I Understanding Time Dilation and Velocity: Debunking Common Misconceptions

[Mohammed Ayaz Quadri]

Hello. I have a question. If I am moving with velocity v for an observer O. If I experience and kind if time dilation and my time slows down with respect to observer O's time. But if my time slows down. For O I will be moving slowly in time. If time dilation is large enough. I will almost freeze in time for him and for me time everything else would be infinitely high. So won't my velocity with respect to decrease if time slows down or become zero if dilation is large enough? Thank you

 

[phinds]

Hello. I have a question. If I am moving with velocity v for an observer O. If I experience and kind if time dilation and my time slows down with respect to observer O's time. But if my time slows down. For O I will be moving slowly in time. If time dilation is large enough. I will almost freeze in time for him and for me time everything else would be infinitely high. So won't my velocity with respect to decrease if time slows down or become zero if dilation is large enough? Thank you

Your time will almost freeze for him and his time will almost freeze for you. He sees you moving very fast and you see him moving very fast. He sees you time dilated and length contracted and you see him time dilated and length contracted. And, of course, you each see yourselves as perfectly normal with no time dilation and no length contraction.

 

[Mohammed Ayaz Quadri]

So if tine freezes for anybody, the relative velocity would decrease, if it does, then time dilation would keep on decreasing. Is this something like a paradox?

 

[phinds]

So if tine freezes for anybody, the relative velocity would decrease

yes

, if it does, then time dilation would keep on decreasing.

not clear what you mean since you seem to be contradicting yourself. You say that "time freezes" and the "time dilation would keep on decreasing". How could both of those things happen at the same time?

Is this something like a paradox?

No, it's not a paradox, it's just the way things work.

 

[Dale]

the relative velocity would decrease

This doesn’t happen. When you have time dilation that does not cause a deceleration.

 

[Mohammed Ayaz Quadri]

Time dilation depends on velocity so if velocity decreases won't my time flow would approach normal time flow?

 

[Dale]

Time dilation depends on velocity so if velocity decreases won't my time flow would approach normal time flow?

Your time flow is always normal to you. It is always the other observer’s clocks that are dilated (assuming both are inertial).

 

[Mohammed Ayaz Quadri]

Exactly. So if I am slowing down in time due to time dilation for observer, he will see my velocity slowing down. Understand with an extreme eg. If my velocity is speed of light my time should stop for observer. So he would see me frozen in time. If I am frozen in time then my velocity would be zero right( I can't move)? But if relative velocity is zero, there would be no time dilation. Thats the confusion. No time dilation, I can move. I can move then there is time dilation...

 

[Orodruin]

he will see my velocity slowing down

No he will not. There is no logic to your statement. The time dilation he is observing is due to your velocity relative to him and that is expressed in his time and lengths. Your velocity relative to yourself is zero. You observe yoyr time to run normally.

 

[Janus]

Exactly. So if I am slowing down in time due to time dilation for observer, he will see my velocity slowing down. Understand with an extreme eg. If my velocity is speed of light my time should stop for observer. So he would see me frozen in time. If I am frozen in time then my velocity would be zero right( I can't move)? But if relative velocity is zero, there would be no time dilation. Thats the confusion. No time dilation, I can move. I can move then there is time dilation...

No. Let's use an example. You have a pair of spheres orbiting a common center of gravity with period of 1 sec as measured by someone at rest with respect to the common center of gravity. The center of gravity of this pair of spheres is moving at 0.866 c relative to you. You will measure this system of orbiting spheres as taking 2 sec to complete each orbit, but this has no effect on the fact that the system as a whole is still moving at 0.866 relative to you.
Time dilation will effect how you measure the velocity of individual components of a system relative to each other, but will not effect the velocity of the system relative to you.

The only time you can in a sense apply time dilation to to the motion of the the system relative to you is when the system is accelerating. In this case, the system itself will measure its acceleration as being constant, but you would measure the acceleration as decreasing. But You are not measuring a decrease in the relative velocity of system, only a decrease in the rate at which it gains velocity relative to you. This drop off in acceleration ensures that no matter how long it accelerates, it will never reach c relative to you.

 

[Mohammed Ayaz Quadri]

I am a bit confused. I am a in junior college now. Can you explain in simpler terms please? Thank you. And wherever I said velocity I didnt meant my velocity with respect to me but to observer.

 

[Orodruin]

O cannot observe a different velocity because it was your initial assumption that the relative velocity was v. It is very unclear what you think would happen, please support your argumentation with maths.

 

[Mohammed Ayaz Quadri]

Sry sir, I can't use maths. As I said I don't have enough knowledge about stuff. Let me simplify the question. Consider an imaginary switch. It can turn all time dilation on and off. It is off. I was moving with a velocity with respect to an observer. Since there is no tine dilation nothing would happen. But now if I just switch on, will it effect the my velocity with respect to an observer? I feel if my time slows down, my velocity with respect to same observer should decrease. Is it true. If yes please explain how much will this effect the velocity. Thank you.

 

[Dale]

he will see my velocity slowing down.

NO! Again, this is incorrect. Time dilation does not cause deceleration.

If I am frozen in time then my velocity would be zero right( I can't move)?

Neglecting the fact that you cannot go at c, this wrong conclusion follows from your wrong assumption above. The fact that the conclusion is wrong should indicate to you that the assumption is wrong.

If a watch is time dilated it can still go past me very fast. The time dilation in no way reduces the speed. The hands may go slowly around the center, even though the center moves past me very fast.

This concept of time dilation that you have in your head is wrong. If you wish to progress then you must abandon it.

 

[Mohammed Ayaz Quadri]

Thank you sir. One last doubt. If velocity does not change then why it is being said that if I go in a black hole, due to time dilation my time would almost stop, so a person outside will see me stopped in my place since my time is passing slowly until I fade away due to shifting of light in infra red region. This is what was creating the confusion. I was introduced to astro and modern physics by videoa about cosmos and about black holes. Most videos said that about black holes. So yes since I was just introduced that time, so there may be some misconception. Please help me clear it.

 

[phinds]

Thank you sir. One last doubt. If velocity does not change then why it is being said that if I go in a black hole, due to time dilation my time would almost stop, so a person outside will see me stopped in my place since my time is passing slowly until I fade away due to shifting of light in infra red region. This is what was creating the confusion. I was introduced to astro and modern physics by videoa about cosmos and about black holes. Most videos said that about black holes. So yes since I was just introduced that time, so there may be some misconception. Please help me clear it.

Gravitational time dilation causes a remote observer to see you red-shifting out of his ability to observe you as you approach / go through the event horizon. It looks to him like you are frozen at the EH. You don't notice anything amiss (assuming the BH is large enough that tidal gravity hasn't already sphagettified you) since you don't even know the EH is there.

 

[Dale]

Thank you sir. One last doubt. If velocity does not change then why it is being said that if I go in a black hole, due to time dilation my time would almost stop, so a person outside will see me stopped in my place since my time is passing slowly until I fade away due to shifting of light in infra red region. This is what was creating the confusion. I was introduced to astro and modern physics by videoa about cosmos and about black holes. Most videos said that about black holes. So yes since I was just introduced that time, so there may be some misconception. Please help me clear it.

In addition to @phinds comments, I would point out that the black hole question is mostly unrelated to your previous question.

Gravitational time dilation occurs due to being at different locations in a specific kind of gravitational field (curved spacetime). It has nothing to do with relative velocity, and in fact it even occurs between two observers that are at rest relative to each other.

In contrast, the velocity based time dilation that you were asking about earlier even occurs between two observers at the same location but moving at different velocities, and regardless of where that location is in any gravitational field.

The two effects can be unified mathematically, but the math does not work out the way you were suggesting above

 

[Orodruin]

It has nothing to do with relative velocity, and in fact it even occurs between two observers that are at rest relative to each other.

Same objection as in my recent Insight on cosmological redshift! This is a coordinate dependent statement. The observers are at rest relative to the flow of the time-like Killing field. If you parallel transport the 4-velocities along the connecting null geodesics corresponding to the path of a light signal, you will find that they are generally not the same.

 

[Dale]

Same objection as in my recent Insight on cosmological redshift! This is a coordinate dependent statement. The observers are at rest relative to the flow of the time-like Killing field. If you parallel transport the 4-velocities along the connecting null geodesics corresponding to the path of a light signal, you will find that they are generally not the same.

I was thinking of “at rest relative to each other” in terms of radar measurements rather than in terms of any specific coordinate chart.

 

[Orodruin]

I was thinking of “at rest relative to each other” in terms of radar measurements rather than in terms of any specific coordinate chart.

Ok, I'll buy that.

 

[sweet springs]

Hello.
Thinking not only time dilation but length contraction and also different simultaneity would help you understand sharing mutual relative speed of v among the observers.

 

[Janus]

Exactly. So if I am slowing down in time due to time dilation for observer, he will see my velocity slowing down. Understand with an extreme eg. If my velocity is speed of light my time should stop for observer. So he would see me frozen in time. If I am frozen in time then my velocity would be zero right( I can't move)? But if relative velocity is zero, there would be no time dilation. Thats the confusion. No time dilation, I can move. I can move then there is time dilation...

Okay, I think I might have a clue as to where your confusion might be coming from. You seem to be trying to consider a situation similar to your riding on a bike past the observer. Thus your thinking goes some thing like this:
"If I'm time dilated according to the observer, then I must be pedaling slower according to him, and since its my pedaling that keeps the bike moving, if I'm pedaling slower, then I must be going slower relative to him.

The problem with this particular scenario, is that it takes more than just time dilation to properly analyze. There are two other effects that also must be factored in. Length contraction and the Relativity of Simultaneity.( in fact, pretty much anytime someone thinks they come up with a way to show a contradiction with SR, it is because they ignored the effects of at least one of these. You have to take all three into account to explain what is happening, and with this particular example, this can be quite complicated. Just examining the behavior of the wheels is a chore.

Because of this, this type of scenario is not the best to use when first learning Relativity. Instead it is better to use one where the relative motion between you and the observer has no connection to anything you or anything else are doing. Such a scenario could involve you being in a spaceship that is coasting at v relative to an observer. It already has a velocity with respect to the observer, and no action on the part of the ship is needed to maintain it. The fact that the observer would see you moving around in slow motion inside the spaceship has no effect on how fast the spaceship is moving relative to him. The time dilation he sees happening to you, anything in the ship, or to the various parts of the ship is unconnected to the velocity the ship has relative to him.

 

[nitsuj]

Is there nothing in space that slows my measure of proper acceleration in an attempt to go c? I don't think there is geometrically, but maybe there are other factors in reality.

Also the point of simultinatity seems to get into the problem of defining a position of something moving at near c speeds; seems it's only a posit that we cannot go c?

 

[Dale]

Also the point of simultinatity seems to get into the problem of defining a position of something moving at near c speeds; seems it's only a posit that we cannot go c?

No. see section 6 here:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[PeterDonis]

Is there nothing in space that slows my measure of proper acceleration in an attempt to go c?

No. Proper acceleration is unbounded in relativity (at least, theoretically; in practical terms there are limits in what can be realized).

 

[nitsuj]

No. see section 6 here:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

I don't at all disagree with gamma factor being accurate, more like we cannot measure the speed c of something moving away from us. As it accelerates away it's exact position measured becoming increasingly difficult until...lol This must be true no matter the gamma factor on the fly by.

I'm thinking the posit of c being invariant includes we cannot go c.

 

[nitsuj]

No. Proper acceleration is unbounded in relativity (at least, theoretically; in practical terms there are limits in what can be realized).

Yea I figured so geometrically, but wondered about in practice. idealizing the ship's fuel, not the ship or the space it will travel in.

 

[Dale]

we cannot measure the speed c of something moving away from us. As it accelerates away it's exact position measured becoming increasingly difficult until...lol This must be true no matter the gamma factor on the fly by.

Please provide a professional scientific reference that claims this.

 

[Altair Tans]

I think you are getting confused here,
You know time slows down for the moving guy
So if speed = distance / time
And if time taken for the same distance has increased because time runs slow then speed should decrease and along with it effect of time dilation should decrease

But think about in the expression
Speed = distance / time
Distance and time are measured in O's frame.there is no time dilation in that frame. The ratio of distance / time still remains same. Speed remains v

 

[Nugatory]

I don't at all disagree with gamma factor being accurate, more like we cannot measure the speed c of something moving away from us. As it accelerates away it's exact position measured becoming increasingly difficult until...

There's a procedure that we can follow to measure the speed of anything, including a flash of light moving away from us. First, we position observers all through space, all at rest relative to us. They all synchronize their clocks (possible because they are at rest relative to us and one another). Each observer also has a piece of paper and a pencil; when and if whatever we're observing passes by, they jot down a note: "My clock read ... at the moment that the thing passed right under my nose". Then at our leisure we collect all the pieces of paper and use that data to work out how fast the object was moving relative to us: speed equals distance traveled divided by time, and we can get that from any two of those pieces of paper.

This procedure is described at the start of Taylor and Wheeler's "Spacetime Physics"' (which I highly recommend). An important point here is that the ensemble of observers collectively make up a reference frame.

 

[Herman Trivilino]

Exactly. So if I am slowing down in time due to time dilation for observer, he will see my velocity slowing down.

I think you're mixing up the rate at which an object moves with the rate at which a clock ticks. You have a clock moving at a very high speed relative to an observer. The observer notices that the clock ticks slow (compared to a pair of well-separated clocks he has at rest relative to him) but that it moves with whatever that high speed was chosen to be. The fact that it ticks slow doesn't mean it moves slow.