# Time it will take when traveling at speed of light

#### Norzog

Hi,

first of all, I would like to apologize if this question is very very trivial or completely stupid, but it's something that was bugging me for a long time.

Let's have a look at an example where a cosmic ship travels at a speed of light from Earth to Sun. Known fact is that for a photon, judging from a point of view of a human positioned on Earth, it takes about 8 minutes to travel from Sun to Earth. So from this point of view, it would take about 8 minutes for the ship to travel to sun as well. But from the point of view of the pilot of that ship, it should take considerably less time than 8 minutes as the relativity theory claims.. So it wouldn't take years for us to travel to nearest stars other than in our solar system (eg. To Alpha Centauri, it wouldn't take about 5 years to travel to, but from a point of view of the pilot, it would take much much less time...)?

Now, if the latter is true, what bugs me is if the pilot ages slower than we do, every atom on that ship traveling at a light speed is slowed down? Should the atoms be slowed, the pilot shouldn't perceive time differently as we do on earth, though. Right? Does that mean, that even if the atoms of his body are slowed, the brain, slowed too, perceive time normally?

Again, considering the latter is true, doesn't that mean the time is not relative? Only the speed of movement of atoms is relative to the speed of framework they are in, right?

But judging from that this sounds strange, I guess I'd made a mistake or am completely of point, please... help me solve my dilemma.

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#### Fredrik

Staff Emeritus
Gold Member
...if this question is very very trivial or completely stupid,...
It's neither of those things, but it's been asked many, many times. So you could try searching for similar threads.

Let's have a look at an example where a cosmic ship travels at a speed of light from Earth to Sun.
Massive objects can't travel at the speed of light. See e.g. this post, so I'm going to have to assume that it travels at a slower speed. (I don't mind trying to answer questions that start with unrealistic assumptions, like "if I just ate 5 billion hamburgers for dinner...", but I can't answer questions that assume something that contradicts the theory that I'm supposed to use to answer the question).

So it wouldn't take years for us to travel to nearest stars other than in our solar system (eg. To Alpha Centauri, it wouldn't take about 5 years to travel to, but from a point of view of the pilot, it would take much much less time...)?
That's right. All clocks on the ship, including the pilot's body (which can be considered a really crappy clock), will measure less time than 5 years.

Now, if the latter is true, what bugs me is if the pilot ages slower than we do, every atom on that ship traveling at a light speed is slowed down? Should the atoms be slowed, the pilot shouldn't perceive time differently as we do on earth, though. Right? Does that mean, that even if the atoms of his body are slowed, the brain, slowed too, perceive time normally?
That's right. Nothing inside the ship looks funny to him.

Again, considering the latter is true, doesn't that mean the time is not relative? Only the speed of movement of atoms is relative to the speed of framework they are in, right?
Not sure I follow you here. Different observers will definitely measure different times between the same two events (because they're actually measuring different things; they're measuring a property called "proper time" of two different curves in spacetime).

#### Norzog

Not sure I follow you here. Different observers will definitely measure different times between the same two events (because they're actually measuring different things; they're measuring a property called "proper time" of two different curves in spacetime).
I would understand it only the perception of time is relative. As it could take 8 minutes for us to watch the ship arrive at sun, and as it could take eg. seconds to arrive at sun for the crew, it would happen at the same point - the only and utter change would be the age of atoms in either of the frameworks - thus the different perception of time by the different subjects. But this perception only originates from the variation of the speed of the movement of their atoms which was caused by the speed of the framework, not because of some change of the timeflow, wouldn't you agree? This can even lead to the assumption there is no time, only space.

#### bcrowell

Staff Emeritus
Gold Member
FAQ: What does the world look like in a frame of reference moving at the speed of light?

This question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers.

The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices. But we can't. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light.

Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. Either the particles collided or they didn't. The arrow either hit the bull's-eye or it didn't. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. (An easy way to see that it can't be one-to-one is that the length contraction would reduce a finite distance to a point.)

#### I_am_learning

Hi Norzog.
One of the easy way to escape from being taught the theoretical impossibility and contradiction related with travelling with the speed of light rather than being answered what you want, is to begin your question by saying that the ship don't travels at c but very very very very close to c.

#### Norzog

Hi Norzog.
One of the easy way to escape from being taught the theoretical impossibility and contradiction related with travelling with the speed of light rather than being answered what you want, is to begin your question by saying that the ship don't travels at c but very very very very close to c.
Yea, I wanted to imply that the ship doesn't have to fly at light speed but I also wanted to simplify the question and thought it wouldn't matter...

But you could also exchange the ship with photon, which age as well and travel at c.

#### JesseM

But you could also exchange the ship with photon, which age as well and travel at c.
A photon doesn't have any sort of internal clock that would tell us how it is aging, so it isn't physically meaningful to talk about how photons age.

If you're just talking about an astronaut moving close to the speed of light then your question can be addressed:
Norzog said:
Now, if the latter is true, what bugs me is if the pilot ages slower than we do, every atom on that ship traveling at a light speed is slowed down? Should the atoms be slowed, the pilot shouldn't perceive time differently as we do on earth, though. Right? Does that mean, that even if the atoms of his body are slowed, the brain, slowed too, perceive time normally?

Again, considering the latter is true, doesn't that mean the time is not relative? Only the speed of movement of atoms is relative to the speed of framework they are in, right?
Time is relative--it's true that in the Earth's rest frame all the astronaut's bodily processes are slowed down, but in the astronaut's rest frame his bodily processes are running normally while we on Earth (and any observers on Alpha Centauri) are the ones whose bodily processes are slowed down. Both perspectives are equally valid in relativity, there's no objective way to say whose bodily processes are "really" running slower. And despite the disagreement about who is aging more slowly, all frames agree about local events happening at a single point in space and time, like how old the astronaut is when he lands on a planet circling Alpha Centauri.

Also, in the astronaut's frame the reason he can get to Alpha Centauri quickly has nothing to do with time dilation, it has to do with length contraction which means that the distance between Earth and Alpha Centauri is much less in his frame than it is in our frame.

#### Norzog

Time is relative--it's true that in the Earth's rest frame all the astronaut's bodily processes are slowed down, but in the astronaut's rest frame his bodily processes are running normally while we on Earth (and any observers on Alpha Centauri) are the ones whose bodily processes are slowed down. Both perspectives are equally valid in relativity, there's no objective way to say whose bodily processes are "really" running slower. And despite the disagreement about who is aging more slowly, all frames agree about local events happening at a single point in space and time, like how old the astronaut is when he lands on a planet circling Alpha Centauri.
I always thought that from the Astronaut's frame the earth would look sped up, not slowed... ?? Or at least, they taught us that.

#### JesseM

I always thought that from the Astronaut's frame the earth would look sped up, not slowed... ?? Or at least, they taught us that.
Assuming the astronaut's frame is an inertial one, then they taught you incorrectly--in his frame Earth clocks would be running slow. The relation between a clock's velocity in a frame and its rate of ticking in that frame has to work the same in all inertial frames, otherwise all frames could not be considered equal and the first postulate of relativity (that the laws of physics work the same in all inertial frames) would be violated.

#### jnorman

this is a fun question, and worth contemplating a bit. however, since no mass can travel at "c", let's modify the question just a bit, by assuming that our space ship can travel at 0.99999999 C, and then ask how long it takes to get to alpha centauri, for example.

at that speed, the rate of time passage for the ship, as measured by a stationary viewer on earth, will be extremely retarded, and the ship's clock will indicate that it only took about 1 year to travel to alpha centauri. then you face the dilemma of either the ship just traveled faster than the speed of light (by going 4LY in one year), or that the star is really not 4 LY way. oye vey!

#### JesseM

at that speed, the rate of time passage for the ship, as measured by a stationary viewer on earth, will be extremely retarded, and the ship's clock will indicate that it only took about 1 year to travel to alpha centauri. then you face the dilemma of either the ship just traveled faster than the speed of light (by going 4LY in one year), or that the star is really not 4 LY way. oye vey!
It's not really a dilemma, the answer is definitely going to be the latter if you are analyzing things in the ship's inertial frame, the smaller distance in this frame is just a straightforward consequence of length contraction.

#### jnorman

jesse - indeed. so, how far is it exactly to alpha centauri? and if i can get there in a spaceship traveling at .99999c in one year, why does it take light 4 years to get there traveling at c? :-)

#### JesseM

jesse - indeed. so, how far is it exactly to alpha centauri? and if i can get there in a spaceship traveling at .99999c in one year, why does it take light 4 years to get there traveling at c? :-)
Well, there's no frame-invariant definition of distance, or of the time it takes something to get from Earth to Alpha Centauri. In the rest frame of Earth and Alpha Centauri the distance is a little over 4 light-years, so it takes anything (including light) at least 4 years to travel from one to the other in this frame. In the rest frame of a ship traveling at 0.99999c relative to the Earth, the distance is only about 0.0045 what it is in the Earth's frame, so about 0.018 light years, which means the ship goes from one to the other in 0.018/0.99999 years in this frame. Light takes even less time in this frame since the light is moving to the right at 1c while Alpha Centauri is moving to the left at 0.99999c in this frame, for a "closing velocity" of 1.99999c (the distance between two objects can shrink faster than light in a given frame, even though neither object individually can be traveling faster than light in this frame), so it would only take 0.018/1.99999 = about 0.009 years for light to get from Earth to Alpha Centauri in this frame. We can't ask how long it takes light to get from one to the other from light's own perspective, since light doesn't have an inertial rest frame of its own.

#### welshvegan

jesse - indeed. so, how far is it exactly to alpha centauri? and if i can get there in a spaceship traveling at .99999c in one year, why does it take light 4 years to get there traveling at c? :-)
This question is the very reason that I have joined physicforums.com. My understanding is this so far:

If I am standing on earth, watching the spaceship heading for Alpha Centuri, to me it will take the spaceship four years to get there. However, for the astronaut, who is actually on the spaceship, it will seem to him mentally that the trip actually took just one year. His body would only age one year too, right? How? Sorry still not clear.

Also Jesse, how did you figure out 0.0045 distance, and 0.018 light years?

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#### Fredrik

Staff Emeritus
Gold Member
This question is the very reason that I have joined physicforums.com. My understanding is this so far:

If I am standing on earth, watching the spaceship heading for Alpha Centuri, to me it will take the spaceship four years to get there. However, for the astronaut, who is actually on the spaceship, it will seem to him mentally that the trip actually took just one year. His body would only age one year too, right? How? Sorry still not clear.
That's right. From his point of view the distance is length contracted, so he's traveling a shorter distance.

#### welshvegan

That's right. From his point of view the distance is length contracted, so he's traveling a shorter distance.
Thanks Fredrik. So the secret to this is in the length contraction on the astronaut?

#### Fredrik

Staff Emeritus
Gold Member
Not sure what "on the astronaut" means. I'm talking about the length contraction of the distance between the astronaut and the star. If you are too, then yes, this length contraction is what solves this particular mystery.

#### welshvegan

I hope that you can bear with me on this, as I till cannot grasp:

1. Does length contraction only affect the astronaut and his spaceship?

2. How is 4 light years actually 1 light year if traveling at .99999c?

3. Why does time contract for the astronaut but not for a beam of light?

#### DaveC426913

Gold Member
1. Does length contraction only affect the astronaut and his spaceship?
It affects anything that is travelling relative to something else.

From Earth, the astronaut and his spaceship are travelling near c, and thus are length contracted.

From the astronaut's point of view, the entire universe is travelling with respect to him, and thus the entire universe is length contracted.

2. How is 4 light years actually 1 light year if traveling at .99999c?
See above. When travelling near c, the astronaut measures Alpha Centauri as much closer than we would. It is also flattened.

3. Why does time contract for the astronaut but not for a beam of light?
Photons do not experience time.

#### welshvegan

1. If a photon does not experience time, then why does it take time to reach somewhere?

#### DaveC426913

Gold Member
1. If a photon does not experience time, then why does it take time to reach somewhere?
Here's an analogy I came up with a while back.

Spacetime, that which everything including photons lives in, is 4-dimensional. Let's eliminate one of the dimensions (vertical) and put the time dimension in there instead. You now have cvomplete spatial freedom thpough the two horizontal spatial dimensions but you pass through the time dimension by moving vertically.

You are in a service elevator in a building under construction. The elevator ascends at one floor per second and it does not slow or stop or go backwards. This is you, moving through spacetime. Your spatial coordinates are not changing but your time coordinate is, as can be seen by the passing floors.

As you go up through level after level of floors, you realize that there are loooong strands of yarn tied to pillars from floor to floor at all sorts of angles. The first piece is tied to the the 2nd floor pillar right next to the elevator. The other end of that same piece is tied waaaaay up on the 6th floor to a pillar out on the north east corner of the building.

These strands are photons. They are joined at two ends, one end at point 2 in time (2nd floor), and the other at point 6 in time (6th floor).

You can only experience one floor at a time, so you only see sections of yarn that are horizontally in your line of sight. What you see is that the line of yarn (that is, only the short section you can see on the floor you're on) starts (is emitted) very close to you (right by the elevator) and "moves" away from you, ending up, four floors later, way out at the north east corner (where it is absorbed). When you were on the first floor there was no yarn to be seen, and when you passed the sixth floor, there was no yarn to be seen.

You have experienced this bit of yarn as an apparent movement through the building's space as a function of your travel through the floors (and, incidentally, through time). It was "emitted" on the second floor, and "absorbed" on the sixth floor.

But note that the yarn has experienced no travel at all through the vertical time dimension. It is static. It has had no experience of "moving" from floor to floor, no experience of emission or absorption - or of any "time" whatsoever.

#### Frame Dragger

Photons do not experience time.
There was a thread here a month or two ago about that subject, and I don't believe a consensus was reached.

#### Fredrik

Staff Emeritus
Gold Member
1. No. The length contraction formula tells you how to calculate the length of anything in one coordinate system, given its length in another coordinate system. In other words: The coordinate system that we associate with Alpha Centauri's motion assigns a length to the spaceship that's shorter by a factor of gamma than the length assigned by the coordinate system associated with the spaceship's motion. And the coordinate system that we associate with the spaceship's motion assigns a distance between the ship and Alpha Centauri that's shorter by a factor of gamma than the distance assigned by the coordinate system associated with Alpha Centauri's motion.

2. There is no "actual" distance between the sun and Alpha Centauri. The motion of these stars traces out two curves (called "world lines") in spacetime. Their small velocities relative to each other are negligible, so we can treat the world lines as parallel. The "distance" between the sun and Alpha Centauri would have to be the length of some curve in spacetime that connects a point on one of the world lines with a point on the other. But which two points should we choose, and which curve should we connect them with? The "obvious" choice is to choose two points that are simultaneous and the shortest possible curve between them. But different observers will disagree about which point on AC's world line is simultaneous with a given point on the sun's world line. So one observer will say that the distance between the stars is the length of a specific curve connecting their world lines, and another observer will say that the distance is the length of some other curve.

3. See this quote and the thread I linked to in there:
Your concern about time at the speed of light is answered by the following, which I originally posted in another forum:

The reason why we associate a specific inertial coordinate system with the motion of an inertial observer is that there's a clock synchronization procedure that makes that the natural choice. All the statements about Lorentz contracton, time dilation, etc., are consequences of that choice. The claim that massless particles experience no time comes from applying the usual time dilation formula for speed v and taking the limit v→c, but there's no reason why we should think of the result of that procedure as "a photon's point of view". There is however a good reason not to: The clock synchronization procedure doesn't work for massless particles. See my posts in this thread (at Physics Forums) for more about this.
1. If a photon does not experience time, then why does it take time to reach somewhere?
It doesn't. Not in its own rest frame, because it doesn't have a rest frame. (Note that this doesn't mean that it experiences zero time. It just means that the concept of "experienced time" is undefined).

The reason why it takes time for a photon to get somewhere is of course that its speed is finite. Speed is defined as distance/time, so 0 time means infinite speed.

There was a thread here a month or two ago about that subject, and I don't believe a consensus was reached.
There are threads about it every month, but have you ever heard a reasonable argument for why it should make sense to define a photon's point of view by doing a Lorentz transformation with speed v and taking the limit v→c? (I don't consider "Brian Greene did it" an actual argument. )

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#### welshvegan

Thanks guys so much, it is very slowly getting clearer. I'm going to continue to do a lot more studying on this, as it is no way as simple as I thought. In our worldly everyday idea of time, it is just very difficult for me to get my brain around the concept of someone aging slower at .99999c than someone on earth, and how a light year is not a light year for someone traveling at .99999c, but is a light year for a beam of light. Whew! My brain is gonna explode!!!!

#### Fredrik

Staff Emeritus
Gold Member
...and how a light year is not a light year for someone traveling at .99999c, but is a light year for a beam of light.
A light year for you isn't a light year for the guy on the rocket, but there's no such thing as "for a beam of light", so the last statement doesn't make sense.

I recommend that you study spacetime diagrams. That's the best way to learn about SR. (It's almost impossible to understand SR without them, and they are much easier to understand than the algebraic expressions representing Lorentz transformations).

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