Objects at Speed of Light: Time Dilation on Stop

[giograf]

[Edited]

Suppose we have two objects: (1) object number one with an observer onboard and (2) the Earth (with an observer onboard).

Object #1 is moving with speed which is reasonably close to the speed of light, the object has mass, and is moving relative to the Earth. Two systems are considered equivalent, therefore, it can be said that the Earth is moving with the speed close to the speed of light with respect to the object #1.

The formula for time dilation is known, so that observers in both systems can measure how differently time flows in their systems relatively to one another.
Both observers would observe that time flows slowlier in a system which is different from where they are.

But what does happen when they stop? If the systems are equivalent then time must get to the state where it was before the object #1 started to travel with the speed close to the speed of light. And not only (1) the difference in time measured before and after the travel by two observers must be exactly the same, but also (2) the change in time (between the start of the trip with the speed of light and it's end) in system #1 as perceived from the Earth!

How can it possibly be so that as long as the object #1 was moving with speed of light we had been seeing time there flowing so slowly, but when it stopped, boom. The time in both systems was the same. Did the flow at which time flows in system #1 as perceived from the Earth get an almost infinite acceleration at the moment the object #1 stopped? (If not so, why if systems are equivalent?).

 

[DaveC426913]

Object #1 moves with speed of light (c) relative to the Earth.

OK, so object 1 is a massless photon.

Two systems are considered equivalent, therefore, it can be said that the Earth moves with the speed of light relative to object #1.

No. There is no reference frame in which an object of mass moves at c.

But what does happen when they stop?

A photon cannot stop.

I suggest you reformulate your question with valid physics. You will find that your follow up questions can then be answered sensibly.

 

[jartsa]

[Edited]

Suppose we have two objects: (1) object number one with an observer onboard and (2) the Earth (with an observer onboard).

Object #1 is moving with speed which is reasonably close to the speed of light, the object has mass, and is moving relative to the Earth. Two systems are considered equivalent, therefore, it can be said that the Earth is moving with the speed close to the speed of light with respect to the object #1.

The formula for time dilation is known, so that observers in both systems can measure how differently time flows in their systems relatively to one another.
Both observers would observe that time flows slowlier in a system which is different from where they are.

But what does happen when they stop? If the systems are equivalent then time must get to the state where it was before the object #1 started to travel with the speed close to the speed of light. And not only (1) the difference in time measured before and after the travel by two observers must be exactly the same, but also (2) the change in time (between the start of the trip with the speed of light and it's end) in system #1 as perceived from the Earth!

How can it possibly be so that as long as the object #1 was moving with speed of light we had been seeing time there flowing so slowly, but when it stopped, boom. The time in both systems was the same. Did the flow at which time flows in system #1 as perceived from the Earth get an almost infinite acceleration at the moment the object #1 stopped? (If not so, why if systems are equivalent?).

Object #1 thinks like this:
"A while ago when I was moving my clock was ticking slowly, although I remember that I though that I was standing still and I remember that I thought that my clock was ticking normally. Now I am really standing still and the reading on my clock is what it is because it was ticking slowly when I was moving. Those clocks that I thought to be ticking slowly ticked normally and now their readings are what they are because they have ticked normally all the time."Earth thinks like this:
"Clocks attached to object #1 were ticking slowly when object #1 was moving"

 

[DaveC426913]

Object #1 thinks like this:
"A while ago when I was moving my clock was ticking slowly, although I remember that I though that I was standing still and I remember that I thought that my clock was ticking normally. Now I am really standing still and the reading on my clock is what it is because it was ticking slowly when I was moving. Those clocks that I thought to be ticking slowly ticked normally and now their readings are what they are because they have ticked normally all the time."

No.

The OP was correct:

Two systems are considered equivalent, therefore, it can be said that the Earth is moving with the speed close to the speed of light with respect to the object #1.

i.e. You and all clocks in your frame of reference are ticking normally. The Earth does not get to corner the market on valid frames of reference.

 

[DaveC426913]

[Edited]

Suppose we have two objects: (1) object number one with an observer onboard and (2) the Earth (with an observer onboard).

Object #1 is moving with speed which is reasonably close to the speed of light, the object has mass, and is moving relative to the Earth. Two systems are considered equivalent, therefore, it can be said that the Earth is moving with the speed close to the speed of light with respect to the object #1.

The formula for time dilation is known, so that observers in both systems can measure how differently time flows in their systems relatively to one another.
Both observers would observe that time flows slowlier in a system which is different from where they are.

All correct so far.

But what does happen when they stop?

Be specific. At least one of them had to undergo (negative) acceleration in order for them to end up in the same frame of reference (stopped wrt each other). That means that the two systems are no longer equivalent. And don't forget, one of them had to accelerate in the first place.

It is possible to set up the scenario so that both objects accelerate and decelerate equivalently, in which case, you will get a symmetry of time dilation.

 

[DaveC426913]

How can it possibly be so that as long as the object #1 was moving with speed of light we had been seeing time there flowing so slowly, but when it stopped, boom. The time in both systems was the same. Did the flow at which time flows in system #1 as perceived from the Earth get an almost infinite acceleration at the moment the object #1 stopped? (If not so, why if systems are equivalent?).

When they return to the same frame of reference, the rates of time passage will match, but that does not mean that they will have experienced the same passage of time.

If a spaceship flies out to A.Centauri at .99999c and back again, stopping in Earth orbit, they will both find their clocks are currently ticking at the same rate. But they weren't ticking at the same rate during the elapsed time. Earth will measure the round-trip journey as having taken 8 years, but the spaceship will have experienced a journey of mere weeks (or less). So, the occupants of ship debark after a short few week's journey to find that 8 years have passed on Earth.

 

[jartsa]

You and all clocks in your frame of reference are ticking normally.

Well if you say that it was an error for object #1 to think that he was moving, then I guess that object #1 must think like this:

"A while ago when I was not moving my clock was ticking normally. Then I accelerated, so now I am moving, and the Earth seems to be moving with me. Me and the Earth have now equally time dilated clocks. Earth's clock has been time dilated all the time, while my clock was not time dilated when I was not moving."

 

[DaveC426913]

Then I accelerated, so now I am moving, and the Earth seems to be moving with me.

I accelerated, but in my frame of reference, I am not moving. It is the Earth that is moving.

 

[Janus]

[Edited]

Suppose we have two objects: (1) object number one with an observer onboard and (2) the Earth (with an observer onboard).

Object #1 is moving with speed which is reasonably close to the speed of light, the object has mass, and is moving relative to the Earth. Two systems are considered equivalent, therefore, it can be said that the Earth is moving with the speed close to the speed of light with respect to the object #1.

The formula for time dilation is known, so that observers in both systems can measure how differently time flows in their systems relatively to one another.
Both observers would observe that time flows slowlier in a system which is different from where they are.

But what does happen when they stop? If the systems are equivalent then time must get to the state where it was before the object #1 started to travel with the speed close to the speed of light. And not only (1) the difference in time measured before and after the travel by two observers must be exactly the same, but also (2) the change in time (between the start of the trip with the speed of light and it's end) in system #1 as perceived from the Earth!

The systems are equivalent right up to the point where Object #1 "stops". When it does, it has to undergo an acceleration and thus for that interval shifts from an inertial frame to an non-inertial or accelerated frame. The Earth on the other hand remains in an inertial frame. The rules for observations made in an accelerated frame differ from those made in an inertial frame. For one, clocks placed in different positions at rest with respect to an inertial frame all run at the same rate while clocks placed at different positions in an accelerated frame do not; clocks in the direction of the acceleration run faster than clocks in the other direction with the difference in rate being tied to the distance between them and the magnitude of the acceleration. This applies to all clocks whether they are rest with respect to the accelerated frame( share in the acceleration) or not.

Thus from Object #1's perspective, when it begins to "apply the brakes", the Earth is far away in the direction of the acceleration, and thus the Earth clock runs fast during the braking period. Once it come to rest with respect to the Earth, the Earth clock will have advanced to the from the perspective of Object#1 as an Earth observer measures his clock as advancing. So at the End, Both the Earth and Object#1 will agree that Object#1 aged less and by how much. ( just for different reasons. Earth will it was because Object#1's clock ran slow for the entire time until to a stop, while Object#1 will say that The Earth clock ran slow for a good part of the time, but then ran very fast while Object#1 was matching speeds with the Earth at the end.

 

[Janus]

Well if you say that it was an error for object #1 to think that he was moving, then I guess that object #1 must think like this:

"A while ago when I was not moving my clock was ticking normally. Then I accelerated, so now I am moving, and the Earth seems to be moving with me. Me and the Earth have now equally time dilated clocks. Earth's clock has been time dilated all the time, while my clock was not time dilated when I was not moving."

No. Motion is not absolute. There is no preferred frame or state of absolute rest by which you measure "your" time dilation. In fact, talking about "your" time dilation is meaningless. Time dilation is what you measure happening to clocks with relative motion with respect to you. It always happens to the "other guy", never you. The answer comes from what I posted earlier: The difference in measurements made from an inertial frame vs an accelerated frame.

 

[phinds]

Object #1 thinks like this:
"A while ago when I was moving my clock was ticking slowly, although I remember that I though that I was standing still and I remember that I thought that my clock was ticking normally.

I see that Janus has beaten me to it, but this is such a common misunderstanding that it bears repeating. Time dilation does NOT happen to you. Ever. It is only something that it perceived be an observer who is moving in a frame of reference in which you are stationary. You clock ALWAYS ticks at one second per second regardless of your speed relative to other objects and regardless of your depth in a gravity well.

There is a very simple way to see the truth of this. Right now, as you read this, you are MASSIVELY time dilated according to a particle moving in the accelerator at CERN. You are somewhat time dilated relative to a really fast moving asteroid. You are extremely mildly time dilated relative to the ISS (because you are deeper in the Earth's gravity well). Now, you obviously can't be all of these things at the same time if it actually has any impact directly on you, but it doesn't. It's just something THEY see, not anything you experience.

 

[giograf]

Thank you, everybody, for your help. Your answers were very helpful.