Relativity - Oh dear, here we go again!

[ynot]

They do, as long as they are both inertial. But the traveling twin isn't always inertial.

As I understand it the periods of acceleration of the travelling twin aren’t what causes the time dilation but it’s that the travelling twin is travelling faster than the other that does.

Given your answer to - “No absolute measure of speed can be attributed to anything and it can’t be correctly defined that acceleration represents an absolute increase or decrease in speed.” was - “Good thing it isn't and it's not” (post #533). What determines that one twin is ever travelling faster than the other regardless of the periods of acceleration?

 

[jsfisher]

As I understand it the periods of acceleration of the travelling twin aren’t what causes the time dilation but it’s that the travelling twin is travelling faster than the other that does.

You understand incorrectly.

 

[ynot]

You understand incorrectly.

Care to briefly explain what does cause time dilation then? (non-math)

 

[jsfisher]

Care to briefly explain what does cause time dilation then? (non-math)

Ziggurat already did. You countered his/her remarks with your own misunderstanding of the Twin (non-)Paradox. The final difference in age of the twins is due to one of the twins switching inertial frames.

 

[Paulhoff]

Care to briefly explain what does cause time dilation then? (non-math)

Simple Mechanics, it has to do with how much speed a particle can use in all three dimensions.

Paul

 

[Dancing David]

Angles of perception in the same “relative absolute reality“ (inertial frame) is not the same thing as Relativity claiming that time passes at relatively different rates in different “relative absolute realities” (inertial frames).

There is no absolute, if you view the passage of time as being 'stuff happening' as opposed to some fixed ruler, it makes more sense.

Stuff happens, we measure the rate of the happening of the stuff. If you move close to the speed of light, less stuff happens while you move that fast.

You are in the 'same reality' the whole time. Just stuff happens at different rates.

 

[Fredrik]

I don't agree. It's not a question of "let's pretend" - it's "let's assume". So long as the assumption is useful (i.e. the theory based on it makes useful predictions and doesn't conflict with experiment) we retain it. The minute that fails, we drop it.

But there is neither need nor room for pretending anything.

But we still haven't dropped Newton's theory of gravity for example. We still feel that a person can learn something about gravity by studying his theory. Aren't we sometimes pretending that there's a gravitational force described by an inverse-square law, and isn't this an acceptable thing to do? I mean, we know that this assumption is false (e.g. because orbits aren't exactly elliptical), and we still use it.

I guess that what you're objecting to is that "to pretend" means "to assume something that's known to be false", but we do that all the time. For example, when we're doing GR, we're pretending that matter behaves in a classical way. (Sure, we can do QM calculations that estimate contributions to the stress-energy tensor, but even that doesn't change the fact that we're using a classical stress-energy tensor).

Maybe you object because using the word "pretend" might suggest to some people that we refuse to accept the facts, but I'm not sure that's a valid reason to refuse to use words like that. It would be like changing the name of the "theory of evolution" to "law of evolution", which some people have suggested. I think people should learn what a theory is, so that we can use accurate language without being misunderstood. Now I just have to figure out how to get them to do that.

 

[Dancing David]

It's c for all inertial observers in special relativity. We do need to make the distinction explicit, because some people take the Sagnac effect as evidence against relativity, since c is not constant for non-inertial observers.

I will look up the Sagnac effect, what is a non-inertial frame of reference?

If there is short answer.

 

[Dancing David]

According to Relativity the twins experience different realities of time.

No, they experience different rates of stuff happening. They are in the same reality. Imagine that you travel to Bangor, Maine from Paris, France, you will fly in an airplane and take the shortest circular path to get there.

I will use the secret tunnel that travels through the earth in a straight line between the two station 5 km under each city.

When you arrive you have traveled one distance, but you will find that I am there before you, even if we leave at the same time and travel at the same speed.

Because I have cut a line across the sphere while you have taken a circle. But we both traveled in the same reality. I did not take a separate reality. I took a separate path from you.

Time is a metric, it does not exist outside of it's measurement, it is a 'rate' at which 'change/work' 'happens'.

For some reason when you travel closer to the speed of light you begin to take a short cut through the 'metric' of time. But it seems about the same as the tunnel vs. the circle. One is just a shorter path than the other.

the twin that takes the jet and travels on the circle above the surface of the earth is the one not traveling close to the speed of light.

the one that takes the secret tunnel is the one that travels close to the speed of light.

Does that analogy make sense?

 

[Fredrik]

Care to briefly explain what does cause time dilation then? (non-math)

There is no completely non-mathematical explanation. If you're serious about learning this stuff, I suggest you go back to earlier in this thread where I suggested a way for you to learn about simultaneity. It would make it much easier for you to understand time dilation, and for us to explain it.

The final difference in age of the twins is due to one of the twins switching inertial frames.

That's not the whole story. The dime dilation also contributes to the final ages.

It should be mentioned that the point of that story (my spacetime diagram earlier in the thread) isn't that it shows that twin B is younger. It does, but there are easier ways to see that SR predicts that B will be younger. The point of the story/diagram is that it shows very explicitly what's wrong with the standard argument for the twins being the same age when they meet again.

The easiest way to find out who SR predicts is younger (for those of us who know the theory well) is to note that the statement "What a clock measures is the proper time of the curve in spacetime that represents its motion" is an axiom of the theory. It's a part of the definition of the theory. The proper time of a curve is the integral of [latex]\sqrt{dt^2-dx^2}[/latex] along the curve. Twin A (the one that stays at home) will be older because dx=0 along his curve. (There is a coordinate system such that dx=0 along B's curve instead, but in such a system the quantity under the square root takes a more complicated form. The result of the integration is independent of the coordinates used, so we might as well use A's coordinates because they make the calculation easy).

 

[Ziggurat]

I will look up the Sagnac effect, what is a non-inertial frame of reference?

If there is short answer.

Briefly, an accelerating or rotating reference frame.

 

[Dorfl]

I agree that “relative absolute” is a nonsense/oxymoron. I guess I used the term to highlight that Relativity (as I understand it) also seems to be a nonsense/oxymoron.

I also guess that I often use made-up phrases to replace the conventional ones in an attempt to express the same thing differently so the thing might be considered from a fresh perspective. From a sceptical perspective Relativity seems to use a lot of terms that are “user friendly”. I don’t think this is any form of conscious conspiracy but perhaps there is an ongoing subconscious confirmation bias. It’s most likely however that I simply don’t fully understand the language and how it’s correctly applied to reality.

I get the idea, but in practise it seems to lead to very confusing language. Would it not be quicker to use the standard terms—so everyone here can understand what you are trying to say—and then use those standard terms to show why relativity is inconsistent?

 

[Dorfl]

According to Relativity the twins experience different realities of time.

I am sorry, but I do not understand what this means. They have taken different paths from point A to point B, which means that they have experienced different distances between point A and point B. Does that means they have experienced different realities of that distance?

If you would say that they have, then I guess the above statement is right. However, I am not sure what it is supposed to show. It seems like you are just using a non-standard definition of the word "reality".

 

[sol invictus]

The examples you gave are all controlled approximations. When we use Newtonian gravity we don't pretend it is correct. Quite the contrary - we know by precisely how much it is not correct for the quantities of interest. If that's small enough, it's good enough. If not, we can use GR or a post-Newtonian expansion.

But we never pretend - there's no need.

But we still haven't dropped Newton's theory of gravity for example. We still feel that a person can learn something about gravity by studying his theory. Aren't we sometimes pretending that there's a gravitational force described by an inverse-square law, and isn't this an acceptable thing to do? I mean, we know that this assumption is false (e.g. because orbits aren't exactly elliptical), and we still use it.

I guess that what you're objecting to is that "to pretend" means "to assume something that's known to be false", but we do that all the time. For example, when we're doing GR, we're pretending that matter behaves in a classical way. (Sure, we can do QM calculations that estimate contributions to the stress-energy tensor, but even that doesn't change the fact that we're using a classical stress-energy tensor).

Maybe you object because using the word "pretend" might suggest to some people that we refuse to accept the facts, but I'm not sure that's a valid reason to refuse to use words like that. It would be like changing the name of the "theory of evolution" to "law of evolution", which some people have suggested. I think people should learn what a theory is, so that we can use accurate language without being misunderstood. Now I just have to figure out how to get them to do that.

 

[Dancing David]

Briefly, an accelerating or rotating reference frame.

Thanks. (A later post said that as well.)

 

[Fredrik]

The examples you gave are all controlled approximations. When we use Newtonian gravity we don't pretend it is correct. Quite the contrary - we know by precisely how much it is not correct for the quantities of interest. If that's small enough, it's good enough. If not, we can use GR or a post-Newtonian expansion.

But we never pretend - there's no need.

There's no way to find out what the predictions of Newton's theory of gravity are without treating his assumptions as if they were correct. I mean, when we prove that the inverse square law leads to elliptical orbits, we do it exactly the way we would if we had believed the inverse square law to be correct. I'm not sure why it bothers you that I think it's OK to think of that as "pretending" that the inverse square law is correct while we're doing the calculation. Anyway, it's clear that we only disagree about the semantics.

 

[Fredrik]

what is a non-inertial frame of reference?

If there is short answer.

A coordinate system is a function from spacetime (which you should think of as an abstract set of points) into R⁴. So a coordinate system is what assigns four numbers (coordinates) to each event. ("Event" means "point in spacetime").

It's convenient to associate a specific coordinate system with the motion of a physical observer. We do this by defining the time axis to be his path through spacetime. The coordinates of points on the time axis are defined as (T,0) where T is the time displayed by a clock the observer carries with him (or the time that his clock would show if he had one). Then we use a specific "synchronization convention" to assign coordinates to all other events. If this observer is moving with a constant velocity (and always has been and always will be), the coordinate system constructed this way is what we call a global inertial frame. The word "global" is usually omitted.

A non-inertial frame of reference is a coordinate system that isn't a global inertial frame. In my opinion, it's only appropriate to call a coordinate system a "reference frame" if we at least keep a minimum of what I described above. In particular, we define the time axis the same way, and use the standard synchronization convention to assign coordinates to events that are infinitesimally close to the time axis. One particular way to extend this coordinate system to a larger region (but not all of spacetime) gives us what's called a local inertial frame. The local inertial frame is often what we have in mind when we talk about an object's "reference frame" or "point of view", but it should be noted that there's no universally accepted way to define what an object's "point of view" means far from the curve that represents its motion.

 

[Myriad]

No.

There is an infinite number of different reference frames from which any events can be observed and evaluated, but these are not different realities, any more than the infinite number of different possible camera angles for photographs of the Brooklyn Bridge are actually an infinite number of different bridges.

Angles of perception in the same “relative absolute reality“ (inertial frame) is not the same thing as Relativity claiming that time passes at relatively different rates in different “relative absolute realities” (inertial frames).

Of course they're not exactly the same thing. It's an analogy. But they're very very similar.

Imagine you were a member of an isolated tribe that never invented perspective drawing. So in your whole life you've never seen a drawing with perspective, or a photograph. Then, someone comes along and shows you photographs of the Brooklyn Bridge taken from different angles. Your tribe uses rope suspension bridges, so with a bit of explanation you understand the bridge, but what you can't understand is why the bridge looks different in pictures from different angles.

You tell the stranger: "In this picture, the tower at one end is higher. In this picture, the tower at the other end is higher. And yet you're claiming that they're both the same height, like in this third picture here. Each picture shows the bridge having different properties, and yet you claim they're all the same bridge. That's a contradiction. What you must really mean is that the bridge exists in many different realities, and each picture shows a different reality."

The analogy goes fairly deep, because both our tribesman looking at perspective photographs for the first time, and you when you contemplate relativistic effects, are mistaking the effects of a rotation of viewpoint as changes in the actual properties of the observed object/event. For the bridge photos, the rotation is of the camera position in 3-space relative to the bridge; for relativistic observations, the rotation is of the observer in 4-dimensional spacetime relative to the event observed.

One key point is that just as the camera angle from which it's photographed is not an intrinsic property of a bridge, a reference frame is not an intrinsic property of a moving object. A reference frame is a property of the observer.

It's a language shortcut, and therefore potentially misleading, to speak of "an object observed from its own reference frame." What that really means is "an object observed from a reference frame in which the object's velocity is zero."

It becomes really misleading when you start describing a change in velocity (an acceleration) of an object as the object "changing reference frames." Since a reference frame is not a property of the object, it doesn't change when the object accelerates. It's up to the person evaluating the subsequent events whether to keep the same reference frame and calculate the effects of the acceleration within that reference frame, or change reference frames and calculate the effects of that change in reference frame. This will lead to two different ways of doing the math, but the results will be the same.

In one reference frame, a clock ticks faster than it does in another. In one reference frame, a rocket is longer than it is in another. Not different realties. The same reality, observed from different angles in spacetime.

Respectfully,
Myriad

 

[BillyJoe]

Actually, no. Velocity is purely relative, but I think it's important, especially in this context, to recognize that there are absolutes in relativity. Such things are usually referred to as "invariant". Proper time is invariant. Proper length is invariant. The most meaningful definition of mass is invariant. We can treat these things as absolutes. They are not relative to anything, and all observers will agree on them.

Oh yeah, my diminutive height and weight do not really change whatever someone else may make of my girth and stature, and my life certainly seems to be ticking along at a rather steady rate whatever someone else may think of my tardiness.

BillyJoe

 

[BillyJoe]

...hey, I think I've just made sense of ynot's "relative absolute realities"!
That has to be worth something.