What is the relationship between speed and time dilation in special relativity?

[L Drago]

TL;DR

time dilation if we go at incredibly high speeds clock ticks normally for us but very much time passes on Earth and when we return we have time travelled to future.

Dilated time = Actual time / Square root of 1 - (v²/c²)

Please clear any misunderstanding I have and if I am correct, kindly give me some more details and depth of SR time dilation which I am missing.

 

[PeroK]

TL;DR Summary: time dilation if we go at incredibly high speeds clock ticks normally for us but very much time passes on Earth and when we return we have time travelled to future.

Dilated time = Actual time / Square root of 1 - (v²/c²)

Please clear any misunderstanding I have and if I am correct, kindly give me some more details and depth of SR time dilation which I am missing.

That's not time dilation. That's differential ageing. Velocity-based time dilation is symmetric. Inertial velocity is relative. A clock on Earth is measured to run slow in the reference frame of a high-speed rocket; in exactly the same way as a clock on the rocket is measured to run slow in the Earth's reference frame.

It's time you started working through Morin (or an alternative textbook) systematically.

At the moment, you are piling up half-truths and misconceptions.

 

[Nugatory]

Take a moment to read through the Twin Paradox FAQ: https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[PeroK]

Take a moment to read through the Twin Paradox FAQ: https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

It's a good resource, but I've always thought that the Twin Paradox is a bad place to start with SR. It's far better to learn the basics of SR first and then the Twin Paradox is simply not a paradox at all.

 

[Dale]

TL;DR Summary: time dilation if we go at incredibly high speeds clock ticks normally for us but very much time passes on Earth and when we return we have time travelled to future.

Dilated time = Actual time / Square root of 1 - (v²/c²)

Please clear any misunderstanding I have and if I am correct, kindly give me some more details and depth of SR time dilation which I am missing.

I wouldn’t call one of these “actual time”. They are both times measured on functioning clocks. They are each equally valid times.

If you and I both drive from Miami to New York, but you drive through Denver and I drive through Washington DC, then our odometers will have different readings. They will both accurately report a different distance because we in fact traveled different distances.

That is what is happening here. A clock measures the length of a path through spacetime. Different paths have different lengths.

 

[phinds]

At the moment, you are piling up half-truths and misconceptions.

This.

@L Drago for about the 4th time now I again urge you to STOP with the pop-sci crap that you have filled your head with and start reading some actual science. I have also already suggest that you learn the difference between time dilation and differential aging.

You have come to the right place to learn some actual physics so it puzzles me that you, over and over again, ignore what we are telling you.

 

[L Drago]

This.

@L Drago for about the 4th time now I again urge you to STOP with the pop-sci crap that you have filled your head with and start reading some actual science. I have also already suggest that you learn the difference between time dilation and differential aging.

You have come to the right place to learn some actual physics so it puzzles me that you, over and over again, ignore what we are telling you.

Okay my apologies now I will read actual physics

 

[Herman Trivilino]

TL;DR Summary: time dilation if we go at incredibly high speeds clock ticks normally for us but very much time passes on Earth and when we return we have time travelled to future.

This sounds like you are thinking "incredibly high speed" is something that the traveler possesses. It is not. It only becomes meaningful when you compare it to the state of motion of something else. You can say you're moving at a high speed relative to something else, but at the same time you could be traveling at a low speed relative to a different something else.

And by the way, the effects of special relativity occur at all relative speeds. it's just that the higher the relative speed, the larger the effect. Magnetism is an example of a relativistic effect that occurs at very low relative speeds.

 

[L Drago]

This sounds like you are thinking "incredibly high speed" is something that the traveler possesses. It is not. It only becomes meaningful when you compare it to the state of motion of something else. You can say you're moving at a high speed relative to something else, but at the same time you could be traveling at a low speed relative to a different something else.

And by the way, the effects of special relativity occur at all relative speeds. it's just that the higher the relative speed, the larger the effect. Magnetism is an example of a relativistic effect that occurs at very low relative speeds.

If I am driving car at 100 km hour it's side is low relative to ant beside it and very high with respect to a particle accelerator

 

[Dale]

If I am driving car at 100 km hour it's side is low relative to the particle in particle accelerator if beside it and very high with respect to a moving ant.

Relative to a particle in a particle accelerator you are travelling at about 1000000000 kph. Relative to an ant you are travelling at about 100 kph.

 

[PeroK]

If I am driving car at 100 km hour it's side is low relative to the particle in particle accelerator if beside it and very high with respect to a moving ant.

That's 100km per hour relative to the surface of the Earth, which is spinning at approx 1,000 km per hour; the Earth orbits the Sun at about 100,000 km per hour; the Sun orbits the galactic centre at about 230 km per second. And the Milky way is falling towards the Andromeda galaxy at about 110 km per second. So, what is your speed exactly?

All these motions are relative (that's essentially the first postulate of SR). So, when you talk about speeds although they are absolute, you give away that (quite literally) you have not even learned the first thing about SR! You can talk about black holes and time slowing down and all that other stuff, but it means nothing if you don't know the first postulate of SR. It's just empty talk and vacuous knowledge.

 

[L Drago]

That's 100km per hour relative to the surface of the Earth, which is spinning at approx 1,000 km per hour; the Earth orbits the Sun at about 100,000 km per hour; the Sun orbits the galactic centre at about 230 km per second. And the Milky way is falling towards the Andromeda galaxy at about 110 km per second. So, what is your speed exactly?

All these motions are relative (that's essentially the first postulate of SR). So, when you talk about speeds although they are absolute, you give away that (quite literally) you have not even learned the first thing about SR! You can talk about black holes and time slowing down and all that other stuff, but it means nothing if you don't know the first postulate of SR. It's just empty talk and vacuous knowledge.

Hence what is first postulate of SR exactly

 

[PeroK]

Hence what is first postulate of SR exactly

https://bpb-us-e1.wpmucdn.com/sites.harvard.edu/dist/0/550/files/2023/11/relativity_chap_1.pdf

 

[Herman Trivilino]

If I am driving car at 100 km hour

My point is that's not a property of the car. It simply means that the car's speed relative to the roadway is 100 km/h.