Revisiting the Definition of Speed: Is Distance/Time Arbitrary?

[UltraPi1]

If the Earth observer had a very powerful telescope, he could even take pictures of the people moving around inside the cabin of the starship, and he would think the people appeared to be moving very slowly, too.

In other words - Why would someone taking a journey from (a) to (b) at very close to the speed of C and returning back to (a) at very close to the speed of C, with a travel distance of 20 light years be younger than the person that stays at A by 20 years? Why does the traveler not age? What mechanism or lack thereof provides for this?

 

[chroot]

UltraPi1,

Because the light comprising their images suffers the same way as the light from the ship's beacon.

- Warren

 

[UltraPi1]

Sorry I edited my words.

 

[chroot]

UltraPi1,

The moving twin will have aged less because the proper time along his world-line is less than that of the stationary twin.

- Warren

 

[UltraPi1]

The moving twin will have aged less because the proper time along his world-line is less than that of the stationary twin.

World line?

There is no mechanical reasoning here?

 

[Enos]

The traveler does age but in days rather than years. But if observed the traveler will move in slow motion with respect to the man on earth. And the man on Earth is moving fast with respect to the traveler. But time continues for both.

 

[UltraPi1]

The traveler does age but in days rather than years. But if observed the traveler will move in slow motion with respect to the man on earth. And the man on Earth is moving fast with respect to the traveler. But time continues for both.

I'm thinking there must be some mechanical reason for this. Otherwise this cannot be explianed through physics.

 

[quantumdude]

In science, a common view of explanation is that of reduction. That is, if predictions for a large collection of phenomena can be derived from a smaller set of postulates, then said phenomena are said to be reduced to those postulates, and the postulates are said to constitue an explanation of the phenomena.

That said: Time dilation is derivable from the postulates of SR, which are:

1. The laws of physics are the same in all inertial frames.
2. The speed of light is the same in all inertial frames.

So you want to know why time dilation occurs? The best and only answer we have is that it is a logical consequence of the above two postulates. That is the explanation, and it is physical.

 

[Enos]

Your seeking an absolute answer in a relative universe. Time isn't absolute so one can live a year and and someone moving slower can live 20 years. The traveler lived a year and wonders why the man he saw last year looks 20 years older while the man can wonder why the man he saw 20 years ago has only aged a year. Both are correct statements and once they meet they now travel at the same speed and age at around the same rate.

 

[UltraPi1]

In science, a common view of explanation is that of reduction. That is, if predictions for a large collection of phenomena can be derived from a smaller set of postulates, then said phenomena are said to be reduced to those postulates, and the postulates are said to constitue an explanation of the phenomena.

That said: Time dilation is derivable from the postulates of SR, which are:

1. The laws of physics are the same in all inertial frames.
2. The speed of light is the same in all inertial frames.

So you want to know why time dilation occurs? The best and only answer we have is that it is a logical consequence of the above two postulates. That is the explanation, and it is physical.

Ok the speed of light and the law of physics are the same in all inertial frames, but obviously this falls way short as to why the traveling twin comes back chipper as the day he left, while the stationary twin is having problems with irregularity. Have there been any attempts to quantify this difference with the two twins?

Are you saying that your explanation is as far as anybody has gone on this subject in the passing decades? No theories? No guesses? No shots in the dark?

Why did the apples fall to the ground?
Because apples grow on trees.
Don't you feel like something is missing here?

 

[quantumdude]

Ok the speed of light and the law of physics are the same in all inertial frames,

Glad you like that bit.

but obviously this falls way short as to why the traveling twin comes back chipper as the day he left, while the stationary twin is having problems with irregularity.

Why? Why is the shortcoming 'obvious'?

Why is the explanation in terms of the postulates of SR not good enough for you?

Have there been any attempts to quantify this difference with the two twins?

Yes, it has been precisely quantified in SR.

Are you saying that your explanation is as far as anybody has gone on this subject in the passing decades? No theories? No guesses? No shots in the dark?

It's not my explanation. And as far as shots in the dark go, I could give you mine, buit it wouldn't mean a thing.

 

[cepheid]

I've been reading these replies and I am dumbfounded at the lack of understanding of our most fundamental principles of physics*.

When an object moves through space it does so as a function of time. That means that distance moved depends on the amount of time elapsed.

Now keeping that in mind, consider the inverse of that statement. For t/d to be valid, that would mean that the time elapsed in a given situation would depend on the distance covered. This is clearly absurd. Time contiues regardless whether you're standing still or running. It does not change depending on how much distance you've covered (notice how I say 'distance covered' and not 'velocity traveled at').

You've overlooked something. Speed is not "d/t", referring to them as fundamental features of the universe whatever that means. (what is the ratio of space and time? That's meaningless.) (Average) speed is delta d over delta t, where delta d is the distance an object has traveled since it began moving or since we began measuring how far it has traveled from some starting point (we measure it with rulers). Delta t, is the elapsed time since the object began moving or since the instant we began timing it (with clocks) and measuring its motion. So delta t over delta d does have some meaning, because although he passage of time in general is not altered by the motion of the object, the elapsed time measured since an object has begun moving *does* depend on how far it has gone, ie. at what point in its journey you choose to look at the clock. If it could move some distance in zero elapsed time, delta t over delta d would be zero (but it would be more useful to state that as: it would be traveling with infinite speed). That is what people have been trying to say in this thread. They haven't all gone bananas.

 

[jackle]

Have there been any attempts to quantify this difference with the two twins?

I heard that the principle has been well confirmed using "twin" atomic clocks. The traveling clocks do come back younger but it is beyond our technology to make the age difference noticable to ordinary people.

 

[UltraPi1]

Why? Why is the shortcoming 'obvious'?

Why is the explanation in terms of the postulates of SR not good enough for you?

Because the twin returning would appear as if a magic trick took place. Sr only tells you that the twin comes back younger than the twin that stayed. You can quantify by how much this will happen, but not how this will happen. The reason from my estimates is that to do so, would require the understanding of fundamental entities, something we don't have at this juncture. I'm just a bit surprised by the lack of speculation. Surely someone has delved into the minutiae (you'd think).




Why did the apples fall to the ground?
Because apples grow on trees.
Don't you feel like something is missing here?

 

[UltraPi1]

I heard that the principle has been well confirmed using "twin" atomic clocks. The traveling clocks do come back younger but it is beyond our technology to make the age difference noticable to ordinary people.

This is not the bone I'm picking at. I guess I'm looking for details at the fundamental level.

 

[quantumdude]

Because the twin returning would appear as if a magic trick took place.

It's not magic if you understand the connection between the postulates and the consequences thereof.

Sr only tells you that the twin comes back younger than the twin that stayed. You can quantify by how much this will happen, but not how this will happen.

There are 2 ways that I know of to explain it by analogy.

First, consider a meter stick in 3-space. You're looking at it from the side so that it appears 1 m long. When you rotate it, it appears shorter. And if you rotate it 90 degrees, it appears to have a length that is equal to the width of its cross section. Now if you understand SR, then you know that the Lorentz group is an enlargement of the rotation group. That is, SR is a generalization of rotations. Furthermore, SR couples space and time. So when someone is moving relative to you, there is the possibility that their spatial and time coordinates are rotated.

Second, consider a car moving at 30 mph along the positive x-axis, according to an observer standing on the ground. The x-component of its velocity is 30 mph. Now without changing its speed, it turns such that it is moving at a 45 degree angle with respect to the x-axis. Now, the x-component of its velocity is smaller (by a factor of 1/2^1/2). Well, in SR the norm of the 4-velocity of every body is c. If an object is at rest in some frame, then in that frame its velocity is purely timelike. That is, the t-component of its velocity is c. Now if the object starts moving relative to that frame, its "4-speed" (for the lack of a better word) does not change.

Why did the apples fall to the ground?
Because apples grow on trees.
Don't you feel like something is missing here?

Of course. There's always something missing in science. That's what reductionism is for. We can't know about fundamental entities, because we do not have a priori knowledge of the universe.

 

[Canute]

"We can't know about fundamental entities, because we do not have a priori knowledge of the universe."

Are you sure about that?

 

[quantumdude]

"We can't know about fundamental entities, because we do not have a priori knowledge of the universe."

Are you sure about that?

As sure as I can be. If we did have a priori knowledge of the fundamental workings of the unvierse, physics would not be an experimental science.

 

[Canute]

I wasn't suggesting that we had an a priori knowledge of physics, just of the fundamental nature of the universe. That is, perhaps within us, underneath all the clutter, lies a knowledge of reality that we don't normally notice. After all, we are the universe, or at least a part of it, and made out of the same stuff that the universe is made out of. Just a thought.

 

[quantumdude]

I wasn't suggesting that we had an a priori knowledge of physics, just of the fundamental nature of the universe.

What's the difference?

 

[Futobingoro]

1 universally relative second = 0 (second^2/segment of time) * infinite (segments of time/second)

So if you divide one second into an infinite amount of segments, then multiply by 0 time acceleration (s^2/segment), you get one second.

This operates on the principle that 1/0=infinity, so multiplying both sides by zero makes 1=infinity*0.

Mathematicians: don't despair, if division by 0 is in the problem proposed to me, multiplication by 0 is legal.

So in time acceleration, going from a standstill to motion involves an infinite increase in time relative to distance traveled.

 

[quantumdude]

Mathematicians: don't despair, if division by 0 is in the problem proposed to me, multiplication by 0 is legal.

Not when the other factor is infinite, it isn't. That's an indeterminate quantity.

 

[Futobingoro]

Infinity is definite because everything else is definite. Through deductive reasoning, one can subtract all the definite items and find an exact indefinite. There can only be one infinity, just as there can only be one place where an infinite indefinite belongs. Infinity exists because it belongs in the place where everything else does not belong.

One can define infinity just as one can "see" black.

If it is not finite, it is infinite. 1/0 is not finite, so it is infinite.

Square roots of negative quantities and similar "numbers" are intangible finite numbers.

Everybody knows that 1/0 and the tan (90 degrees) are infinite quantities.

 

[StatusX]

You can't just define infinity as "the only non-finite number". You need more axioms. For example, how would you know from that definition that infinity>3, or infinity+infinity=infinity? Where does minus infinity fit in?

 

[quantumdude]

Infinity is definite because everything else is definite.

And q20[ruasvdojawro;mtf is definite because everything else is definite.

What's this got to do with what I said?

Through deductive reasoning, one can subtract all the definite items and find an exact indefinite. There can only be one infinity, just as there can only be one place where an infinite indefinite belongs. Infinity exists because it belongs in the place where everything else does not belong.

Take a course in calculus. Once you've done that, you will know how to deal with indeterminate forms such as the one you've presented here.

Two concrete examples:

\lim_{x \rightarrow \infty} e^{-x}x
\lim_{x \rightarrow \infty} x^{-1}e^x

Both limits lead to "0 times infinity". But when "deductive reasoning" (aka "L'Hopital's rule") is applied to them, you get two different results (zero in the first case, infinity in the second).

 

[FulhamFan3]

I think a better question is why isn't it d*t instead if d/t.

 

[jdm]

It is interesting to think of what d*t would mean physically, but it is mathematically in a different class from d/t or t/d so I cannot see it replacing either.

To clarify, d*t gives the area under a trajectory curve and d/t and t/d are rates of change of their respective trajectory curves.

That being said the implicit 1 in the dimensional expression (d*t)/1 is interesting. Also, 1/(d*t) is fun to think about. Any dimensional expression that couples space and time like d*t and 1/(d*t) is worth thinking about, especially as a possible fundamental unit in a background dependent theory.

 

[jdm]

Sorry, previous post should read background independent theory.

General relativity is a background independent theory, b/c the background is a dynamic part of the theory, not merely something the theory relies on for a frame of reference.

Newtonian mechanics is background dependent, b/c it relies on the presence of an
absolute space and time, sperate from the dynamics, that is used only as a refernece point.

A fundamental theory should ideally be background independent so that the existence of space and time can be explained, possibly as an emergent property of a more basic set of relationships (LQG), not just assumed as it is in a background dependent theory. For clearer, more intelligible discussions and explanations check out the relavant threads.

 

[jcsd]

Backgorund independce is over-hyped, to take soemthing that philosophically elegant and turn it into a physical requiremnt is going overboard. Many people would say that the geometricla treatemnt of gravity by theories like GR and LQG must ultimately fail at some point anyway and it seems entirely possible that in this case there could only be one possible background which makes the concept of background independence moot.

 

[Futobingoro]

When an object moves through space it does so as a function of time. That means that distance moved depends on the amount of time elapsed.
Now keeping that in mind, consider the inverse of that statement. For t/d to be valid, that would mean that the time elapsed in a given situation would depend on the distance covered. This is clearly absurd. Time contiues regardless whether you're standing still or running. It does not change depending on how much distance you've covered (notice how I say 'distance covered' and not 'velocity traveled at').

You attack t/d on the basis that traveling 5 meters does not determine the time elapsed. You are correct, but d/t is subject to the same limitation. Does traveling for 5 seconds determine the distance covered? Of course it does not! The other variable is required if the rate is to be found. D/T can not exist as a rate if elapsed time is not known just as T/D can not exist as a rate if distance is not known.
Many question t/d's ability to explain a static object's motion. The familiar d/t explains it: if a stationary person endeavors to move at his current velocity for one second he will move zero meters. The t/d view holds that if the same stationary person endeavors to move 1 meter at his current velocity he will wait for an infinite time period.
D/T answers the question: "How far does a stationary person move in one second?"
T/D answers the question: "How long does it take for a stationary person to move one meter?"
D/T has an advantage in that it better illustrates lower velocities, showing the viewer how the velocity approaches zero any time the graph approaches the x-axis.
T/D has an advantage in that it better illustrates higher velocities, showing the viewer how velocity approaches infinity as the graph approaches the x-axis.