Understanding Relativity: The Concept of Time and the Speed of Light Explained

[Hrash0]

I'm REALLY new to relativity and I don't know much... I actually only got an interest in physics after reading Dr. Brian Greene's The Elegant Universe. Anyway, according to relativity, the speed of light c = 3x10⁹ m/s. And the faster you move, the slower time passes. At the speed of light, time stops completely. But the speed of light is the same regardless of your frame of reference... so if that's true, then a photon traveling through a vacuum experiences no time passing... but it still moves, so it's in more than one place at the same time, implying infinite speed. How does this work out?

As I said I'm new to the whole concept, so if there's something wrong with my question please let me know.

 

[mgb_phys]

so if that's true, then a photon traveling through a vacuum experiences no time passing... but it still moves,

The photon experiences no time passing from it's point of view (in "it's frame of reference" in relativity jargon) - but anybody stationary watching it go past measures it's speed as 'c'.

The whole point of relativity is that even things like time depend on how the person doing the measuring is moving.

 

[resaypi]

In 4 dimensional space everything moves at the speed of light. That is if they don't move in space, they move in time and if it moves at the speed of light in space, it does not move in time. You need the see space and time as a whole, rather than time alone or space alone.

 

[Hrash0]

Thank you. That clears things up. Seriously.
Just asking, have you guys studied astrophysics formally or is it a hobby?

 

[mgb_phys]

Used to be a professional astronomer - but know embarrassingly little about relativity!

 

[resaypi]

I was curios and decided to learn on my own, now I take courses formally.

 

[JesseM]

The photon experiences no time passing from it's point of view (in "it's frame of reference" in relativity jargon) - but anybody stationary watching it go past measures it's speed as 'c'.

That's not right, because a photon doesn't have its own "frame of reference" in relativity, all frames of reference are moving slower than light (at least if you're talking about inertial frames, which are the only ones where normal formulas of SR like time dilation apply). This is a subject that gets discussed a lot in this forum, see this thread for example.

In 4 dimensional space everything moves at the speed of light. That is if they don't move in space, they move in time and if it moves at the speed of light in space, it does not move in time. You need the see space and time as a whole, rather than time alone or space alone.

Brian Greene does give his own mathematical definition of "speed through spacetime" for which this statement would be true, but most textbooks don't define such a notion, and personally I think it's more confusing than useful, see this thread for a discussion.

 

[Hrash0]

Brian Greene does give his own mathematical definition of "speed through spacetime" for which this statement would be true, but most textbooks don't define such a notion, and personally I think it's more confusing than useful, see this thread for a discussion.

That definition is actually quite helpful when it comes to comprehension. It does mislead a bit though (my question actually arose from that definition.)

 

[dezso3]

Would a question like "why does time slow down, and eventually stop as you approach, and then reach, the speed of light" be a stupid question to ask? To the average person it would seem that just because something is moving extremely fast, i.e. near the speed of light, doesn't mean that time will slow down or stop. If for example, an observer traveling at close to light speed were going around the solar system, then would it appear to it that the planets are orbiting the sun at a faster rate, since time (on the planets) was passing faster from the frame of reference of the observer? Again, why does this happen? Or is the reason why it happens not known, just like gravitation?

 

[mgb_phys]

Would a question like "why does time slow down, and eventually stop as you approach, and then reach, the speed of light" be a stupid question to ask?

Nope it's a very good question.
in simple terms it's a necessary result of the speed of light being constant - why the speed of light is constant is a harder question.

To the average person it would seem that just because something is moving extremely fast, i.e. near the speed of light, doesn't mean that time will slow down or stop.

That's why it took until 1905 for anyone to think of it!

If for example, an observer traveling at close to light speed were going around the solar system, then would it appear to it that the planets are orbiting the sun at a faster rate, since time (on the planets) was passing faster from the frame of reference of the observer?

Yes, it's just like watching everything else in a high speed film.

Again it's necessary if the speed of light is constant for all observers - the reasoning is failry easy to follow and is in lots of intro relativity books

 

[bcrowell]

In 4 dimensional space everything moves at the speed of light.

This is incorrect.

a photon traveling through a vacuum experiences no time passing... but it still moves, so it's in more than one place at the same time, implying infinite speed. How does this work out?

Interesting thought!

Suppose an observer B is traveling at $(1-\epsilon)c$ relative to observer A, where $\epsilon$ is very small. A says that B's time is very slow -- almost stopped. But B also sees the distance over which he's traveling as being drastically Lorentz-contracted. A and B agree on their relative velocities, but B describes his motion as being a short distance covered in a short time. No matter how small $\epsilon$ is, they agree with one another on their relative speeds.

 

[resaypi]

This is incorrect.

Use the metric to show that constant lengths in 4d spacetime form a hyperbola, and dividing it with freame time would yield the speed of light.

At the speed of light space and time are unmeasurable. Is it correct to talk about them?

 

[Fredrik]

This is incorrect.

I agree with you, but the fact that you're answering with only three words suggests that you're not aware of the fact that one of the reasons why this claim is posted a lot in these forums is that Brian Greene said so in "The elegant universe". Someone needs to give him a wedgie. (What Greene was referring to is that the invariant square of the four-velocity is...uh...invariant, and equal to c² at every point on the world line. That last thing is of course just a choice of normalization ).

 

[Fredrik]

The question about what happens "at the speed of light" comes up ridiculously often. I'll just quote myself and link to some of the other threads. See this quote and the thread I linked to in it, to see why the concept of "a photon's point of view" doesn't make sense:

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 for more about this.

See my posts in this thread for my comments about what Brian Greene said. A lot of it is in #18, but you should probably read all of my posts in that thread. (Just look for the Wolverine avatar as you scroll down).

Also see this post for a calculation of the work required to accelerate a mass m to speed v, and note what happens in the limit v→c. (The work goes to infinity because $\gamma$ goes to infinity).

 

[dezso3]

Let's say that a person is sitting in a spaceship that is traveling at very close to the speed of light. Would a person who is [trying] to observe (see) that spaceship even see it? Because, wouldn't the photons that are reflecting off of it take that much longer to reach you, and thus you wouldn't see the true position of the spaceship? Also, if you were observing the Earth from the spaceship, wouldn't it appear to be a blur around the sun, because the photons from it take so much longer to reach you that the light from the Earth would just be bend around the sun, so that it would appear that the Earth exists everywhere in its path around the sun at the same time? And it seems to me that the reason that time slows down for anything that is traveling at near the speed of light is because the speed of light determines the rate at which time passes? So for example, a person's brain waves, traveling at the speed of light, had to catch up to a different part of the person's brain, which is traveling at very close to the speed of light, it would take an extremely long time for it to reach its destination, thus slowing down the cells' aging process, and thus slowing down time! So basically, an atomic clock traveling at the speed of light would register a very very slow passage of time because the radiation emitted by the atom would take that much longer to catch up to the clock, making it "tick" more slowly. Obviously, this is extremely simplified and in a layperson's terms. But am I on the right track? This stuff is just incredibly mind-boggling.

 

[dezso3]

http://www.youtube.com/watch?v=hbFxNcaJO_Y&feature=related

In the video, it is stated that it is theoretically possible to travel faster than the speed of light, and when you do, time will go backwards. But what I don't understand is that if it's impossible to travel faster than the speed of light, then how on Earth (no pun intended) would you travel faster than light speed, and thus back in time, if you went around a black hole, as is shown in the video? From the outside, it just seems that an object (such as a spaceship) is traveling faster than the speed of light around the black hole, but if that's not possible, then how the heck does it happen? It just doesn't seem to make any sense.

 

[taybot]

" In 4 dimensional space everything moves at the speed of light."

i'm reading Greene's Fabric of the Cosmos and he talks about the same concept. So hopefully it is indeed correct.

 

[espen180]

Yes, that is so. A change of velocity in space is equivalent to rotating the 4-velocity vector in 4D space-time, which always has length c.

 

[JesseM]

http://www.youtube.com/watch?v=hbFxNcaJO_Y&feature=related

In the video, it is stated that it is theoretically possible to travel faster than the speed of light, and when you do, time will go backwards. But what I don't understand is that if it's impossible to travel faster than the speed of light, then how on Earth (no pun intended) would you travel faster than light speed, and thus back in time, if you went around a black hole, as is shown in the video? From the outside, it just seems that an object (such as a spaceship) is traveling faster than the speed of light around the black hole, but if that's not possible, then how the heck does it happen? It just doesn't seem to make any sense.

The explanation in that video (at about 7 minutes in) is actually pretty terrible and I wouldn't recommend paying attention to it. The example with "Bertrand" and "Albert" suggest that if Albert is stationary while Bertrand is flying in circles and repeatedly passign him at close to light speed, then Bertrand will see Albert's clock running slow, approaching being stopped as Bertrand approaches light speed, so if he could go faster than light he could see Albert's clock go backwards. Actually this is complete nonsense, if one observer is moving in circles on a non-inertial path while the other is moving inertially, it will be the one going in circles whose clock elapses less time between each meeting, so Bertrand should actually see Albert's clock running faster on average over each orbit (though depending on what frame you use there may be particular moments where Albert's clock is running slower...all frames agree that the average tick rate of Albert's clock rate is faster than Bertrand's between successive occasions when they pass each other though). And the explanation for why FTL implies backwards-in-time is more complicated than they suggest, it has to do with the relativity of simultaneity and how different frames can disagree about whether two events at different locations (at a separation sufficient so that no signal traveling at the speed of light or slower could go from one event to the other, so there can't be a cause-and-effect relation between them) happened at the same time or at different times, and also on the order in which the events occurred (but again this is only for events which can't be causally related). This means that if one event was an FTL signal being sent and the other was the same signal being received, there'd be some frames that see the second event happening before the first one, and if the receiver was moving relative to the sender and transmitted an FTL reply after receiving the signal, the reply could get back to the sender before he sent the original signal. This is discussed in more detail on this thread if you're interested.

Meanwhile, in general relativity, which deals with how spacetime can be "curved" by the presence of matter and energy, it is theoretically possible to have weirdly-curved spacetimes where you can travel back in time (travel along a closed timelike curve) without ever locally exceeding the speed of light (i.e. at every point in your journey, if you measure the speed of a light beam in your immediate vicinity using the type of very small free-falling reference frame discussed at the end of http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html , you will find the light to be traveling faster than you). The subject of the video is Ronald Mallett, and you can read some stuff about his time travel ideas on his wikipedia page. Basically, he found a curved spacetime in general relativity involving an infinitely long "line singularity" with light beams circulating around it (their paths bent around by its gravity), and discovered that closed timelike curves were possible in this spacetime (since it involves an infinitely long line singularity, it's more similar to something like a Tipler Cylinder than to a black hole). Apparently Mallett offers some vague qualitative arguments as to why he thinks it was really the circulating light rather than the line singularity that made closed timelike curves possible, and that even without a singularity, a bunch of lasers which have been bent optically to travel in circles might allow small particles in the vicinity to go back in time. If you look at the "objections" section of the wikipedia article, though, you'll see that other physicists who have looked at his proposal have found a number of arguments as to why this probably doesn't make sense (the most significant being a general theorem that shows that closed timelike curves can only be created in a finite region of space if something called 'exotic matter' with negative energy is present).

 

[dezso3]

What happens when two particles that are moving at, say, 60 percent of the speed of light move past each other in the opposite direction? Will it appear to one particle that the other one is moving at 120 percent of the speed of light?

 

[jtbell]

No.

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel.html

 

[Aaron_Shaw]

No.

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel.html

Does this mean that if we say the 2 particles, A and B, are moving in opposite directions at 0.6c then these speeds must have been measured by a third, relatively stationary observer, C?

In that case C sees A moving at 0.6c and B moving at -0.6c.

Then, from the perspective of either A or B because the picture is symmetrical, we must assert that the Earth is moving at +/-0.6c because that is the basic premise of this example, and therefore the 'other' particle is moving at $$\frac{0.6c+0.6c}{1+((0.6c*0.6c)/1c^{2})}$$

which equals 0.88c ?

 

[yuiop]

Yep, A sees C moving at -0.6 and B moving at -0.88 and B sees C moving at +0.6 and A moving at +0.88.

 

[prakash kumar]

first of all i say interesting idea you got there Hrash0.
first you must understand that photon rate of flowing of time is same for photon and it will seems to slow for the man who (try to ) obs. it and don't cosidered space alone and time alone in special relativity. if you do this you will encounter problem after problem with it. you must consider it as space-time.
hope u will be satisfied.

 

[yuiop]

" In 4 dimensional space everything moves at the speed of light."

i'm reading Greene's Fabric of the Cosmos and he talks about the same concept. So hopefully it is indeed correct.

I thought I might expand on Brian green's concept for interested readers.

In 3 dimensional space the speed of a particle is given by:

$$v3 = \frac{\sqrt{dx^2 +dy^2 +dz^2}}{dt}$$

which is basically distance through 3 dimensional space per unit coordinate time. v can take any value between between 0 and c, but for a photon v is constrained to be equal to c. In 4 dimensional space a new spatial dimension $c\tau$ (where $\tau$ is proper time) is defined and this is on an equal footing with the other spatial dimensions and the speed of a particle in 4D space is given by:

$$v4 = \frac{\sqrt{c^2d\tau^2 +dx^2 +dy^2 +dz^2}}{dt}= \frac{\sqrt{(dx_0)^2 +(dx_1)^2 +(dx_2)^2 +(dx_3)^2}}{dt} = c$$

Defined like this, the speed in terms of distance through 4 dimensional space per unit coordinate time, is always c for any particle, and not just for photons.

 

[Aaron_Shaw]

I thought I might expand on Brian green's concept for interested readers.

In 3 dimensional space the speed of a particle is given by:

$$v3 = \frac{\sqrt{dx^2 +dy^2 +dz^2}}{dt}$$

which is basically distance through 3 dimensional space per unit coordinate time. v can take any value between between 0 and c, but for a photon v is constrained to be equal to c. In 4 dimensional space a new spatial dimension $c\tau$ (where $\tau$ is proper time) is defined and this is on an equal footing with the other spatial dimensions and the speed of a particle in 4D space is given by:

$$v4 = \frac{\sqrt{c^2d\tau^2 +dx^2 +dy^2 +dz^2}}{dt}= \frac{\sqrt{dx_0^2 +dx_1^2 +dx_2^2 +dx_3^2}}{dt} = c$$

Defined like this, the speed in terms of distance through 4 dimensional space per unit coordinate time, is always c for any particle, and not just for photons.

I could be thinking of this all wrong, but this is how i imagine it in my head...

Say I take a ruler as my measurement unit. If i stand this ruler perpendicular on my desk then it is representing 1 ruler's worth of movement in the up (y) axis. If i lean it to the left a little, then it represents a small fraction of 1 ruler of movement on the negative x axis, and a little less than 1 ruler of movement in the y axis. Then if i lean it away from me a bit it now represents the same movement in the x axis, plus some new movement in the z axis (away from me) at the expense of even less movement in the y-axis which was at 1 complete ruler originally.

By changing the way the ruler is oriented in 3 dimensions i am changing the amount of ruler representing each of the x,y, and z dimensions, yet the overall combined magnitude is always 1 ruler.

If we add a 4th dimension, that being time, then you can see how we can be always moving at 'the speed of light' (1 ruler), for want of a better analogy, by trading magnitudes of different 'speed' components in different dimensions. So if we go really fast in the X,Y and Z axis, then we trade off the time axis, making time pass slower. If we don't move in the x,y, or z axis at all, then all of our 'speed' (of light) is allocated to the time axis, and time passes at it's fastest.

I have no idea whether that makes sense outside of my head :D

 

[yuiop]

I could be thinking of this all wrong, but this is how i imagine it in my head...

Say I take a ruler as my measurement unit. If i stand this ruler perpendicular on my desk then it is representing 1 ruler's worth of movement in the up (y) axis. If i lean it to the left a little, then it represents a small fraction of 1 ruler of movement on the negative x axis, and a little less than 1 ruler of movement in the y axis. Then if i lean it away from me a bit it now represents the same movement in the x axis, plus some new movement in the z axis (away from me) at the expense of even less movement in the y-axis which was at 1 complete ruler originally.

By changing the way the ruler is oriented in 3 dimensions i am changing the amount of ruler representing each of the x,y, and z dimensions, yet the overall combined magnitude is always 1 ruler.

If we add a 4th dimension, that being time, then you can see how we can be always moving at 'the speed of light' (1 ruler), for want of a better analogy, by trading magnitudes of different 'speed' components in different dimensions. So if we go really fast in the X,Y and Z axis, then we trade off the time axis, making time pass slower. If we don't move in the x,y, or z axis at all, then all of our 'speed' (of light) is allocated to the time axis, and time passes at it's fastest.

I have no idea whether that makes sense outside of my head :D

Yep, that is one way of thinking of it. Motion in 4D space is hard to picture but it actually quite easy to measure. Distance moved by an object in the regular 3 space dimensions can be measured by using rulers. Distance moved in the fourth space dimension, is physically measured by strapping a clock to the object and comparing the time shown by that clock (the proper time) to your clock (and scaling by a factor of c).