunderstand: it isn't that we can't tell what something's absolute speed is, it's that absolute speed does not exist. One of them really isn't traveling faster than the other.

Mm yes I see, spacetime is the only absolute.. Well then is there ever a scenario where a viewer would see the other person moving exceptionally fast? And if so, what's the difference from the situation I previously presented?EDIT: Also, doesn't kinetic energy increase as speed increases? And if so, isn't an objects kinetic energy absolute enough to distinguish speeds?

 

[Janus]

EDIT: Also, doesn't kinetic energy increase as speed increases? And if so, isn't an objects kinetic energy absolute enough to distinguish speeds?

Kinetic energy is only relative too.

 

[Odrabmug]

Kinetic energy is only relative too.

Oh wow okay, things are starting to make more sense now that I know that...

But again, is there ever a situation that you'd see someone moving exceptionally fast? Or is it always the preferred option (I understand preferred is a physics term which I have no idea what it means, I'm using it colloquially) to assume that you're the one traveling at a slower velocity and thus you see the person moving slower than normal relative to your time?

 

[ghwellsjr]

Now I know there's another thread like this, and I read through it but still don't understand... So I'll present my own 'case' here.

Two astronauts pass each other in space at speeds close to that of light (let's say one is at rest while the other one has a velocity greater than zero). As they pass each other they wave. To my understanding, both of them sees the other waving at a slower than normal rate (thus they both think that the others "clock" is ticking slower than theirs).

Now I get the point that you'd never know which is the one moving, but does that really matter? One of them IS traveling faster than the other, does it really matter that the minds of the humans don't know which one is moving faster, isn't it sufficient enough that the universe 'knows'? I mean, a tree falling with no one around to hear it still makes a sound...

Another question, why don't they both see each other waving exceptionally fast? How come the default position is that they each believe they're the ones traveling slower, why don't they each believe they're the ones traveling faster and thus see the other person moving faster than normal?

Thanks in advance.

You can pick a frame of reference where the first astronaut is at rest and the second one is traveling near the speed of light and as the astronauts are approaching each other, they will both measure the other one as approaching at whatever fast speed is the actual speed difference between them, they both measure the same speed. Furthermore they will both "see" each other waving much faster than normal and they both "see" the other one's clock spinning much faster than their own, but when they use the Relativistic Doppler formula to calculate the time dilation of the other one's clock, they each realize that the other one's clock is running slower than their own, and by the same amount.

And then as they pass each other, all of a sudden they will "see" the other one waving much slower than normal and they both "see" the other one's clock spinning much slower than their own, but when the use the Relativistic Doppler formula to calculate the time dilation of the other one's clock, they each realize that the other one's clock is running at the same slow rate as before but not as slow as it "looks" like it is going. They also continue to measure the same speed difference between them.

Now after doing all that, you can pick another frame where the second astronaut is the one at rest with the first one traveling and all the same analysis that was done before will apply again. Or you could pick a frame where each astronaut is traveling at the same speed but in opposite directions and again, all the same analyses will apply.

One point is that when traveling at very high speeds, the color of light actually shifts outside the visible range which is why I put a lot of words in quotes. These astronauts would have to look through some field glasses that let them see into the invisible wavelengths, but that's a minor point for what you are asking about.

Another point is that Relativistic Doppler combines the effects of time dilation plus the compression or expansion of light so that time related things (hands waving, clocks ticking) appear much faster or slower than they are actually, but the relative speeds of motion always appear just as they really are for constant speed, like you are describing,

 

[Odrabmug]

I see, last few questions then:

Is it true that no matter what, observers will see moving clocks ticking more slowly than their own? Is there a situation where observers will see moving clocks ticking faster than their own?

 

[lugita15]

I see, last few questions then:

Is it true that no matter what, observers will see moving clocks ticking more slowly than their own? Is there a situation where observers will see moving clocks ticking faster than their own?

Someone has already made this point, but let me just reiterate it. There's a bit of ambiguity in your question. In the fantastic introductory book Spacetime Physics, a distinction between "seeing" and "observing" is made. You have to remember that an observer don't just magically know how the tick rates of all the clocks in the universe, so that he can determine which ones are going faster or slower than normal. He has to acquire that information somehow. For instance, every time a clock ticks, it can emit light which reaches his eyes. But he can't just naively take the rate at which light pulses hit his eyes as the tick rate of the clock. This is because of the relative nature of time, which implies that frequency is different in different inertial reference frames.


So you may "see" a clock ticking unusually fast, but then if you correct for the transformation of frequency, you'll find that you "observe" that the clock is ticking unusually slow.

This is a bit counterintuitive, but that's relativity for you.

 

[Odrabmug]

Ah now I understand the difference, but then I'll just rephrase my questions to include observe:

Is it true that no matter what, observers will observe moving clocks ticking more slowly than their own? Is there a situation where observers will see observe clocks ticking faster than their own? (This is all at constant velocities without any acceleration)

 

[lugita15]

Is it true that no matter what, observers will observe moving clocks ticking more slowly than their own?

Yes, that is always true. If an observer in an inertial frame sees a clock that is moving with uniform velocity with respect to him, then he will "observe" the clock to be ticking slower than usual.