# How does time stop at C?

1. Feb 9, 2006

### physicscrap

I never understood how time can slow down as you reach the speed of light then it stops...

I see time as a measurement by a mechanical clock. One second will always be one second.

My ap physics teacher said they did this experiment. They took a photon or something with a very small half-life. They shot these across a measured distance x and predicted that only like 2% of them should be left when they reach impact or whatever. v=d/t, them knowing the initial velocity and distance, the time calculated showed a ton of decay. But there was 98% left, which they concluded time stopped...

Ya anyways is it the process in which it is decaying that is lowing down, not time itself? Can someone clarify this for me? Like is you traveled at the speed of light, someone on earth with a stop watch would read 10min, so would your watch right? I need understanding ahh!

I have tons of questions, but it is late!

Thanks

2. Feb 9, 2006

### rbj

as one person (with a clock) whizzes past another at very high speed, they both measure the speed of the very same beam of light to be the same value, even when they are moving relative to each other.

the normal textbook explanation of time dilation uses a "light clock" consisting of a burst of light bouncing back and forth between two parallel mirrors whose plane are parallel to the direction of motion (from the perspective on one observer) which means that the path the light is boucing back and forth is perpendicular to the direction of motion.

now if both persons, the one with the light clock moving past a "stationary" observer at high speed, and the "stationary" observer saw the "ticking" of this light clock as the same rate, then for the "stationary" observer, he would have to see the speed of light to be faster than the "moving" observer because it would have a component of c going up and down and a component of v going forward, giving you a diagonal speed of $\sqrt{c^2+v^2} \ge c$. but that contradicts the axiom of Special Relativity that all observers must see the speed as the same.

so, instead, the diagonal velocity is c and, since the forward component is still v, then the "stationary" observer sees the up and down component of the speed to be $\sqrt{c^2-v^2} = c \sqrt{1-v^2/c^2}$ which is slower than what the moving observer sees for the up/down speed of light (which is c). but the distance between the mirrors are the observed by both observers as the same (that distance is perpendicular to the direction of motion and has no reason to be observed differently), so the "stationary" observer has to see the rate of ticking of the light clock to be a factor $\sqrt{1-v^2/c^2}$ slower than the rate of the "moving" observer.

3. Feb 9, 2006

### dicerandom

It is time itself which slows down, at least comparitively. However you cannot say "such and such happens at c" since you can never get there, you can only discuss what happens as you approach c.

The experiment you describe isn't something that can be done with photons to my knowledge, photons always travel at c (whatever c might be in the particular medium). One classical example of the effect you're talking about is the muons which are created by cosmic ray impacts in the Earth's upper atmosphere. Muons decay in an extremely short ammount of time, so quickly that they should have never been able to make it down to the Earth's surface. They are fairly common, however, and this is because when they are created by the collision in the upper atmosphere they have a very large velocity. We on the earth see them taking some ammount of time to travel from the upper atmosphere down to our detectors, however for the muon's own internal clock only a small fraction of that time has elapsed.

4. Feb 10, 2006

### Staff: Mentor

Well, if you observe the same phenomena with a half dozen different types of clocks, it is probably safe to say that it isn't coincidental clock effects, but time itself that is affected.

5. Feb 10, 2006

### bernhard.rothenstein

Have you ever tried to synchronize two clocks that would move with speed c relative to each other?

6. Feb 10, 2006

### physicscrap

Well what rbj explained to me was kind of confusing.

I still don't understand... well what exactly is time?

If you are approaching the speed of light, you are doing so for a period of time. Like you are superman flying and approaching c, while you are counting 1, 2, 3, 4.... so the measurement of time is the same as it would be a guy standing still counting.

Confusing. I just need someone to explain it to me logically or something. I am a visual learner, so make it visual :)

Thanks

7. Feb 10, 2006

### pervect

Staff Emeritus
You might try "Al's relativistic adventures", the winner of the (edit) 2005 Pirelli award. It can be found at

http://www.onestick.com/relativity/

(and possibly other places as well, try google).

It's very visual, and it has a "quiz" feature to help you see if you've understood it.

But you'll need a flash player and a fairly high-speed connection, according to the website.

Last edited: Feb 10, 2006
8. Feb 10, 2006

### robphy

Here's something visual [and animated]
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/ [Broken]

(pervect, that's 2005... not 1995)

Last edited by a moderator: May 2, 2017
9. Feb 10, 2006

### pervect

Staff Emeritus
I guess I'm stuck back in the 90's :-( - anyway I'll fix the post to give the correct date.

What did you think of the presentation, by the way? I recalll that you contributed to the contest. I remember thinking that I had a few minor reservations about the way some of the material in the award-winner was presented, but that on the whole I thought it was very worthwhile.

Last edited by a moderator: May 2, 2017
10. Feb 10, 2006

### rbj

yeah, it wasn't the best explanation possible. Al's Relativistic Adventures is a good illustration.

it's how fast the light clock ticks.

oh no, as Superman is counting 1,2,3,4 it sounds like "wwwwuuuuunnnn, ttttoooooooooo, thhhhhhrrrrreeeeee, fffooooouuuuurrrrr" to me as he whizzes by. but it sounds like 1,2,3,4 to Superman.

if you still have questions after seeing Al's adventure, i'll try to spell it out again with some kinda different language.

11. Feb 11, 2006

### Loren Booda

Imagine counting, from any outside point, the swings of a pendulum bob as time. The time may vary according to observer-bob relative velocity, but at least its passage is non-zero.

Then imagine riding on the bob and trying to count time by the bob alone. This seems anomalous, but actually demonstrates that the relativity of standard bob speed vs standard bob speed results in static signaling.

12. Feb 11, 2006

### MathematicalPhysicist

let's see, a time measured by a mechanical clock has a constant motion in comparison to light is also constant, but what really is fascinating that perhaps you neglected to mention is how do you observe that light motion doesn't have any time elapsed.
well this is (as i can rememeber) a convention that was made in order to make sense to the phenomona of time contraction, i don't think they can observe that light motion is absent from time.

anyway, time is man made, so it's not impossible that nature doesn't see it fit, in the light case.

13. Feb 11, 2006

### physicscrap

Alright I just watched Al's Adventures and have some questions.

Why can't a mass reach the speed of light or beyond? How does something seem squished relative to you if the ship is going at 99.5% of c?
Also, they use a clock measured by a photon bouncing between two mirrors, forming a second. I understand how that time slows down. But lets say you use a mechanical clock with gears, how does that slow down? It doesn't right, so time actually does not slow down, but the photon just takes longer to form a second for that particular clock. And how does one's brain function slow down. If you approached c, and the clock slowed down, you would notice that you are bouncing your ball faster. How do you think slower???

Also, when Al only took two years to travel to and back, it was only two years according to HIS clock, which is affected by his speed due to it being measured by a photon. But the actual time was 20 years, but Al thought it was 2. Is this correct? Furthermore, how can something be massless?

It gave me info that I already knew, but did not answer my questions in detail.

14. Feb 11, 2006

### pervect

Staff Emeritus
An object cannot reach the speed of light because velocities do not add linearly. Velocities do not add linearly because space and time get "squished" by motion.

"Why" space and time get squished by motion doesn't really have an answer - we simply observe that it happens. Specifically, we observe that the speed of light is constant for all observers, and from this observation we infer that space and time must get squished in the manner which is described in "Al's relativistic adventures" in order to explain these observations.

The detailed velocity formula addition in SR is

vtotal = (v1+v2)/(1+v1*v2/c^2)

Thus .9c + .9c = 1.8/1.81 c

If you add up ANY NUMBER of velcities, v, which are less than c, the result will still be less than c.

.9c + .9c + .9c + .9c + .9c .... + .9c

for any finite number of terms n

is less than c.

We observe that all clocks slow down by the same amount. If they didn't, we wouldn't see the speed of light as being constant, which is what started the whole theory.

Our most accurate clocks nowadays are made out of atoms, not gears, but they keep the same time as clocks with gears do. Note that atoms and gears are both held together by electomagnetic forces, the same forces that mediate light.

Back in Einstein's day, they didn't have atomic clocks, the best clocks were based on gears and pendulums(!). But the theory applies to any sort of clock.

Relativistic effects are pronounced enough that we can see the effect of relativistic time dilation on the lifetime of short-lived particles like muons. Fast moving muons live longer than slow moving ones. This has been observed both with cosmic muons, and muons in accelerators.

The mechanism of muon decay is not even electromagnetic, so we can see that the concept of "time" slowing down applies even to clocks that are based on nuclear phenomenon and not E&M phenomenon.

I think you missed the point of the illustration :-(. If your brain slowed down, and your body slowed down, right along with the ball, if _everything_ slowed down exactly the same amount, you wouldn't notice anything. Which is the main point of that particular part of the animation.

Al's mechanical clock, Al's atomic clock, Al's brain, Al's light clock, and Al's bouncing ball all measured two years during his journey.

This means that by any means you can measure, Al "really" experienced two years.

The people on the ground also "really" experienced 20 years.

These two statemetns are not contradictory.

When it's mass is zero, an object is massless. (I've never understood why this would be a sticking point with anyone.)

Last edited: Feb 11, 2006
15. Feb 11, 2006

### physicscrap

That didn't help lol.

How could a physical mass, such as you and your ship, be physically squished? That seems impossible. Also, if you are in space, with no resistance, and have a ton of power, how do you not reach c or past? Of course you said because of being squished which makes no sense. Also, light would not seem to be going at c if you were going 1/2 its speed. Like if you were driving at 50mph, the car that is going 100mph seems to be going 50mph faster, not 100mph. Again, you said space and tiem is squished which i don't understand. I just don't understand.

I also don't understand how the universe could be here. Since something has to make something, we can't exist, but we do. What made matter? what made that thing that made matter? etc... it is infinit, which is impossible for us to be here. ahhhhhh too confusing.

16. Feb 11, 2006

### dicerandom

It does seem that way, but it isn't. Keep in mind that from the perspective of the moving object everything is normal, it's everyone else who are squished.

If you accept the fact that light must travel at the same speed in all inertial reference frames then all of these effects which we have discussed here are logical conclusions which must be true, there's simply no avoiding it.

Measuring the speed of light as being constant is an experimental fact, it's been measured to a very high degree of accuracy. After that everything else falls into place if you're willing to work through the logic, all these consequences such as time running more slowly and distances being measured differently are also experimentally verified to a high degree of accuracy.

Edit: By the way, it's a good thing that you're resisting all this. Special Relativity is usually the first instance in physics where people encounter an idea that simply goes against everything they've ever known to be true. Deep in our bones we "know" that velocities add linearly, we "know" that moving observers do not see time or distance any differently than we do. These things have been true for all of our lives, we've never encountered anything in our daily experiences which would indicate otherwise. Fact of the matter is that the only reason we "know" those things is because we generally travel extremely slowly. Even with cars the largest relative velocity I've ever had with respect to someone else is about 160mph or so.

Do not feel discouraged because you don't feel ready to accept these strange ideas, believe me when I say that it literally took me months for it all to soak in when I was first learning this stuff. If you keep plugging away at it and think about the concepts, work out the thought experiments, calculate some numbers for yourself, etc. you will eventually come to understand why everything we're saying must be true. It's just a bit of a journey to get to that point

Last edited: Feb 11, 2006
17. Feb 11, 2006

### robphy

I thought the presentation was good. It was creative and effective for the target audience.... but I think I liked the physics better in Ehrlich's presentation (see the blog entry https://www.physicsforums.com/blog/2005/12/03/pirelli-relativity-challenge-2005-winners-announced/ [Broken] ). In my opinion, however, the physics presented in these winning entries is rather ordinary and superficial. I would have been more impressed with (say) a multimedia presentation emphasizing more concrete operational methods as done in the little books by Bondi and by Geroch. I tried to do this in my attempt... but I didn't realize that it had to have more entertainment value.

There's "massless" and "frictionless" ... but the connotation is different for "priceless". A related suffix is -free... as in trace-free. Maybe one should adopt the prefix zero- .

Last edited by a moderator: May 2, 2017
18. Feb 11, 2006

### physicscrap

I accept that light travels at the same speed. But how does a fast moving person view the light at the speed of light? I would think that it would seem slower relative to the moving person.

I understand that distances are shorter when traveling close to c. Because time is slower, thus calculating distance using d=vt the distance is less then measured by a normal moving person.

But again, I am not sure about time. How does one's mental thinking slow down? moving close to c in space makes that person feel normal. So that person would think normal, and thus bounch his/her ball at the same pace of a second if that person were NOT refering to a clock.

*just thought of this* Ok you know that the light clock with the ship is traveling close to c. So the photon has to bounch extra distance thus slowing time. But refering to the ball bouncing, doesn't the ball have to travel a diagnal distance such as the photon? same concept right? That makes no sense. What I mean is that if the photon is maintaining the same speed as the ship, could it just bounch in a straight line? ahhh I am having trouble thinking this through.

EDIT: When time theoretically slows down, and so does everything else, does the human body biologically slow down so you ACTUALLY don't age as much, or you just don't age as much relative to time? hmm

Last edited: Feb 11, 2006
19. Feb 12, 2006

### MathematicalPhysicist

what do you mean by not add linearly?
i think you can add velocities by simple algebraic arithematics and vector calculus which is linear (if you don't take into consideration non inertial accelerating motion which is not linear).

20. Feb 12, 2006

### robphy

Let VBA denote the relative [spatial] velocity of observer B with respect to observer A.

In relativity,
VCA =/= VCB + VBA.
Thus, the spatial velocities don't add linearly. (Part of the problem is that you are trying to relate spatial velocity vectors in different inertial frames of reference, where their notions of space don't coincide. So, one has to project down into the respective spaces. Vector methods do work... but you must use 4-vectors [for example, see my post, #5, in https://www.physicsforums.com/showthread.php?t=73582].)

("Addition of velocities" should really be called "Composition of velocities".)
What does add linearly is the rapidity, where VBA=c tanh(rapidityBA)...
then
VCA=c tanh(rapidityCA)=c tanh(rapidityCB+rapidityBA),
which can be rewritten using the hyperbolic-trig identity for the tanh of a sum to obtain the velocity composition formula:
VCA=( VCB + VBA )/(1 + VCBVBA/c2 )