Time Dilation: Object slowing down vs Subject speeding up

coktail

Why is it that when describing time dilation, we say that the object (the thing observed) slows down relative to the subject (the observer), rather than vice versa? If the subject were to speed up, everything around them would appear slowed down, correct?

Let me take a crack at this myself before I open the floor (gratefully) for your input:

The subject reports that the object has slowed down, and since relativity is all based on the frame of reference of the observer, we must therefore report that the object has slowed down, since there is no evidence from the observer's perspective that they (the observer) has sped up. The observer always appears "normal" from their own frame of reference.

As always, thank you.

Mentz114

If I understand your question, then the answer is that if either subject or object changes their velocity they will undergo a proper acceleration, and proper acceleration is detectable.

So if I'm coasting and my speed changes, I will be able to tell by detecting a force.

Naty1

Coktail:
[edit: I see Mentz took a different interpretation of your wording while I was typing]

Your wording is such that one might think you were discussing accelerations ["the subject reports the object has slowed down"] but you also use 'time dilation' which means the relative tick of clocks in different frames. I'll briefly address slowing of time, 'time dilation'.

An observer [subject] carrying her own clock always observes that it ticks at the same rate. They are in the same frame of reference with no relative speed between them. Such locally recorded time is 'proper time' for that observer [subject]. It's how fast she ages, for example, in that frame.

Wikipedia describes distant observations of clock tick rates nicely:

http://en.wikipedia.org/wiki/Time_dilation

In other words, each observer sees the OTHER distant clock as ticking slower.

Two things affect the relative passage of time: relative speed, as described above, and also differences in gravitational potential. In other words, the presence of mass affects the relative passage of time as recorded by different distant observers. This is called
gravitational time dilation and is discussed in the same Wikipedia article.

You should note these statements about time are contradictory and incorrect:

"If the subject were to speed up, everything around them would appear slowed down, correct?" [This doesn't happen. ]

The observer always appears "normal" from their own frame of reference. [Local clocks ALWAYS tick 'normally', at their regular fixed rate. ]

ghwellsjr

The easiest way to understand time dilation is to stick to one Inertial Reference Frame (IRF). You don't have to link each observer to their own reference frame, especially if an observer accelerates and changes his speed in which case you will need to resort to a non-inertial reference frame which changes the problem from a simple one to a very, very complex one.

So present your scenario in the context of a single IRF. Then any observer/clock that is moving in that IRF will be time dilated based on his/its current speed in the IRF. That means that his time is stretched out compared to the coordinate time of the IRF. After you describe everything in this IRF to your heart's content, then you can transform the coordinates all the events into any other IRF moving at any speed with respect to the first one using the Lorentz Transformation process. This will correctly allow you to see the same scenario with respect to the coordinates of the new IRF and you will see now that the different observers/clocks will be traveling at different speeds and therefore time dilated by different amounts compared to the first IRF.

You never have to have any observer stationary or remain stationary in his own IRF. You can create a scenario in which all the observers/objects/clocks are moving at different speeds and in different directions and changing their speeds and directions multiple times throughout the scenario. You will be able to calculate how time progresses for each of them with no problem. It's simple. The Lorentz Transformation process is also simple but it's cumbersome if you don't have a computer application to do it for you.

Naty1

ghwells:
agreed.....How does one describe this??

ghwellsjr

For example, an observer/clock moving at -0.866c with gamma (the time dilation factor) equal to 2 will look like this (each blue dot is another one-second tick of his clock):



A speed of -0.866c is very close to -7/8 c so you can see that in 8 seconds, he has moved -7 light-seconds. You can also see that his clock takes twice as long to tick out another second compared to the coordinate time.

Naty1

ghwells
no issue....I did not ask my question clearly....

I had not previously thought about your statement that...

I don't object, nor disagree, but I am wondering in what way it's easier....just seems like the same concept and calculations are required....

coktail

Thanks everybody.

I wasn't so much wondering how time dilation works as I was questioning the way in which we describe it.

A stationary clock appears to slow down to a moving observer. We tend to describe that as "the clock slowing down," but why not say that the observer sped up, which made the clock appear to slow down?

My shot at an answer to that is that we can only discuss things from the FoR of the observer, whomever that may be, and that from the observer's FoR, the clock slowed down, and there is no evidence of their self "speeding up."

I know I'm not talking about this technically, and glossing over a great many details, but I hope my point is clear.

Maybe my idea about the world seeming slowed down to something that is sped up is fundamentally flawed...

Naty1

That's it!!

The next step is the one I already posted:

"An observer [subject] carrying her own clock always observes that it ticks at the same rate. They are in the same frame of reference with no relative speed between them. Such locally recorded time is 'proper time' for that observer [subject]. It's how fast she ages, for example, in that frame."

Proper time such as this is also described as the time along the worldline of an observer...they personal, local, history of time and place.

coktail

Thanks!

ghwellsjr

The OP asked about an accelerating observer and then linked him to his own frame of reference which of necessity must be a non-inertial frame which is much more complicated than an IRF, don't you agree? And completely unnecessary as it doesn't provide him with any more insight or information about what is happening, don't you agree?

phinds

It's a matter of terminology and reference frames. What do you really mean when you say "a stationary clock" ? You mean "from the reference frame of that clock".

What do you mean when you say "the observer sped up" ? You mean "from the reference frame of that clock".

What do you mean when you say "the clock appeared to slow down" ? You mean "from the reference frame of that observer".

When you leave off "in the reference frame of ... " then things can sound confusing because you are using confusing terminology. If you leave it in, then it should not be confusing.

From the reference frame of the clock, the observer sped up which means that from the reference frame of the observer, the clock slowed down. Is that confusing?

From the reference frame of the observer, the clock sped up which means that from the reference frame of the clock, it has not slowed down or sped up but it would see any clock that the observer has on him as having slowed down. Is that confusing?

ghwellsjr

And it's especially confusing when you use the terms "sped up" and "slowed down" and you don't make it clear whether you are talking about the motion of the subject/object or the tick rate of the subject/object. Maybe you should pose your question all over again.

coktail

Sorry for any confusion.

By "slowed down" up I meant the tick rate of the object's clock as observed by the observer.

I feel like if I try to explain this any more I'll end up confusing myself along with the rest of you :)

ghwellsjr

But an observer cannot observe the tick rate of a moving clock. It's frame dependent as Naty1 pointed out in post #3. What an observer can observe of a moving clock is called the Relativistic Doppler and it can be either faster or slower than the tick rate of his own clock and this is not frame dependent. So you need to be very clear when you are describing a question or a scenario about whether you are referring to what an observer actually sees and observes and can report about or what is defined according to a particular frame of reference. Even if you want to consider an observer at rest in a frame of reference, that still does not enable him to see, observe, measure or report on the tick rate of a clock moving in that frame and with respect to himself.

coktail

Now I'm confused. Why can't an observer view and report on the tick rate of a clock that is moving relative to him (the observer)? I understand that he reports with disagree with what an observer sitting on top of the clock would report, but that doesn't invalidate it, does it?

ghwellsjr

He can report what he sees as a function of the time on his own clock but what he sees is delayed by some amount of time that is a function of the reference frame that you choose to analyze the scenario in and he can't know what frame that is. You can switch to a different frame and get different answers. Time dilation is a function of the reference frame and the speed of the clock moving in that frame.