Bernoulli wrote:

Cito di Pense wrote:

Bernoulli wrote:What is the reference frame in space? I'm assuming it's space-time. But how does one tell whether space time is moving relatively to one or not?

It is space-time, and you deal with events which help to determine your choices. You choose the reference frame that makes your calculations the easiest without letting them be incorrect.

That doesn't answer the question. There has to be a privileged frame for acceleration to be experienced by one body and not another body relative to it.

That's a big part of the problem. Acceleration isn't a subjective experience, as long as you follow the rules for identifying frames. That is because the accelerating frame experiences forces equivalent to gravitation that can be measured in that frame. The other frame just sees a starting velocity for the other frame and some other velocity later. Where's the privileged frame? There's an accelerated frame, but still no privileged frame. An inertial frame is by definition not experiencing any net force because (guess what) it isn't accelerating. What's a force? It is that which accelerates a mass. Seems circular, don't it? Let's expand the scope of the inquiry, and ask what 'mass is'. Pretty soon, you no longer care about the twin 'confusion'.

Evolving wrote:You can only say how fast a clock is running once you have decided on your frame of reference.

I haven't decided anything. The author of the SA article did that. If it takes 8 years on traveller's clock to get to a star, and 10 years on homebody's clock, then that's 1.25x, not 2x. As I said, if one clock really was running at twice the speed of the other, then the age difference when the twin returned would be greater than what it is.

Cito di Pense wrote:Where's the privileged frame?

The accelerating frame is the privileged one in the relativity equations.

Bernoulli wrote:

Cito di Pense wrote:

Bernoulli wrote:

Cito di Pense wrote:

It is space-time, and you deal with events which help to determine your choices. You choose the reference frame that makes your calculations the easiest without letting them be incorrect.

That doesn't answer the question. There has to be a privileged frame for acceleration to be experienced by one body and not another body relative to it.

That's a big part of the problem. Acceleration isn't a subjective experience, as long as you follow the rules for identifying frames. That is because the accelerating frame experiences forces equivalent to gravitation that can be measured in that frame. The other frame just sees a starting velocity for the other frame and some other velocity later. Where's the privileged frame? There's an accelerated frame, but still no privileged frame. An inertial frame is by definition not experiencing any net force because (guess what) it isn't accelerating. What's a force? It is that which accelerates a mass. Seems circular, don't it? Let's expand the scope of the inquiry.

The accelerating frame is the privileged one in the relativity equations.

Then that's that. I don't think you have to call it 'privileged', and can just call it 'accelerated'. To call it 'privileged' gets into all sorts of idiocy about who ordered what at that table.

As Dylan says, "Everybody's movin', if they ain't already there."

Bernoulli wrote:

Evolving wrote:You can only say how fast a clock is running once you have decided on your frame of reference.

I haven't decided anything. The author of the SA article did that.

Fine: it is only possible to say how fast a clock is running once a frame of reference has been selected.

The only verifiable acts are the observations. Until the travelling twin accelerates, each twin sees the other's clock running half as fast as his own. How fast that is in absolute terms, depends on their frame of reference.

Bernoulli wrote:If it takes 8 years on traveller's clock to get to a star, and 10 years on homebody's clock, then that's 1.25x, not 2x.

That's an interpretation, not an absolute fact. Homebody doesn't see traveller at the star at t = 10. He works out that, from his point of view, that must be when it happened.

Bernoulli wrote:As I said, if one clock really was running at twice the speed of the other, then the age difference when the twin returned would be greater than what it is.

No, because the twins only see each other's clocks running half as fast as their own for as long as they don't change their frames of reference. But one of them does change his frame of reference, and from then on the difference between the speeds of the clocks changes too, right up until the travelling twin gets back to Earth.

Cito di Pense wrote:

Bernoulli wrote:

Cito di Pense wrote:

Bernoulli wrote:

That doesn't answer the question. There has to be a privileged frame for acceleration to be experienced by one body and not another body relative to it.

That's a big part of the problem. Acceleration isn't a subjective experience, as long as you follow the rules for identifying frames. That is because the accelerating frame experiences forces equivalent to gravitation that can be measured in that frame. The other frame just sees a starting velocity for the other frame and some other velocity later. Where's the privileged frame? There's an accelerated frame, but still no privileged frame. An inertial frame is by definition not experiencing any net force because (guess what) it isn't accelerating. What's a force? It is that which accelerates a mass. Seems circular, don't it? Let's expand the scope of the inquiry.

The accelerating frame is the privileged one in the relativity equations.

Then that's that. I don't think you have to call it 'privileged', and can just call it 'accelerated'. To call it 'privileged' gets into all sorts of idiocy about who ordered what at that table.

As Dylan says, "Everybody's movin', if they ain't already there."

What?

It's privileged if the equations are applied to it and not another frame of reference. As Thommo explained, there is only no privileged frame in terms of inertial frames. The same restriction doesn't apply to accelerated frames.

Bernoulli wrote:You are over-analysis this. The wording is assuming the hypothetical where the observers can see (and therefore measure) each other's clocks. The author saying that one clock is running twice as fast as the other is a measurement. But it's not running twice as fast. It's running 10/8 = 1.25 times as fast. If it was running twice as fast, then the age difference when the traveller returned would be greater than what it is.

I'm telling you what the author means, and what the author says is most certainly a correct description of special relativity. He describes what each person "sees" and he uses that word very deliberately to make that clear.

Each brother "sees" the clock of the other running half as fast. Each brother can "calculate" a γ for the clock of the other, and that will be 1.25, but there is no absolute simultaneity to make a statement like "it's not running twice as fast" correct, as this is merely the assumption that there is some absolute statement of how fast the clocks are running.

It is also not correct to say "If it was running twice as fast, then the age difference when the traveller returned would be greater than what it is.", because, for example, from the point of view of homebody he sees the clock of the traveler running at half the speed of his for the outward journey and twice the speed for the return journey. For the homebody brother the outward journey is 16 of the 20 years of what he "sees", for the traveler brother it is 8 of the 16.

Evolving wrote:

Bernoulli wrote:If it takes 8 years on traveller's clock to get to a star, and 10 years on homebody's clock, then that's 1.25x, not 2x.

That's an interpretation, not an absolute fact. Homebody doesn't see traveller at the star at t = 10. He works out that, from his point of view, that must be when it happened.

The speed of light is an absolute fact. He knows with absolute certainty how long the light takes to get from the star to the Earth. It takes 6 years. Therefore, when he subtracts 6 years from the 16 years on his clock he gets 10 years. 10/8 = 1.25.

I must be missing something in plain site if you guys can't see what I'm saying. I feel like you are trying to tell me that if you walk away from me to the shops and I time it, the time I register will be the time it takes you to walk to the shops and then wander over to the park and sit down. That's not the time it took you to walk to the shops. That's the time it took you to walk to the shops and then walk over to the park and sit down.

Thommo wrote:

Bernoulli wrote:You are over-analysis this. The wording is assuming the hypothetical where the observers can see (and therefore measure) each other's clocks. The author saying that one clock is running twice as fast as the other is a measurement. But it's not running twice as fast. It's running 10/8 = 1.25 times as fast. If it was running twice as fast, then the age difference when the traveller returned would be greater than what it is.

I'm telling you what the author means, and what the author says is most certainly a correct description of special relativity. He describes what each person "sees" and he uses that word very deliberately to make that clear.

Each brother "sees" the clock of the other running half as fast. Each brother can "calculate" a γ for the clock of the other, and that will be 1.25, but there is no absolute simultaneity to make a statement like "it's not running twice as fast" correct, as this is merely the assumption that there is some absolute statement of how fast the clocks are running.

So how can the author make the statement "it's running half as fast"?

Bernoulli wrote:

Evolving wrote:

Bernoulli wrote:If it takes 8 years on traveller's clock to get to a star, and 10 years on homebody's clock, then that's 1.25x, not 2x.

That's an interpretation, not an absolute fact. Homebody doesn't see traveller at the star at t = 10. He works out that, from his point of view, that must be when it happened.

The speed of light is an absolute fact. He knows with absolute certainty how long the light takes to get from the star to the Earth. It takes 6 years. Therefore, when he subtracts 6 years from the 16 years on his clock he gets 10 years. 10/8 = 1.25.

I must be missing something in plain site if you guys can't see what I'm saying. I feel like you are trying to tell me that if you walk away from me to the shops and I time it, the time I register will be the time it takes you to walk to the shops and then wander over to the park and sit down. That's not the time it took you to walk to the shops. That's the time it took you to walk to the shops and then walk over to the park and sit down.

The speed of light is an absolute fact, but not the length of time which the light takes to travel between the twins. Until the twin in the spaceship stops and turns round, each twin is equally justified in thinking that his frame of reference is stationary. In the case of the twin in the spaceship, that means that the rest of the universe is moving relative to him, and that means that distances outside his own frame of reference experience length contraction: including the distance between Earth and the star.

Bernoulli wrote:
So how can the author make the statement "it's running half as fast"?

He doesn't. He says that the twin sees the other twin's clock running half as fast.

This seems appropriate:-

https://en.wikipedia.org/wiki/Relativit ... multaneity

Evolving wrote:

Bernoulli wrote:

Evolving wrote:

Bernoulli wrote:If it takes 8 years on traveller's clock to get to a star, and 10 years on homebody's clock, then that's 1.25x, not 2x.

That's an interpretation, not an absolute fact. Homebody doesn't see traveller at the star at t = 10. He works out that, from his point of view, that must be when it happened.

The speed of light is an absolute fact. He knows with absolute certainty how long the light takes to get from the star to the Earth. It takes 6 years. Therefore, when he subtracts 6 years from the 16 years on his clock he gets 10 years. 10/8 = 1.25.

I must be missing something in plain site if you guys can't see what I'm saying. I feel like you are trying to tell me that if you walk away from me to the shops and I time it, the time I register will be the time it takes you to walk to the shops and then wander over to the park and sit down. That's not the time it took you to walk to the shops. That's the time it took you to walk to the shops and then walk over to the park and sit down.

The speed of light is an absolute fact, but not the length of time which the light takes to travel between the twins. Until the twin in the spaceship stops and turns round, each twin is equally justified in thinking that his frame of reference is stationary. In the case of the twin in the spaceship, that means that the rest of the universe is moving relative to him, and that means that distances outside his own frame of reference experience length contraction: including the distance between Earth and the star.

The speed of light constant in all frames of reference. If the star is 6 light years away in the frame of the homebody, it must by the laws of physics take 6 years in the frame of homebody to reach the earth.

Evolving wrote:
The speed of light is an absolute fact, but not the length of time which the light takes to travel between the twins. ...

... distances outside his own frame of reference experience length contraction: including the distance between Earth and the star.

The light takes a shorter time to traverse the contracted length, in the frame of reference of the twin in the spaceship.

The figure of six years only applies in the frame of reference of the twin on Earth.

Evolving wrote:

Bernoulli wrote:
So how can the author make the statement "it's running half as fast"?

He doesn't. He says that the twin sees the other twin's clock running half as fast.

It doesn't matter whether he's seeing reality or he's on acid. When he takes 6 years light travel from the 16 years on his clock, he gets 10 years. 10 divided 8 isn't 2. I'm preparing my hand to slap myself upside the head when I finally get what's going on. Because it must be something so obvious that I'm missing the tree for the forest (to misappropriate the saying). If you told me that it took you 2 minutes to walk to the shops and 1 minute to walk to the park after that, and then said it took you 3 minutes total to walk to the shops, I'd think you were nuts.

Evolving wrote:

Evolving wrote:
The speed of light is an absolute fact, but not the length of time which the light takes to travel between the twins. ...

... distances outside his own frame of reference experience length contraction: including the distance between Earth and the star.

The light takes a shorter time to traverse the contracted length, in the frame of reference of the twin in the spaceship.

The figure of six years only applies in the frame of reference of the twin on Earth.

Which is the frame the author of the article is using when he says "to the homebody, the traveler's clock appears to be running at half the speed of his clock"

Bernoulli wrote:It's privileged if the equations are applied to it and not another frame of reference. As Thommo explained, there is only no privileged frame in terms of inertial frames. The same restriction doesn't apply to accelerated frames.

But there still isn't a privileged reference frame. The twin who accelerates simply ends up in a different reference frame after accelerating. Which one to choose? Which? Which?

"Sees" =/= "calculates".

The reason he's talking about what homebody "sees" is that it's very easy to understand and get the right answers about which twin is younger and by how much. If you calculate 10/8 (which is the lorentz factor γ for inertial frames moving with relative speed of 0.6c), then the twin paradox is harder to understand, because there's a funny calculation to make at the point of the change of inertial frames (acceleration) of the traveling twin as he turns around at his destination for the return leg.

Both brothers "calculate" that the other brother's clock runs slow by γ=1.25 for both the outward and return journeys. And yet the clocks don't match. That is why it's know as the twin "paradox".

Cito di Pense wrote:

Bernoulli wrote:It's privileged if the equations are applied to it and not another frame of reference. As Thommo explained, there is only no privileged frame in terms of inertial frames. The same restriction doesn't apply to accelerated frames.

But there still isn't a privileged reference frame. The twin who accelerates simply ends up in a different reference frame after accelerating. Which one to choose? Which? Which?

I'm talking about accelerating frames. Not inertial frames "after accelerating".

Thommo wrote:"Sees" =/= "calculates".

double/half is a calculation. "Half" is the term the author used. And he literally provided the calculation (16/8).