# The speed of light and time dilation

1. Sep 15, 2006

### Repertoire

If a body's time must slow down when it moves in order for the speed of light to remain constant then how can the speed of light remain constant if two waves of light are moving toward the body from two different directions?
Say the body has two light particles coming towards it. Particle A and Particle B. If the body is moving towards Particle B and away from particle A then, relative to the body, particle B would to be moving faster than the the speed of light and particle A would be moving slower.

2. Sep 15, 2006

### Staff: Mentor

To measure the speed of light, you need a source from which to measure the time and distance. The moving observer measures the time and distance to the two light sources such that the light beams are always calculated to be traveling at C. Remember: both the time and the distance the observer measures are affected by Relativity.

3. Sep 15, 2006

### JesseM

And it's not only time and distance, but the fact that different reference frames define simultaneity differently, meaning that they disagree about whether two events at different locations happened "at the same time" or not. For example, suppose I'm in a rocket ship zooming past you at a high fraction of the speed of light, and I want to synchronize two clocks at the front and back of the rocket. Since I assume light travels at the same speed in both directions in my frame, I can synchronize them in my frame by setting off a flash at the midpoint of the two clocks, and making sure that they both read the same time when the light from the flash reaches them. But from your point of view, the front of the rocket is moving away from the point where the flash was set off, while the back is moving toward that point, so if you assume light travels at the same speed in both directions in your frame, you must conclude the light will reach the clock at the back before it reaches the clock at the front, and thus that the two clocks are out-of-sync.

For a simple example showing how time dilation, length contraction and different notions of simultaneity all come together to insure different observers measure light moving at the same speed, see my first post on this thread.

4. Sep 17, 2006

### Repertoire

So in the body's frame of reference does the space in front of it shrink and the space behind it grow?

5. Sep 17, 2006

### Sojourner01

No; that's the point of the theory. The moving body should never be able to tell it's moving - at least when it's moving at a constant velocity relative to 'everything else'.

The dilation/contraction effect comes into play when an outside observer looks at the information taken by an observer in/on/that is the object. Relativity works in terms of comparisons with moving and stationary observers; the moving body's clock will have measured less time than the stationary observer's at the end of the journey, while every stationary observer sees rapidly moving objects contract.

Consider a car moving at an appreciable fraction of the speed of light toward your garage. To an observer, the car contracts - to the point that it's small enough to fit into the garage whereas a car of the same type when it's stationary would not - while if you were to look at its onboard clock, it would be ticking too slowly. If you were in the car, however, you'd see a compressed garage hurtling toward you at near the speed of light, with the clock on the wall running slow...

6. Sep 17, 2006

### Repertoire

three questions:

1 if you are standing at the side of a road and you see a car going at 0.6c and 8 light seconds down the road in both directions someone is shining a flashlight toward the car, then without time dilation or contraction or anything the car would see the a beam of light travelling at 1.6 c towards him and would reach him after 5 seconds and he would see a beam of light coming at him at 0.4 c after 20 seconds. Even if his clock slows down so that those first 5 seconds seem like 8, the second beam of light would then appear to be travelling at 0.25 c and it would take it 32 seconds for the second beam to reach the car. So if the car does not see the road in front of him double and the road behind him half and time dilation cannot make the two beams of light reach him at the same time then what will?

2 If the observer sees the car shrink because it is moving compared to it then shouldn't the car see the observer grow? But then he should see the observer shrink at the same time because compared to the car the observer is moving.

3 If gravity is simply objects following geodesics in curved spacetime then:
a) how does something that isn't moving fall?
b) why doesn't light fall with the same acceleration as as matter?

Last edited: Sep 17, 2006
7. Sep 17, 2006

### pervect

Staff Emeritus
You need to take a close look at the Lorentz transforms.

$$x' = \frac{\left( x - \beta t \right) } {\sqrt{1-\beta^2}}$$
$$t' = \frac{\left( t - \beta x \right) }{\sqrt{1-\beta^2}}$$
$$\beta = \frac{v}{c}$$

The primed observer computes that the unprimed observer's clocks slow down and his rulers shrinks. But when one takes the inverse transform, the unprimed observer computes that the primed observer's clocks slow down and his rulers shrink. You just replace v by -v to get the inverse transform.

The explanation for this is that the definition of simultaneity is not the same for the primed and unprimed observers. This can be seen in the first expression - not only is there time dilation t' = gamma t, but there is an additional term as well, t' = gamma t - beta*gamma x.

The term beta*gamma*x is the term responsible for the relativity of simultaneity.

More physically, you might look at the classic "train and platform" experiment to see why which events are simultaneous depends on the observer.

You might take a look at the wiki article:
http://en.wikipedia.org/wiki/Relativity_of_simultaneity

(currently it's in pretty good shape)

8. Sep 18, 2006

### Repertoire

Ok well what would it look like if you used the lorentz transformations to solve the problem? (I keep getting intead of t = 8 and t = 8 I get t = 4 and t = 16) and what about question 3?

Last edited: Sep 18, 2006
9. Sep 18, 2006

### michael879

The basic principle of relativity is that no reference frame is special from any other. If the observer sees the car moving at v, then the car sees the observer moving at v. If the observer sees the car shrinking (which he does) then the car must see the observer shrinking because the two frames are equal.
a) you would have to except some force that masses feel even at rest pulling them to an earlier time so that they fall into gravitational "wells". Its basically the same as the forces things feel towards lower potential energies (which is another way to explain gravity).
b) I think light just falls twice as fast as it would if it were just something of mass hf/c^2 going at a velocity of c. I have no clue why tho sorry.

10. May 5, 2010

### chaslie

I haven't figured out how to post a new thread but I have a similar question so am posting it here. I am a layman but I have a question that I am hoping someone can answer for me.

There are two twin brothers. On their thirtieth birthday, one of the brothers goes on a space journey in a superfast rocket that travels at 99% of the speed of light. The space traveler stays on his journey for precisely one year, whereupon he returns to Earth on his 31st birthday. On Earth, however, seven years have elapsed, so his twin brother is 37 years old at the time of his arrival. This is due to the fact that time is stretched by a factor of 7 at approx. 99% of the speed of light, which means that in the space traveler’s reference frame, one year is equivalent to seven years on earth. Yet, time appears to have passed normally to both brothers, i.e. both still need five minutes to shave each morning in their respective reference frame.

Comment:
Can it not be equally said that the brother who stays on earth is travelling at 99% the speed of light away from the brother who is traveling at 99% of the speed of light away from the brother who stays on earth? So, how can it be inferred that time will have passed slower for the brother who is traveling on a superfast rocket and not for the brother who stayed on earth?

Time dilation can be inferred from the observed fact of the constancy of the speed of light in all reference frames. This constancy of the speed of light means, counter to intuition, that speeds of material objects and light are not additive. It is not possible to make the speed of light appear faster by approaching at speed towards the material source that is emitting light. It is not possible to make the speed of light appear slower by receding from the source at speed. From one point of view, it is the implications of this unexpected constancy that take away from constancies expected elsewhere.
Consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. The separation of the mirrors is L, and the clock ticks once each time it hits a given mirror. In the frame where the clock is at rest, the light pulse traces out a path of length 2L and the period of the clock is 2L divided by the speed of light:

From the frame of reference of a moving observer traveling at the speed v, the light pulse traces out a longer, angled path. The second postulate of special relativity states that the speed of light is constant in all frames, which implies a lengthening of the period of this clock from the moving observer's perspective. That is to say, in a frame moving relative to the clock, the clock appears to be running more slowly.

Observer at rest sees time 2L/c
Observer moving parallel relative to setup, sees longer path, time > 2L/c, same speed c

Comment: If there is a greater distance initially between A and B where the observer is moving then shouldn’t take longer for light to travel from A to B than when the observer is at rest? Otherwise, wouldn’t it be impossible to determine distances between planetary objects? Also, in order to accurately measure the distance between objects using light wouldn’t time need to be constant?

11. May 5, 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.

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? And supposedly wormholes work using the same principle of bent space-time. But even if an object (such as a spaceship) were to exceed the speed of light in bent space-time, how it travel back in time? In other words, if you're traveling faster than a photon, how would that cause time to run in reverse? For some reason I seem to understand that time slows down near light speed and how it does it, but what I do NOT understand is how it can run in reverse. It just doesn't seem to make any sense.

12. May 18, 2010

### Roke_0

Oh boy, so explaining without diagrams...haha let's see. I hope someone will correct me as I am also a layman but I thought a couple of your guys' questions here were really interesting, and also thought that I had some long shot at answering them properly. I basically read A LOT of my astronomy textbook when I took the class, and physics courses, so here goes...

Repertoire: Light does funny things! :P I might be wrong, but I think some of the apparent trouble exists because we tend to think about light in terms of particles when it does not behave entirely like a particle. If you were traveling at 100 m/s (in a vacuum thank god) and fired a gun with a muzzle velocity of 100 m/s, the projectile would be traveling 200 m/s with reference to the total stationary frame. So at c, as a limit, it seems intuitive that if you were traveling at .9c and turned on a flashlight, the beam must only be traveling .1c faster than you (It can't be measured at 1.9c from any reference frame anywhere). Unfortunately for our sanity, the light from your flashlight's speed is measured by you as 1c not as .1c, even though that is the amount its velocity exceeds yours. The stationary observer would record your speeds "correctly" at .9c and 1c, but you still observe the light's velocity to be 1c, and it would appear to race away from you at that velocity.

And why? Well, we're not sure. I don't think we know why this is the case. This is really tough for me to explain in writing and I'm not sure this is making sense, but it might help to realize too that the object in your scenario doesn't "know" that it is moving at whatever velocity it has. And even if the light particle B reached the object first, none of the individual particles would have exceeded c. In other words, the distance covered between it and particle B could exceed the distance that light can travel in that time, even though nothing went faster than the speed of light.

For example, say you have two particles A and B which are 2c apart (as a distance, the distance light travels in 2 seconds let's say). Each particle is moving at c (the speed of light). In one second the two particles will meet right in the middle. While it seems the 2c distance was traveled in just 1 second, neither particle exceeded c. An observer would see that the 2c distance had been closed in just 1 second, but that each particle moved towards each other at exactly c. Since particle A doesn't "know" that it's moving, even though it began the time 2c away from B, it observes B covering a distance of 2c/2, or half of the total initial distance between the particles, and it observes B covering this 2c/2=c in 1 second.

So even though the distance covered is greater than light could have traveled in that time, the particles are obsevered from any reference frame in the example to be traveling at no greater than c.

Chaslie: I believe that it is true, that in a situation where the velocities are already established (ie- no more acceleration), you cannot say whether you are approaching an object or the object is approaching you. In the case when you have experienced the acceleration, you would be able to judge. There's really no paradox. While it seems that because the twin is flying away, neither of them could tell which description of the event is "true", both brother's do not experience the same acceleration or same "events". The time dilation occurs in the one way because their experience of events is not similar, though at times they would be unable to tell in an instant what was happening, they started from the same reference frame. The brother who stays home never leaves that reference frame and experiences no relevant accelerations besides the normal earth ones, while the twin in the rocket leaves their initial reference frame and experiences acceleration while he is leaving, and as he turns around. Though they "couldn't tell" in the sense you mean, anyone on the earth would see the one brother accelarate to and fly away at that speed, swing around a star, and then come back.

The description of the events for both brothers as judged from the initial reference frame are different.

Supposedly (I found this interesting), due to gravitational time dilation, as a person is approaching the surface of a massive black hole, an observer from a sufficient distance from this, will see that time has slowed down for him, while the person near the black hole will see that time appears faster for everyone else. As the "astronaut" crosses the event horizon, time will appear to stop completely for him, while he will see the enternity of time in the universe pass in a blink, although time for him, as perceived by him, remains unchanged and he will otherwise pass through the event horizon as if nothing had happened (assuming he could survive being strectched). At which point he would never be heard from again... ^^

"Because, wouldn't the photons that are reflecting off of it take that much longer to reach you?"
Nope. And couldn't tell you why. They bounce off and would still apparently travel at the speed of light. Don't know why. "This stuff is just incredibly mind-boggling." True!

I also used to be of the understanding that time itself was slowed for the person moving at high speeds, but that's not actually the case. For them, time, and chemical and aging processes, etc., go on as normal. It's just that their high velocity relative to someone else's velocity makes their time "seem" different, relative to the other person. If someone were traveling at .99c, they still perceive and experience 15 minutes in exactly the same way, except that their 15 minutes was a different length of time in a different refernce frame. If that makes any sense -.-

Like, observering the fast moving moving person, you would conclude that they are moving in slow-motion, or that their brain function is slowed, but they would experience it just as you do sitting here, and if they could observe you, you would be moving in hyper time.

Now, I might be wrong about this, but two people moving at high speeds who never shared a reference frame, and are moving constant with relation to each other, can both see the other as being slowed down even though that seems like a contradiction, or that it would cause some sort of inconsistency in "actual" time, except that actual time apparently doesn't exist. I mean, if intelligent conciousness were not in the universe to perceive time, would it be a dimension? Wouldn't the universe come and go without any recognition or notion of time, without the passage of any events? Like it slept through the whole thing and nothing really happened...during all that ~time~? Just Kidding!

Anyways, I hope that answered some of the questions. Although Chaslie I didn't quite understand your second ones?

13. May 18, 2010

### Roke_0

Oh also, quickly, if you could exceed the speed of light, as they propose, I don't think it would allow you to travel back in time. It might allow you to view past events, but you wouldn't exist with those events simultaneously. If you could "pass" the light that left our solar system when it was forming, you could stop and "turn around" and view the solar system's formation, but it would still be a long past event that you could not interact with. And you'd have to bring a real nice telescope, because even if you did, you would be viewing events that were billions of light years away.

I think that moving at faster than light speeds could theoretically allow you to view the past, but not to actually exist there or travel to that different time.

It's like when we view a solar event, it actually happened some time ago. If you went a couple hundred years back and were watching Thomas Jefferson go to the bathroom, even if you could communicate or send information to him "instantaneously" to amend the constitution, he would never get it, because he still would have been dead for that many Earth years.

Obviously speculation here, but I think that our covering distances faster than light can travel will probably be done by circumventing the limit of speed, not by exceeding it. Possibly via the Mass Effect