From the photon's perspective, it passes earth immediately. From our perspective, it takes 7 or 8 minutes.
> And let's say, i travel one light-year at the speed of light, that should be instantaneous, right? The odometer would show 1 light-year, my watch would should 0 seconds and some decimals. How much would I have aged by the end of the journey?
You would have aged as much as your watch says you would have aged. Zero seconds.
>If I travelled at one percent of speed of light, same distance, i suppose 100 years would elapse for me, how much would elapse on earth?
I don't know how to do the math, but a very, very long time would have passed on earth.
> And what if I left earth at 50percent of light speed , traveled 1 light-year away and did a turn and came back to earth at same speed. For me, it would be 1 year, but if I had a twin brother who was waiting on earth, would i now be a year younger than him? And how is this possible?
Yes, you would be younger than him, and it's possible because that's just how relativity and time dilation work. It's even practically measurable in "real" life: http://www.leapsecond.com/great2005/tour/
> I don't know how to do the math, but a very, very long time would have passed on earth.
Eh, at .01c, not so much: https://www.omnicalculator.com/physics/time-dilation?c=USD&v...
(=100.005y, not even two days extra)
So, saying time stands still for the light is a misnomer.
To go even further: to a photon's perspective, it is able to teleport instantly anywhere in the universe, because time doesn't elapse for it.
Is travelling at the speed of light, actually travelling a a fraction of the speed of time?
This is probably one of the more counter-intuitive simple calculations you can do in physics.
In special relativity, distance is given by:
ds^2 = dx^2 + dy^2 + dz^2 - (c^2)dt^2
dX^2 = dx^2 + dy^2 + dz^2
Further, your velocity is given by dX/dt. If you are traveling at the speed of light, you have:
dX/dt=c
dX^2 = (c^2) dt^2
dX^2 - (c^2) dt^2 = 0
ds^2 = 0
> just curious... does "time" have a "speed" ?
It is not clear how to parse this question. Traditional "speed" is defined as distance over time. We can give this meaning for time itself by realizing that there is no single notion of time in relativity. As such, you could consider the line parallel to the time axis in the coordinate system of observer A. Since dt=0 in the coordinates of observer A, the speed of this line is not well defined. However, we could consider the coordinates of observer B. Assuming B is moving relative to A, he would see this line as being slanted, with both a time component, and a space component. As such, B could compute the speed of this line as dX'/dt', where X' is the total displacement along B's 3 spatial dimensions, and dt' is the displacement in B's time dimension. As such, B could meaningfully answer "what is the speed of A's time". Assuming I didn't mess up on the math, dX'/dt' turns out to be the velocity of A relative to B. This is a curious result that I have never seen before, but I can't really see any physical significance to it.
B could also compute dt/dt', where t' is the time axis in B's coordinate system. This computation seems more useful as it gives a direct measure of time dilation. Unsurprisingly, it also works out to be the Lorentz factor.
- Time relative to an observer: Designating a non-accelerating massive object ("observer"), you get a coordinate system which assigns a time and distance to each event (point in spacetime). In this coordinate system, the observer moves along the time axis.
- Proper time: For an object taking any path through spacetime, you can measure the "subjective" time which has passed between two points on its trajectory.
The two notions coincide along the path of an observer: For each second of subjective time, the observer moves one second along the time axis in its coordinate system. Observer time moves at one second per second, if you will.
What you usually call "velocity" is distance/time in the coordinate system of some observer. For massive objects, this is always smaller than the speed of light. If you want, you can define another notion of speed, to illustrate the original commenter's point: distance in some coordinate system per proper time. This can be arbitrarily high, because at high velocities the proper/experienced time becomes shorter.
To get back to the speed of time: If you measure coordinate distance per proper time, it is only natural to also measure coordinate time per proper time. If you take earth as the observer and follow a spaceship, this is earth time per spaceship time. For a fast spaceship, time on board passes slower than on earth (time dilation), so reciprocally, the spaceship moves through (earth) time faster than 1s/s.
(Unfortunately, the notion of proper time becomes useless for massless particles moving at the speed of light: proper time along their trajectory is constant. They "do not experience time".)
The 'speed of light' is nothing but a coefficient between seconds and meters (or in general, between units of time and units of distance and is equal to 1 in any sensible measurement system) since the spacetime in GR is unified
Even the 5-dimension tesseract was a decent representation as well.
Matthew Mcconaughey using love to navigate through the 5-dimension is classic hollywood.
Another one would be cause and effect, if that had already happened it means it must happen again... and so whatever he does there it will succeed in setting events in motion again... Interesting bit would have been how it all started.
His book was intended to help people understand these exact questions, without getting into any complex math.
Regarding "how is this possible?": This was experimentally verified in the 70s in the Hafele–Keating Experiment. Read more here: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experim...
Time slows down for the faster moving particles. And by time slowing down we mean all the particles in your body equally all start to move slower and more sluggishly in sync.
This is because it takes more energy to accelerate a particle as it approaches the speed of light. So if you had a pendulum clock moving almost at the speed of slight, that velocity of the pendulum at rest would be at X m/s, but if the whole system is already moving super fast the extra X m/s would take too much energy. So since the energy is constant the relative speed of the pendulum just becomes much slower.
The main ”paradox” found by experimention is that the speed of light is a constant, regardless of your velocity. The only way this could be true, if you do a thought experiment, is if time was dialating for you. As for the physical and mathematical “why is this happening”, that’s where Einstein comes in.
It’s an exponential. At 0.5c 100 years to you would be 115 years elasped to an observer, 0.9c 229 years, 0.999c 2,236 years, etc.
Here’s an online calculator for the dilation effect https://www.omnicalculator.com/physics/time-dilation
Both observers, looking at one another, would see the other moving near c. Neither would know who was ‘actually’ moving. Yet, you assume there would not be a symmetry in their respective views of the other’s passage of time.
Explain why.
In simpler terms, a twin in a c-speed rocket could very well assume he was still and the earth was moving away. He should expect to find a younger twin when the earth ‘returned.’ Yet the examples only have the earth twin age, so to speak, and not the rocket twin.
https://m.youtube.com/watch?v=cPEwkMHRjZU (7 minutes)
It doesn’t answer your question directly, but the tricky part of a twin paradox is not that the earth twin observes his brother in a slow motion (the space twin also does that, thus a paradox). It’s because a space twin actually changes direction by acceleration at some point B, and at that time he skips over a big part of earth’s timeline. The video above only addresses why it’s NOT the earth twin who changes direction by acceleration, which you’re reasonably questioning. The universe somehow knows who is really “steering” and what remains more or less inertial. The pendulum example at the end may give a hint on why.
Edit: also, the space twin doesn’t have to experience any additional acceleration from the “engines” - looping around some gravity well would work too. E.g. an entire trip could be that the space twin goes to the orbit around the earth, gets slung away by a quickly passing blackhole, loops around a distant blackhole and returns, all in a complete free fall.
What actually matters is who travels the longest World Line a.k.a. the longest path in 4-d spacetime https://en.wikipedia.org/wiki/World_line . That is all.
A person on a non-curved geodesic spacetime path ages more quickly than a person on a curved non-geodesic spacetime path
It's not intuitive but time actually warps and there is no true concept of "simultaneous" in a special relativity world.
This did my head in. Wikipedia has a great explanation.
If I travelled at one percent of speed of light, same distance, i suppose 100 years would elapse for me, how much would elapse on earth? Odometer would still show one light year?
And what if I left earth at 50percent of light speed , traveled 1 light-year away and did a turn and came back to earth at same speed. For me, it would be 1 year, but if I had a twin brother who was waiting on earth, would i now be a year younger than him? And how is this possible?