What is time dilation? (1 Viewer)

[Stopsign]

Does time dilation mean that it takes longer for events to occur?
If yes, that means that at the speed of light, time stops. Am I right?

 

[airie]

http://en.wikipedia.org/wiki/Time_dilation

That's the wikepedia explanation. So basically, time dilation means time runs slower as the speed of the coordinate system approaches the speed of light; And your perception that 'it takes longer for events to occur' really depends on where you're looking. If you are in this coordinate system with a great speed (eg. a spaceship, just for now), to you, all events that take place (like, uh, you push something away? ) would seem to be happening at their 'normal' rate; however, if you're an onlooker from outside this system, it would seem to you as if time has been slowed in there. But's it's all relative, as you can see And yes, by Einstein's theory of relativity, time comes to a complete halt if this coordinate system is travelling at the speed of light.

Hope that helped

 

[insert-username]

Time dilation is the slowing down of time as you approach the speed of light. The faster you go, the slower things move for you compared to things not moving at the speed of light. The effect is caused by the constant speed of light. Check out your textbook's explanation of Einstein's thought experiment for more on this.

As an example, if you're on a spaceship travelling at 0.1c, and you travel to Proxima Centauri (about 4 light years away), the journey appears to take you 40 years from Earth (0.1 of the speed of light, 4 light years). However, on the spaceship, it only appears to take you 39 years 292 days - since you're moving so quickly, time slows down fractionally for you. What seems to take 40 years observed from Earth takes 39 years 292 days observed on the spaceship.


I_F

 

[gordo]

is there an echo in here?

 

[Riviet]

Does time dilation mean that it takes longer for events to occur?

It depends on who's point of reference we are taking. From the point of reference of the spaceship that's travelling at the high speed (some fraction of c) it will take less time from your point of view, whereas someone outside observing the spaceship will see it normally.

 

[Stopsign]

So that means that, according to the stationary observer, the time for the moving observer, time slows (or it takes longer for events to occur).
If in the same instance, the moving traveller travels at a speed at c, then time stops and it takes an infinate amount of time for anything to occur.

 

[insert-username]

So that means that, according to the stationary observer, the time for the moving observer, time slows (or it takes longer for events to occur).
If in the same instance, the moving traveller travels at a speed at c, then time stops and it takes an infinate amount of time for anything to occur.

The time dilation equation itself says that you can't move at the speed of light. The equation involves division by √(1 - v²/c²), and when you reach the speed of light that equals 0. You can't have division by 0, so everything falls apart.

Anyways, time wouldn't stop. Time doesn't stop at all - it simply seems to move at different speeds depending on your velocity. It may look like it's moving really slow, but it's still moving. Well, that's what works for us now, so until another explanation is found we'll stick with that.


I_F

 

[Stopsign]

Ok then. How about a traveller going at 0.99999999c.
Wouldn't time 'almost' stop and events take longer to occur, as recorded by the stationary observer.

PS. I've got another question on exceeding the speed of light. If a spacecraft travelling at 0.5c, fires a rocket at 0.5c, wouldn't the rocket travel at c?

 

[LostAuzzie]

No because mass dilation causes the rocket to gain mass as it moves faster and faster thus it cannot accellerate to the speed of light but rather to a point just below the speed of light. If the rocket were to travel at the speed of light it would have infinite mass.

EDIT: In regards to your 1st question yes at speeds close to c time slows down significantly as seen by outside (stationary) observers,

 

[acullen]

Nothing within your own frame of reference will ever appear to slow down, if you were to travel in a spacecraft at near-light speed, although from our reference, your time would infact slow down; everything within your frame of reference is governed by your localised rate of time. The rate at which neurons firing in your brain slow down will be at the exact same rate a clock in your reference frame slows by, hence when all time-related events occur at an equal rate, everything appears as if it otherwise would.

 

[Stopsign]

I'm confused.

I'll just use this example.
There are a set of twins. Two boys.
One stays on Earth. The other sets out onto a spaceship travelling at a speed close to that of light. Their lifespans are 100 years apiece.

Who'll die first?

 

[del pietro]

The guy on Earth will die first, as his 100 years pass faster than, the guy in space. They both interpret their life as a normal 100 years, because the laws of physics are the same for any frame of reference. Time travels slower for the brother in space, in the persective of his twin on Earth.

 

[Gowr]

In regards to that question about the rocket travelling at 0.5c firing a missile that travels at 0.5c, a more accurate answer would be as follows...

(Considering that the calculations are way beyond the maths we need for this course, I will omit them)

Relativistic Velocity Addition

Simply put, if according to one frame of reference there is an object travelling at velocity v which projects something at velocity u, the sum of the velocities will equal (u+v)/(1+uv/c^2)

At speeds that are much slower than light, the uv/c^2 becomes so close to 0 that that the addition of the velocities = u+v, which is what you learn in classical mechanics, but using your example, the resultant velocity would be c/ (1 +0.25c^2/c^2), which equals 0.8c, not the speed of light.

This is very nice, and by putting in known values i am sure you can see that this formula holds. For example, if I am moving at velocity v and project a beam of light, the light travels at velocity (v+c)/(1+v*c/c^2), which equals (c)(c+v)/(c+v) = c, confirming that light travels at the speed of light in any frame of reference.

Also, in regards to your second question, I dont see how you can postulate that the guy on earth will die first, unless you specify that you are observing the events from earth, as the guy in the spaceship will observe himself dying first considering that he sees his brother moving at close to the speed of light, and sees himself as stationary.

 

[Bennah0]

I would just like to ask a question to do with gravity and light speed.
The acceleration due to gravity on an object is always x m/s^2 - right, there is no mass involved in this.
So if you were to fire a particle or anything at a superhuge mass that has a huge gravitational field around it, would it not begin to accelerate exponentially and the mass increase would be irrelevent, so wouldnt the object exceed light speed?

 

[zeek]

No...
You are actually partly correct Bennah0. If the particle was fired at a super huge mass then it will proceed to the mass with an EXPONENTIAL VELOCITY. This means that the acceleration would be constant @ x m/s^2. (look below for reason)
If you graph the exponential curve (representing the velocity) and then differentiate it, then you will find that it will have a linear gradient of e. Hence, the particle is experiencing constant acceleration.

EDIT:
=======
Sorry, i have made a mistake in graphing the derivative of e. The derivative of e is e so therefore, it will accelerate exponentially, so yes, you are correct Bennah0. I'm still unsure about the exceeding light speed thing, i will have to think about that.

 

[Bennah0]

i dont really understand how the accleration due to gravity could be constant, because according to the equation g=GM/r^2 where g is the acceleration due to gravity a specified distance from a mass the r^2 suggests that the acceleration is going to raise exponentially as an object gets closer to the mass, but that is not really what i was asking.
I was asking whether a particle could be shot at a superhuge mass a large distance away and if the gravity from this superhuge mass would accelerate the particle to beyond light speeds...and if not then why?

 

[zeek]

I was asking whether a particle could be shot at a superhuge mass a large distance away and if the gravity from this superhuge mass would accelerate the particle to beyond light speeds...and if not then why?

Okay i edited my previous response to your question about varying acceleration.
Now as to whether or not the particle can approach or succeed the speed of light, i think i have read something about it, but i don't think that it was due to the gravitational pull of a celestial body.

I'd try and work out the energy requirement to pull a neutron (i chose this particle because it shouldn't have any attraction or repulsion forces affecting it) so that it approaches the speed of light first.
=======================
E_t=E_k + E_r
E_t=1/2mv² + mc²
E_t=1/2m(v² + 2c²)

Now the mass of a neutron is : 1.674 927 16 × 10⁻²⁷ kg
The speed of light c is : 299,792,458 metres per second
Let v = c (since we want the velocity of the neutron to be at light speed):

E_t=1/2m(3c²)
E_t=2.258... x 10^-10 J

Now... this is a surprising result lol and i have no way to explain it other than i mucked up somewhere or i have applied the formula wrongly. (if anyone finds an error please say where)

Anyways, if this was the energy requirement to allow a neutron travel at light speed then it should be easily achievable by the acceleration to the gravity. To be honest, i don't understand WHY light HAS to be the maximum achievable velocity or why nothing can go faster than it.

In fact.... In 2002, physicists Alain Haché and Louis Poirier made history by sending pulses at three times light speed over a long distance for the first time, transmitted through a 120-metre cable made from a coaxial photonic crystal.
http://en.wikipedia.org/wiki/Speed_of_light#.22Faster-than-light.22_observations_and_experiments

 

[rama_v]

I suggest people interested to read this website for more information on special relativity..its quite cool..

http://www.phys.unsw.edu.au/einsteinlight/

 

[macoboi]

i don't understand WHY light HAS to be the maximum achievable velocity or why nothing can go faster than it.

i guess, like most things in HSC physics, it's because the syllabus says so.

 

[rama_v]

Okay i edited my previous response to your question about varying acceleration.
Now as to whether or not the particle can approach or succeed the speed of light, i think i have read something about it, but i don't think that it was due to the gravitational pull of a celestial body.

I'd try and work out the energy requirement to pull a neutron (i chose this particle because it shouldn't have any attraction or repulsion forces affecting it) so that it approaches the speed of light first.
=======================
E_t=E_k + E_r
E_t=1/2mv² + mc²
E_t=1/2m(v² + 2c²)

Now the mass of a neutron is : 1.674 927 16 × 10⁻²⁷ kg
The speed of light c is : 299,792,458 metres per second
Let v = c (since we want the velocity of the neutron to be at light speed):

E_t=1/2m(3c²)
E_t=2.258... x 10^-10 J

Now... this is a surprising result lol and i have no way to explain it other than i mucked up somewhere or i have applied the formula wrongly. (if anyone finds an error please say where)

Anyways, if this was the energy requirement to allow a neutron travel at light speed then it should be easily achievable by the acceleration to the gravity. To be honest, i don't understand WHY light HAS to be the maximum achievable velocity or why nothing can go faster than it.

In fact.... In 2002, physicists Alain Haché and Louis Poirier made history by sending pulses at three times light speed over a long distance for the first time, transmitted through a 120-metre cable made from a coaxial photonic crystal.
http://en.wikipedia.org/wiki/Speed_of_light#.22Faster-than-light.22_observations_and_experiments

The equations for energy you use above are low-velocity approximations, and do not apply when speeds are very large.