I'm new to Relativity. I have a quick question.

1. Apr 26, 2010

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.

2. Apr 26, 2010

mgb_phys

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.

3. Apr 26, 2010

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.

4. Apr 26, 2010

Hrash0

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

5. Apr 26, 2010

mgb_phys

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

6. Apr 26, 2010

resaypi

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

7. Apr 26, 2010

JesseM

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.
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.

8. Apr 26, 2010

Hrash0

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

9. Apr 28, 2010

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?

10. Apr 28, 2010

mgb_phys

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.

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

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

11. Apr 29, 2010

bcrowell

Staff Emeritus
This is incorrect.

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.

12. Apr 29, 2010

resaypi

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?

13. Apr 29, 2010

Fredrik

Staff Emeritus
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 ).

Last edited: Apr 29, 2010
14. Apr 29, 2010

Fredrik

Staff Emeritus
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:
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).

Last edited: Apr 29, 2010
15. May 4, 2010

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.

16. May 5, 2010

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.

17. May 6, 2010

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.

18. May 6, 2010

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.

19. May 6, 2010

JesseM

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 [Broken], 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).

Last edited by a moderator: May 4, 2017
20. May 11, 2010

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?

21. May 11, 2010

Staff: Mentor

22. May 12, 2010

Aaron_Shaw

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 ?

23. May 12, 2010

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.

Last edited: May 12, 2010
24. May 13, 2010

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.

25. May 13, 2010

yuiop

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.

Last edited: May 13, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook