The twin paradox

[tar]

Delta1212,

 

So how exactly are we to determine how fast something is going?

 

My sticking point is just this. If you say the traveler is traveling at 1/2 C, but he doesn't think he is traveling at 1/2 C, by what standard can we set his speed. He is either not traveling at 1/2 C by the Sun's standards, or he is not traveling at 1/2 C by his own.

 

Regards, TAR2

[Delta1212]

Delta1212,

 

So how exactly are we to determine how fast something is going?

 

My sticking point is just this. If you say the traveler is traveling at 1/2 C, but he doesn't think he is traveling at 1/2 C, by what standard can we set his speed. He is either not traveling at 1/2 C by the Sun's standards, or he is not traveling at 1/2 C by his own.

 

Regards, TAR2

You can't. Things only move with respect to other things. There is no "real" velocity at which anything is traveling. All motion is relative to something else, hence the name.

[michel123456]

If you put a mirror on the White dot, then what the left part will show is the light coming straight down, hitting the white dot and then retracing its path straight up and returning to the source.

 

The right side (according the white dot) has the light coming in a an angle from the right, bouncing off at an angle to the left, and intercepting the yellow dot as it travels to the left.

Why is it different?

The white dot on the left is moving like the yellow dot on the right.

Rotate the right side 180degrees and explain me the difference

[md65536]

So how exactly are we to determine how fast something is going?

 

My sticking point is just this. If you say the traveler is traveling at 1/2 C, but he doesn't think he is traveling at 1/2 C, by what standard can we set his speed. He is either not traveling at 1/2 C by the Sun's standards, or he is not traveling at 1/2 C by his own.

Use a clock and a ruler, measure distance traveled and divide by elapsed time. Just make sure that you use a clock and ruler in the same frame.

 

Correction: Re. post #205, 206, better safe than sorry, I think that's just wrong. Relative velocity between two objects, as measured by an arbitrary observer, isn't simply change in separation distance per time.

 

 

 

The traveler is traveling at .5 c according to Earth's clock and ruler, and it is traveling at .5 c relative to Earth according to its own clock and ruler. Or .5 c relative to Earth according to the sun's measurements or according to some passing alien or according to anyone. There's no measure of velocity here that has it not traveling at .5 c relative to the Earth.

 

Why is it different?

The white dot on the left is moving like the yellow dot on the right.

Rotate the right side 180degrees and explain me the difference

One's the source and one's the observer. However they both can observe each other, they both can be both source and observer, and you can make it symmetrical. In that case there's no difference; both see the other distorted by aberration effects. The effect is symmetrical.

Edited May 25, 2013 by md65536

[Delta1212]

Use a clock and a ruler, measure distance traveled and divide by elapsed time. Just make sure that you use a clock and ruler in the same frame.

 

The traveler is traveling at .5 c according to Earth's clock and ruler, and it is traveling at .5 c relative to Earth according to its own clock and ruler. Or .5 c relative to Earth according to the sun's measurements or according to some passing alien or according to anyone. There's no measure of velocity here that has it not traveling at .5 c relative to the Earth.

I think that may be slightly misleading, because I can interpret what you just said in two ways. One of those ways is obviously correct, but seems like it would be misleading given the way you worded it, and the other seems like it would be wrong, although I'm on shaky ground here.

 

If by "traveling at 0.5c relative to Earth" you mean that everyone's measurements agree that the Earth sees the shpaceship moving at 0.5c, then yes obviously. If you mean that everyone measures a 0.5c difference between the velocities of Earth and the spaceship, that doesn't seem like it would be correct.

 

You probably mean the first, but it sort of sounds like you're saying the second, especially in the context of addressing someone who (no offense, michel) has expressed difficulty in grasping certain aspects of how relativity works to begin with.

 

Or, alternatively, I'm wrong to presume that the second case is inaccurate and I have more to learn.

[md65536]

If by "traveling at 0.5c relative to Earth" you mean that everyone's measurements agree that the Earth sees the shpaceship moving at 0.5c, then yes obviously. If you mean that everyone measures a 0.5c difference between the velocities of Earth and the spaceship, that doesn't seem like it would be correct.

 

You probably mean the first, but it sort of sounds like you're saying the second, especially in the context of addressing someone who (no offense, michel) has expressed difficulty in grasping certain aspects of how relativity works to begin with.

I meant the second. I doubted what I wrote but after thinking about it figured it was right, even though I'm not 100% convinced.

Edit: But I DO mean "relative velocity of Earth and the spaceship" and not just difference of velocities, or in other words we must use composition of velocities instead of just adding or subtracting them.

 

Certainly it's an unnecessary complication to this discussion, I think, in exactly the same way that introducing a new observer is, and questioning whether what they see is consistent ("what about the sun's point of view" etc).

 

 

But for sake of argument...

Say traveling twin B is moving relative to Earth E at velocity v.

Consider the measurements of an arbitrary inertial observer, for whom Earth is moving at relative velocity vE and the traveler at vB, then using composition of velocities *I think* you should find that in the new observer's frame, B is moving with relative velocity v relative to E.

 

 

I know that velocity c is invariant regardless of who measures it. I'm not sure about other velocities but I can't think of any way to make two observers measure different velocities of two specific objects relative to each other.

 

 

Edit: Yes, I see some additional possible confusion. I do mean "relative velocity of one object relative to another" and not anything like separation rate or closing rate, which is like... the rate of change of E relative to the new observer plus the rate of change of B relative to the new observer... or the relative velocities of two objects relative to a third... :S --- So like you said, velocity is relative to something, and we must be clear about what we're measuring relative to. So with an arbitrary observer's instruments, it should measure B moving at v relative to E, but generally not so relative to the observer.

 

(For example if B is leaving E at v near c, an observer in the middle might see B and E receding at near c in opposite directions, at a separation rate that can approach 2c, but still measures the velocity of B relative to E (or vice versa) as v, using composition of velocities.)

 

 

Edit: And one more complication!: In light of this, I must admit that an arbitrary observer can't simply take its ruler and clock measurements and divide to get v, it must deal with things like relative simultaneity ... and basically adjust for the differences between what is seen and what is measured. Or in other words the correct velocities must still be properly calculated from whatever observations are used to measure it.

Edited May 25, 2013 by md65536

[Delta1212]

Edit: And one more complication!: In light of this, I must admit that an arbitrary observer can't simply take its ruler and clock measurements and divide to get v, it must deal with things like relative simultaneity ... and basically adjust for the differences between what is seen and what is measured. Or in other words the correct velocities must still be properly calculated from whatever observations are used to measure it.

Yeah, this is what I was getting at.

 

Edit: Well, that and the fact that the difference between relative velocity and separation/closing rate is not obvious if you're already having trouble with relativity.

Edited May 25, 2013 by Delta1212

[md65536]

I think that may be slightly misleading, because I can interpret what you just said in two ways. One of those ways is obviously correct, but seems like it would be misleading given the way you worded it, and the other seems like it would be wrong, although I'm on shaky ground here.

Thanks, after struggling with it a bit I think the first half of what I wrote was misleading and plain wrong, but I'm 99% sure the second half is okay if the first half is ignored!

 

Edit: Make that 50% sure. Or maybe 10%. Let me try again!...

 

I guess velocity is rate of change of position, so velocity of one object relative to another is rate of change of position measured in coordinates where the second object remains fixed. To speak of a ship's velocity relative to Earth's, it is the change in position of the ship as measured with the Earth fixed, which is what is measured in Earth's frame. To say others "measure" the same thing is essentially translating what they measure into what the Earth would measure. This is essentially what you wrote, "everyone's measurements agree that the Earth [measures] the spaceship moving at 0.5c".

 

Less misleading would have been to say "Everyone uses the same measure of the ship's velocity relative to Earth's, which is d/t as measured in Earth's frame."

 

 

Edit: Well, that and the fact that the difference between relative velocity and separation/closing rate is not obvious if you're already having trouble with relativity.

Definitely... I think one ought to approach learning about this by either striving to first look at only the simplest setup possible (eg. forget about a third observer or alternative measures of speed), until it makes sense, or consider more complicated situations with an expectation that it DOES work out consistently, but the calculations can get complicated.

Edited May 25, 2013 by md65536

[tar]

MD65536 and Delta121,

 

Considering that everything is relative, relative to what is still going to be a consideration.

 

I see no actual harm or "incorrect" thinking, to lay out an actual grid of wavefronts of light in the Sun's FOR and work out, everything else from there. Here of course you would have to "count" and label each wavefront to differenciate between "which" wavefronts are passing through E and which ones are passing through B and which ones B is passing through by virtue of his motion through the grid.

 

For instance since this is a changing grid in that the wave fronts that left E last Saturday are now 7 lightdays out, the .5C B will NEVER encounter them. However his destination, one lightyear out, in the Earth's FOR, will not enounter those particular waves for 51 weeks.

 

Conceptually, this view seems realistic to me, and things would "have to" happen that way.

 

The "count" from behind would lag B's count, the count from infront would increase in rate, and when he got to the turn around point, the count in the direction of E would be "off" his own count by one year/s worth of the frequency of light he was counting, and the count of this frequency from the destination would have a 1 year surplus. Effectively putting B one ly away from Earth, as he is now experiencing the exact same numbered wavefronts, that the destination is encountering.

 

Who is, or should be on what count of what wavefront coming from what apparent direction, should be figurable from any observer on the grid, moving in reference to the Sun's frame, at any v.

 

That different positional observers are experiencing differently labeled wavefronts, ie. the 498,948th from event e with a duration of 500,000, or the 334th, is a matter of position in the grid. In fact, some positional observers, even in the Sun's FOR, far enough away have not even encountered wavefront 1 yet, and those very close positionally to e saw the whole event already and wavefront 500,000 is already a thing of their past.

 

Time dilation doesn't factor in as an actual occurence, but as a shifting of mental position, without accounting for actual shifts in position on the grid.

 

Maybe.

 

Regards, TAR2

 

From a philosopical point of view, it is the mental shift between the "actual" now that all points must be experiencing simultaniously at "one" time, "this" time, which can only be experienced at once in an imaginary way, that is difficult to connect with the actual view which we have of everything happening at once, here and now, as the wavefronts hit our equipment, which is after all, actual reality, which puts our mental image of an "actual" now, into the imaginary category.

 

I do not think it is hard to imagine another "not getting it", nor to imagine oneself in the same position.

Edited May 25, 2013 by tar

[Delta1212]

I'm not entirely sure what some of that meant, but I'll try to address what I can.

 

Could you treat the sun's FOR as a preferred frame, calculate everything from the frame of the sun, and get consistent results? Yes. You can also do this with literally any other frame, however, so there is no objective basis for treating any of them as the true "rest frame" for everything. It would be an arbitrary selection with no basis in reality. There simply isn't any way to tell whether something is at rest or in uniform motion except in relation to something else, and it is equally valid to say that that something else is moving.

 

As far as time dilation goes, we've measured a difference in the rate at which time passes depending on how fast an object is moving, as well as how deep in a gravity well it is. I'm not sure how what you've described would negate time dilation as a physical occurrence.

[md65536]

I see no actual harm or "incorrect" thinking, to lay out an actual grid of wavefronts of light in the Sun's FOR and work out, everything else from there.

 

[...]

 

Effectively putting B one ly away from Earth, as he is now experiencing the exact same numbered wavefronts, that the destination is encountering.

Yes, you can work it out from any frame and it will be consistent.

 

B and the destination counted the same number of wavelengths from Earth since B left. Where time dilation comes in is that B's clock is slower*; it has ticked 0.866 times as many as the destination's clock has during B's trip. So the frequency of the signals is also measured differently. Time dilation is real.

 

The observed frequency is also measured differently... there is Doppler shift as well as time dilation. (Note the destination, at rest with Earth, receives the signals at the same rate they were sent, though still delayed. If Earth sent 104 signals over 104 weeks, delayed 52 weeks according to destination, they both receive 52 signals by the time B reaches the destination.)

 

 

 

* This assumes B starts at rest relative to Earth, so that everyone can allow Earth's and the destination's clocks to be synchronized. Unnecessary complication: If B is already moving (eg. just passing Earth) then B and the destination both think the other's clock is slower than their own, but it still works out because they disagreed on the time at the destination when B passed the Earth!

[tar]

I'm not entirely sure what some of that meant, but I'll try to address what I can.

 

Could you treat the sun's FOR as a preferred frame, calculate everything from the frame of the sun, and get consistent results? Yes. You can also do this with literally any other frame, however, so there is no objective basis for treating any of them as the true "rest frame" for everything. It would be an arbitrary selection with no basis in reality. There simply isn't any way to tell whether something is at rest or in uniform motion except in relation to something else, and it is equally valid to say that that something else is moving.

 

As far as time dilation goes, we've measured a difference in the rate at which time passes depending on how fast an object is moving, as well as how deep in a gravity well it is. I'm not sure how what you've described would negate time dilation as a physical occurrence.

Delta1212,

 

Under the circumstances that one cannot objectively consider themselves a stationary frame of reference, it would be difficult to say that anything else was moving at a particular velocity. Since the other thing could just as well be stationary, and ones whole frame of reference could be moving, under what reasoning does one say a things clock is ticking slower, because of its velocity?

 

I would still vote for considering here and now, a singlular place and time, from which all else can be referenced. There is no purpose or value in considering any other reference point as a starting or end point. Even if it is true that there are really an infinite number of "other" reference points, concievable, we have no access to the others, until we should get there ourselves. At which point we would still be in complete possession of our own frame of reference. And the separation from what we consider here and now, would be a matter of real time, and real distance. Our own frame of reference is still the only one available, and still includes, the rest of the universe.

 

I have asked before, in other threads about which is true about the star 4.2 lys from here.

That it exists now, doing what we see it doing.

That it exists now, and we will not see what it is doing for 4.2 years.

 

If there is only one instance of said star, there cannot be two answers to the question.

 

One consideration must be real, and the other imaginary.

 

Personally it seems the most real "timeline" that joins that star to this Earth is the one considering the arrival of light from that star, here, now. Its been the truth for as long as human history is.

 

The consideration that that star "also" exists in a manner that will not present itself to us, for 4.2 years, is not "real" to us in any testable, meaningful way, except in the sense that its already proved itself existing 4.2 years ago, as its presenting itself to us now.

 

We are insulated in time and space from that star's "actual" now. If we could get ourselves there, there would not be that separation any longer, and the Earth's Sun, would be in that same "dual" position as that star is in to us, now.

 

There is nothing more understandable, and presently available to us, than the Earth's frame of reference.

 

Why not use it exclusively to define, everything else?

 

Regards, TAR2

[md65536]

I would still vote for considering here and now, a singlular place and time, from which all else can be referenced. There is no purpose or value in considering any other reference point as a starting or end point. Even if it is true that there are really an infinite number of "other" reference points, concievable, we have no access to the others, until we should get there ourselves.

That's like voting that the Earth is flat because you never plan to leave your village, and you can't imagine anyone else ever leaving their villages.

 

People do have "access" to other frames of reference (GPS, particle colliders, astronomical observations, etc).

[Delta1212]

Besides which, by convention, we do treat Earth as the default "rest frame" for most measurements of speed. Scientifically speaking, if you were doing 100mph down the highway and a cop pulled you over, you'd be correct to state that you weren't doing 100mph. In fact, you were at rest and the Earth was zipping by you.

 

Same for the velocities of spacecraft and celestial objects and such. Any time you see anything at all described as moving at any speed other than "at rest" it's generally being given in comparison to either the Earth or, occasionally, the sun.

 

But we also recognize that this is just a convention, that it is arbitrary, that literally any other frame would work just as well, and that sometimes you'll want to calculate results according to a frame other than the conventional one.