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# Time Dilation

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I have this doubt.

Let us assume an observer independently accelerating from 0 to the speed of light. If an other observer starts accelerating consequently, let us say after a particular time they reach the same speed, let us say 0.95C. Would they observe a time dilation with respect to each other? My idea is yes since with respect to a stationary observer they have a velocity v each. So they have a time dilation with respect to each other though the magnitude is the same. If a cup breaks in one of their frames, the other sees a time dilation. If cup breaks in the other frame, the other observer sees the time dilation.

Another doubt.

If we place a ruler of some particular length. Along the same length a long distance away we have an observer acceleration to the speed of light, let us say he reaches the speed of light (well, almost. let us say v = 0.9999c) before he reaches the ruler. Will he collide with the ruler? I don't think so. The length of the ruler contracts to almost 0. So he will never see himself colliding with the ruler because its not there. Not the same for a stationary observer.

I am not so sure about my deductions. Different views, opinions and of course the right one will be appreciated.

Thanks.

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I have this doubt.

Let us assume an observer independently accelerating from 0 to the speed of light. If an other observer starts accelerating consequently, let us say after a particular time they reach the same speed, let us say 0.95C. Would they observe a time dilation with respect to each other? My idea is yes since with respect to a stationary observer they have a velocity v each. So they have a time dilation with respect to each other though the magnitude is the same. If a cup breaks in one of their frames, the other sees a time dilation. If cup breaks in the other frame, the other observer sees the time dilation.

You have frequency, and you have phase, which it the time reading. Two objects moving with respect to each other will have a different frequency. Two objects with a different history of motion (with respect to a common reference) may have a different phase — it will depend on the details — even if they end up in the same frame and thus have the same frequency again.

Another doubt.

If we place a ruler of some particular length. Along the same length a long distance away we have an observer acceleration to the speed of light, let us say he reaches the speed of light (well, almost. let us say v = 0.9999c) before he reaches the ruler. Will he collide with the ruler? I don't think so. The length of the ruler contracts to almost 0. So he will never see himself colliding with the ruler because its not there. Not the same for a stationary observer.

I am not so sure about my deductions. Different views, opinions and of course the right one will be appreciated.

Thanks.

You can't dilate an object to zero length.

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@swansont - if we assume the masses are the same, the frequency is the same, will there be a time dilation with respect to each other? what details do you mean?

I never mentioned that the length becomes 0. almost 0 is what i said. Let us say, the size of an electron. That would hardly hinder the object travelling at such a large speed. So what say?

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The details of the acceleration. What speed you're traveling at and for how long tell you the dilation. So even if the final speeds are the same, the dilation may be different.

Length contraction is only in the direction of motion. So the target will be vanishingly thin, but the width and height are still there.

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I understood the length contraction idea. Thanks.

But what about the time dilation again? I don't understand how the acceleration really affects the dilation at a particular time.

Dilated time between 2 instances in the event = Actual time between 2 instances in the event*gamma factor.

Gamma factor makes use of the velocity. Where does the acceleration come into picture?

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Acceleration means v is changing.

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There are two kinds of differences each might observe in the other. A difference in the rate at which the other's clocks tick, and a difference in what those clocks say. The rate will be different if they have a nonzero velocity relative to one another. The clocks will give different readings (i.e., more time will have passed for one or the other), even if they rejoin the same reference frame, depending on how much each has accelerated in the past.

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I understand what you say. You mean that the clocks on the whole will show a difference when checked after the experiment. But for that particular instance when the velocity is the same, there will be absolutely no difference in the time dilation. Thanks.

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I understand what you say. You mean that the clocks on the whole will show a difference when checked after the experiment. But for that particular instance when the velocity is the same, there will be absolutely no difference in the time dilation. Thanks.

That's true if by time dilation you mean the rate (i.e. frequency) rather than the reading on the clock (the phase). The term "time dilation" by itself is ambiguous.

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why do you think there is a time dialation when they reach the same speed please explain?

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why do you think there is a time dialation when they reach the same speed please explain?

The dilation will be with respect to a different observer, not moving at their speed.

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@swansont - Yes I meant the frequency. The clock will show an entirely different interpretation as it is based on the history of the frame.

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• 1 month later...
I have this doubt.

Let us assume an observer independently accelerating from 0 to the speed of light. If an other observer starts accelerating consequently, let us say after a particular time they reach the same speed, let us say 0.95C. Would they observe a time dilation with respect to each other? My idea is yes since with respect to a stationary observer they have a velocity v each. So they have a time dilation with respect to each other though the magnitude is the same. If a cup breaks in one of their frames, the other sees a time dilation. If cup breaks in the other frame, the other observer sees the time dilation.

Another doubt.

If we place a ruler of some particular length. Along the same length a long distance away we have an observer acceleration to the speed of light, let us say he reaches the speed of light (well, almost. let us say v = 0.9999c) before he reaches the ruler. Will he collide with the ruler? I don't think so. The length of the ruler contracts to almost 0. So he will never see himself colliding with the ruler because its not there. Not the same for a stationary observer.

I am not so sure about my deductions. Different views, opinions and of course the right one will be appreciated.

Thanks.

You want to clear this up and understand this time dilation/lenght contraction stuff?

Answer these questions:

Is time a physical energy? If you say that it is, please provide scientific evidence or a definition.

In this lenght contaction idea, can you find any reference that states that the object actually contracts?

You have two objects, one is made of iron, the other is made of foam padding. Both objects are traveling at near the speed of light. Both we are told contract at to the same lenght.

It takes more energy to contract iron then foam, yet both contract the same. How is this possible? What forces are at worK?

If you say that the objects APPEAR to contract you would be correct according to Einstein and S.R. They appear to contract, but acctually do not contract.

There is no science that explains the forces that act on an object to contract it during high speed. Force is not mentioned.

The objects do not actually contract.

Just think about it, if an object were contracted by some force, what is the force that brings it back to it original lenght? And why is this force never mentioned?

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You want to clear this up and understand this time dilation/lenght contraction stuff?

Answer these questions:

Is time a physical energy? If you say that it is, please provide scientific evidence or a definition.

In this lenght contaction idea, can you find any reference that states that the object actually contracts?

You have two objects, one is made of iron, the other is made of foam padding. Both objects are traveling at near the speed of light. Both we are told contract at to the same lenght.

It takes more energy to contract iron then foam, yet both contract the same. How is this possible? What forces are at worK?

If you say that the objects APPEAR to contract you would be correct according to Einstein and S.R. They appear to contract, but acctually do not contract.

There is no science that explains the forces that act on an object to contract it during high speed. Force is not mentioned.

The objects do not actually contract.

Just think about it, if an object were contracted by some force, what is the force that brings it back to it original lenght? And why is this force never mentioned?

The contraction doesn't occur in the object's frame; the energy or force it takes to compress foam vs iron is never an issue. The contraction is the difference in length itself between frames. All items 1 meter in length on one frame will be 0.5 meters in length according to an observer moving with a speed such that gamma=2. It is not a physical compression, it is the difference in observation, which is relative to the frame you are in.

To say it appears to contract isn't correct; there is no "true length" of the object, since there is no absolute reference frame. Measurements will be relative to the frame of the observer, because c is constant.

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