Help me understand time dilation

[Nuri]

I understand that since light needs time to travel, observing distant objects through a telescope means you are viewing them as they were in the past. That makes sense. So here's where I get confused...

Imagine if I had a spaceship capable of travelling at the speed of light and you and I carried out an experiment... You watched me blast off to a hypothetical planet orbiting Proxima Centauri today, 11 Aug 2011. For arguments sake, the planet is exactly 4 light years away. So, 4 years later on 11 Aug 2015 I arrive at the planet and at that same time, you look through an incredible telescope that is capable of seeing me wave back at you. But all you see is a bare planet with nobody there, right? I understand that this is because you are looking at the planet as it was when you watched me leave Earth, 4 years ago, even though I'm actually there on 11 Aug 2015. So my question is, to see me waving back at you on 11 Aug 2015, WHEN would you need to look through the telescope? 11 Aug 2019?

[renormalised (Carl)]

You've answered your own question there

However, what you wrote about isn't strictly time dilation. If you wanted to observe the effects of time dilation, you would need to carry a clock with you and have it synchronised to a clock I had sitting on my desk at home (or in the lab) on the day you left for Proxima. What you would find is that the closer to the speed of light you traveled at, the more out of sync with the clock back in the lab you'd become. A second to you, would still be the same length of time to me as well. But because you're moving much faster than I am, the actual amount of time that you would experience traveling to Proxima would be less than what I would experience here at the lab. To me, your clock would appear to have slowed down. To you, the 4 light years would seem to be covered in a matter of weeks (at, say 0.99c), or even instantaneously at precisely c, however, here at the lab something like 4.5 years would've passed by. The faster you traveled, the less time it would appear to take for you to get there, but for me it would take whatever time it did...whether that was 4 years, 5 years or more (depending on your velocity). However, the slower you traveled, the more in sync our clocks would be because time dilation only becomes considerable at substantial fractions of c. At, say, 0.5c the differences between our clocks might only be about a month or so.

That is the whole idea about Special Relativity...that time, velocity and location of any object within spacetime are all relative. It depends on who is making the observations of the objects in question and what is their position/velocity/time in relation to the objects. There is no absolute fixed point of reference within spacetime.

[Nuri]

Thanks, Carl.

I don't see how I've answered my question though. I'm trying to arrive at a finite number of when you would see me waving back (from your perspective of time), given that I travel at exactly c. Can you please explain how I can arrive instantaneously at precisely c?

I'm thinking, from my perspective it takes me 2 weeks to get there and if I wave back straight away, you would see me waving back 4 years later?

[GeoffW1 (Geoff)]

Hi,
Relativistic time dilation tells us that if you blast off in a spaceship and travel very fast, your clock ticks more slowly than clocks back on Earth. So, for you on the spaceship, the journey might take, say, 10 years, or whatever. However back on Earth, a longer time has passed for those left behind.

Another way of thinking about this is that at relativistic speeds, the distance you have to travel is seen by you to shrink down. So in traversing it, a much shorter time appears to pass for you, than for an observer back on Earth.

You need to travel quite fast for this to be noticeable at all, according to the well known formula Gamma (the usual symbol used) = 1 / sqrt (1-(v^2 / c^2)) where v is your speed and c is the speed of light.
You plan a journey to a star 4 light years away. Alpha Centauri is a bit further, but what the heck.

Say you were on a spaceship which accelerated at 1 G (so you felt comfortable) to 80% of light speed, which is 240 000 km/sec. This would take about 6800 hours, or about 283 days. The distance traversed while doing this would be 113 light-days, or about 0.3 light years, so you still have a way to go before you have to begin decelerating at 1 G, say roughly 3.4 light years.

All measured by who, though? Remember, distances appear to shrink, for you on the spaceship. That began to happen while you accelerated, as well, but we ignored that bit for simplicity.

At 80% of light speed, the Gamma time dilation factor is 1 / sqrt (1-(0.8^2)) = 1.67. So, for you on the space ship, the remaining distance has shrunk by that factor, to just 2 light years. So you must cruise along for 2.5 years, your time, at 80% light speed, before turning around and firing your rockets backwards.

However back on Earth, a longer time passes, roughly 4.55 years to this point since you took off, and about 4.9 years when you finally touch down. However for you, it only took 2.8 years to touchdown.

Now you wave to your friends and rellies back on Earth with a powerful torch. This light must take 4 years to travel back to Earth, so they must begin to look out for you 8.9 years after you left.

If I got all that maths right, they might well forget to keep a lookout!!

With present technology and costs we can't really do this anyway. Chemical rockets just can't carry enough fuel aloft to make it feasible, as most of the weight they must lift is the fuel itself.

With future designs though, it appears that 10% of light speed might be feasible, but we still couldn't get very far in cosmological terms. It's Nature's quarantine I think.

Cheers

[renormalised (Carl)]

Originally Posted by Nuri

Thanks, Carl.

I don't see how I've answered my question though. I'm trying to arrive at a finite number of when you would see me waving back (from your perspective of time), given that I travel at exactly c. Can you please explain how I can arrive instantaneously at precisely c?

I'm thinking, from my perspective it takes me 2 weeks to get there and if I wave back straight away, you would see me waving back 4 years later?

You have answered your question. It's taken you 4 years to get to Proxima. So, you arrive on 11 Aug 2015. I have a telescope that has the resolution to see someone waving their hands from that distance (wish I did!!!!!), but because light has a finite velocity (300,000kms) and the distance to Proxima is 4 light years, it takes 4 years for the light coming from your waving hands to get to me watching you with the telescope. So, I will see you waving back on 11 Aug 2019...4 years after you started waving. If you started on you journey back to Earth and arrived before that date (so you've discovered how to beat the speed limit), you could actually watch yourself through the same telescope, waving back.

You would arrive instantaneously, from your own perspective, at Proxima (or anywhere else for that matter) if you were traveling precisely at c, because time stops entirely due to the time dilation effect, at c. Distance also shrinks to zero. From my perspective, your clock has wound down to a halt. For you no time will have passed at all in your journey and you'd have traveled no distance either. But if you looked back at me, my time would become infinite in scope and all of time would've passed on by. Essentially, moving at precisely c, you could be everywhere and anywhere all at once, from your own perspective. From my perspective, you'd be frozen still in time and space.

[taxman (Matt)]

Carl beat me to it. Meh, my redundant response is below anyway.

First, let me have a crack at an explanation of relativity in terms of spacetime.

** No maths (well, not much), I promise **

Let's say you are sitting on the nose of a ship traveling 1 meter per second slower than the speed of light and I am watching you from a stationary point. If you point a torch in the direction you are travelling in and switch it on, after one second, you will see the light travel its approximate 300 million meters in front of you, but I will only see it one meter in front of you.

There is the first part of an explanation: A contraction of space in the traveller's frame of reference occurs the faster they travel - 300 million metres to you is only 1 metre to me.

Now, in your frame of reference, to travel 300 million metres from your perception at any single point in your journey at constant speed will take slightly less than 1 second, but for you to travel the same distance in my frame of of reference will take 300 million seconds, as it took you one second to travel that one meter to catch up to the light from the torch.

And here is the second part of the explanation: The closer an object gets to the speed of light, the more their spacetime contracts in comparison to a stationary observer.

As Carl ponted out, relative time contracts to nothing at all if an object travels at the speed of light. This is because in a speed of light frame of reference, there is no distance to form the dimensions of space and without space, time cannot exist. Attributes that exist at sub-light (e.g. mass or charge) cannot exist at any other point than the one point where all faster than light existence occurs.

Again this is because there is no distance, and everything is in the same place at the same time (such as it is). So these attributes if not ceasing to exist entirely, at the least become meaningless.

So to give you an answer: If you stepped into a craft that immediately dropped into and out of light speed, your journey would take no time to you or the ship, but four years to a stationary frame of reference such as your departure or arrival points.

However, any lightspeed message sent by you (say laser or radio transmission) would take another 4 years to get back to Earth, making a total of 8 years after you left before any evidence to those on Earth is available that you got there.

[renormalised (Carl)]

Only if you restrict yourself to the confines of SR, Geoff. GR affords you several ways to overcome the speed of light barrier. Even SR itself, actually doesn't preclude objects traveling faster than light. It's traveling at the speed of light, which is the problem. There are outcomes to the equations for SR which require that the object obeying those equations must always be traveling faster than light. Those objects (particles) are called tachyons (as you will already know). They're existence is theoretical in nature and we haven't detected any, but it doesn't mean they don't exist. Just that we don't have the means, presently, to detect them.

[Nuri]

Thanks Matt, that's also a nice simple explanation. So theoretically, if time gradually slows down as you go faster and stops at the speed of light, is it logical to assume that it starts going backwards as you (theoretically) keep accelerating faster than light? I don't recall the Enterprise going back in time at Warp 2?

[renormalised (Carl)]

Originally Posted by Nuri

Thanks Matt, that's also a nice simple explanation. So theoretically, if time gradually slows down as you go faster and stops at the speed of light, is it logical to assume that it starts going backwards as you (theoretically) keep accelerating faster than light? I don't recall the Enterprise going back in time at Warp 2?

That's because of the physics employed by the drive system of the Enterprise. The warping of space around the ship only occurs in a confined area surrounding the ship itself...in a bubble surrounding the ship, where the warping of spacetime is confined to the "surface" of the bubble. The space that the ship sits in is not being affected by the warp field. It's being pushed along by the warp field. Essentially, the ship isn't breaking any laws of physics by traveling through space faster than c. It's space itself...the bubble in which the Enterprise sits, which is traveling along faster than c.

[sjastro]

The Lorentz transformations don't apply at v=c.

Time doesn't "stop" at v=c.
If it did the Universe would be a very dark place as no photons would reach the observer.

Regards

Steven

[sally1jack (Phil)]

Thanks guys i thought i had a reasonable understading of this topic , now its a little clearer
phil

[renormalised (Carl)]

Originally Posted by sjastro

The Lorentz transformations don't apply at v=c.

Time doesn't "stop" at v=c.
If it did the Universe would be a very dark place as no photons would reach the observer.

Regards

Steven

Thanks, Steven, for pointing out my error there. I know what I meant to write. Brain hasn't been working at its best lately

[sjastro]

Originally Posted by renormalised

Thanks, Steven, for pointing out my error there. I know what I meant to write. Brain hasn't been working at its best lately

I know the feeling. My brain turns to mush when I suffer from insomnia.

Regards

Steven

[renormalised (Carl)]

Originally Posted by sjastro

I know the feeling. My brain turns to mush when I suffer from insomnia.

Regards

Steven

Got in a few days of reasonably good sleep. But still feel a little on the outer. Might keep my comments to more mundane stuff for awhile

Like...how to annoy the EU crowd and why that is so satisfying

Just mention...."Einstein!!!!....redshif t!!!!....Hawking!!!!, etc". One word phrases. Enough to confirm to them where they think I'll be going after I pass on

In any case, time dilation to them is blowing up their watches with compressed air

[mishku]

So does this mean that if I stowed away on Nuri's craft and also waved, that upon arriving back on earth, I could observe myself in 2019 waving in 2015??

[renormalised (Carl)]

Originally Posted by mishku

So does this mean that if I stowed away on Nuri's craft and also waved, that upon arriving back on earth, I could observe myself in 2019 waving in 2015??

So long as you jumped to warp speed

But, if you did and got back here on the 10 Aug 2019, you could watch yourself wave back at yourself

[GrampianStars (Rob)]

Originally Posted by taxman

Let's say you are sitting on the nose of a ship traveling 1 meter per second slower than the speed of light and I am watching you from a stationary point. If you point a torch in the direction you are travelling in and switch it on, after one second, you will see the light travel its approximate 300 million meters in front of you, but I will only see it one meter in front of you.

Ah.. Isn't this Wrong?
In the ship your traveling at 299,000 Mil mt/sec the torch light should theoreticaly be gaining 1Mt per second in front of you ?
The speed of light can not increase to 599,000 Mt / sec
The speed of light is constant from all vantage points

[taxman (Matt)]

To a stationary frame of reference - yes, it will only gain 1 meter. But in the frame of reference of the rocketship, spacetime is contracted.

Originally Posted by GrampianStars

Ah.. Isn't this Wrong?
In the ship your traveling at 299,000 Mil mt/sec the torch light should theoreticaly be gaining 1Mt per second in front of you ?
The speed of light can not increase to 599,000 Mt / sec