How time dilation occurs

[LaurieAG]

Hi. I am confused about travelling near the speed of light. If a star is, say, 10 light years away, then it obviously takes light 10 years to travel from the star to us. Why then does it take someone travelling at, say, half the speed of light, less than 10 years to get there? I just can't figure it out.

 

Hello Kalexia,

 

It would theoretically take approximately 20 years to get there.

 

Are you thinking of a 'relative to the speed of' light clock as that type of device starts ticking when a photon leaves point A and arrives at point B. It therefore contains quite a lot of trigger lag. Add the trigger lag back onto the trip time and you get the amount of time elapsed as you would expect from identical non relative clocks at both points A and B.

[Jay-qu]

At .5c there would not be much time dilation, but if yes for the traveller it would take less time (less than 20 not less than 10), but for any outside stationary relative to the star observer it would still take 10/.5 years to get there.

[Janus]

Hi. I am confused about travelling near the speed of light. If a star is, say, 10 light years away, then it obviously takes light 10 years to travel from the star to us. Why then does it take someone travelling at, say, half the speed of light, less than 10 years to get there? I just can't figure it out.

 

Actually, you would have travel at almost 90% of c to make the trip in under 5 years shiptime.

 

That being said, why this is is true depends on who you ask.

If you ask someone sitting home at Earth, they will say it is because the traveler's time ran slow during the trip.

 

If you ask the traveler, he will say it was because the distance between the Earth and the star contracted to less than 5 lightyears while he was traveling.

[CraigD]

Why then does it take someone travelling at, say, half the speed of light, less than 10 years to get there? I just can't figure it out.

As a few people have already pointed out, for a speed of half the speed of light, more than 10 years passes on a 10 LY trip.

 

According to the theory of special relativity, time (and length, and mass) dilation are all calculated using a simple term known as the Lorentz term (“gamma”, written [math]\gamma[/math]), or its reciprocal, (“tau”, written [math]\tau[/math]). Practically every relativity thread at hypography uses it. They are:

 

[math]\gamma = \frac1{\sqrt{1- \left ( \frac{v}c \right )^2}[/math]

[math]\tau = \sqrt{1- \left ( \frac{v}c \right )^2}[/math]

 

Where: [math]v[/math] is the accelerated observer’s speed, as measured by the stationary observer;

and [math]c[/math] is the speed of light (about [math]3 \times 10^8 \mathrm{m/s}[/math]).

 

It’s traditional and convenient to use [math]c[/math] as a speed unit, to avoid having to divide by the speed of light in some other units.

 

For time dilation calculations, you multiply the time observed (after compensating for light travel time, which is consequence of classical Newtonian physics, not relativity) by a stationary observer ([math]t[/math]) by [math]\tau[/math] to get the time observed by the accelerated observer ([math]t’[/math]).

 

So, for the example of a ship accelerated rapidly (this keep the calculation simple, by allowing us to ignore the brief period where the ship is traveling at many different speeds) to .5 c, then traveling 10 light years, we calculate:

[math]t = \frac{d}v = \frac{10 \mathrm{LY}}{.5 c} = 20 \mathrm{years}[/math],

[math]t’ = t \tau = t \sqrt{1-\left ( \frac{v}c \right )^2} = 20 \mathrm{years} \sqrt{1-.5^2} = 20 \mathrm{years} \sqrt{1-.25} = 20 \mathrm{years} \sqrt{.75} \dot= 20 \mathrm{years} \cdot .8660254 \dot= 17.320508 \mathrm{years}[/math].

 

So, to a passenger on the .5 c spacecraft, the trip takes [math]t’[/math], more than 10, but less than 20, 17.320508 years.

 

If you increase [math]v[/math], you can get a [math]t’[/math] less than 10. For example, using [math]v= .9 c[/math] gives:

[math]t’ = \frac{10 \mathrm{LY}}{.9 c} \sqrt{1-.9^2} \dot= 4.843221 \mathrm{years}[/math]

 

In practical terms, Special Relativity tells us that, from the point-of-view of a traveler, given a spacecraft capable of safely traveling any velocity less than c, you can travel any distance in as little time as you would like. From the point-of-view of a stationary observer back on Earth, it appears to take always at least a little longer than the time light takes to travel a particular distance.

 

It’s worth noting in threads like these where we casually discuss spacecraft with velocities of .5 and .9 c, that these speeds are fantastically greater than any available to present-day technology, or any likely to be available in the near future.

 

It’s also worth noting that “tau” is a cool-sounding letter, and “tau zero”, the approachable but never reachable Lorentz term for [math]v=c[/math], an cool-sounding phrase, and the title of an old (1971) but hugely fun sci-fi novel about … you guessed it: nearly reaching the speed of light in a spacecraft. A good story can communicate the principles of special relativity better than mathematical description.

[kalexia]

Thanks for the replies. So basically it only takes light 10 years to get there from the viewpoint of a stationary observer. To the light itself (or if you yourself were travelling at light speed) then you would think you got there instantaneously? (I realize we can't go at c, but just for example)

[CraigD]

So basically it only takes light 10 years to get there from the viewpoint of a stationary observer. To the light itself (or if you yourself were travelling at light speed) then you would think you got there instantaneously? (I realize we can't go at c, but just for example)

Yes. :)

 

A math purist might argue that you would think you got there in an Indeterminant amount of time, but it’s hard to imagine what that might feel like. :Exclamati To avoid offending math purists, let’s just say that, as your speed becomes arbitrarily close to c, the amount of time it appears to you it took to get there becomes arbitrarily close to zero.

[Uclock]

CraigD

 

Uclock:

And the same must be said for the velocity of the Earth from the ships frame.

 

No, it must not. This point is crucial to the whole demonstration. The idea that, because each observer observes the others clock to run slower (on the outbound trip) and faster (on the inbound) by exactly the same ratio (about .2679 outbound, 3.732 inbound), neither knows who is “moving” and who is “stationary”, is incorrect.

 

So now you are saying velocity is not relative?

 

Tony

[CraigD]

So now you are saying velocity is not relative?

I am not saying that. Even if the universe was not consistent with Special Relativity, distance, which is required for the fundamental definition of velocity ([math]v=\frac{\Delta d}{\Delta t}[/math]), requires 2 points, so both the distance and velocity of a point associated with some body must obviously be stated as relative to some other point.

 

I suspect I don’t fully understand what Uclock means by the statement “velocity is relative”.

 

To restate, what I am saying is

The idea that, because each observer observes the others clock to run slower (on the outbound trip) and faster (on the inbound) by exactly the same ratio (about .2679 outbound, 3.732 inbound), neither knows who is “moving” and who is “stationary”, is incorrect.

In other words the change of velocities of each observer, relative to any observer, (In the example in post #25 and #37, 0 for Earth relative, .866 c for the ship, relative to either Earth or the ship) is both observable, and important. Or, as stated in these posts’ titles “Velocity being relative does not require all inertial frames to be identical”.

 

Special Relativity does not require that observers (“inertial frames”) can’t be distinguished from one another, only that there is no special, “absolute” observer that is in some special way distinct from all other observers. There is no deep, philosophical reason for this lack of a requirement – it is a consequence of simple geometry and the postulate that the speed of light is the same when accurately measured by any observer).

[kalexia]

Since anything passing the event horizon of a black hole remains there infinitely (when viewed by a distant observer, from time dilation) does this imply that one would be able to see everything ever pulled into the hole (although redshifted)?

[CraigD]

Since anything passing the event horizon of a black hole remains there infinitely (when viewed by a distant observer, from time dilation) does this imply that one would be able to see everything ever pulled into the hole (although redshifted)?

In principle, yes, limited by the usual optical factors – resolution, sensitivity, obscuring by intervening objects, etc. However, other than telling about conditions around a black hole, such observations wouldn’t be very interesting. Conditions near a black hole are very hot and stressful, reducing bodies into the essentially structureless plasma that produces the x-ray radiation characteristic of black holes. Interesting objects, such as planets or a spacecraft, would be ruined before they were dramatically time dilated, so we shouldn’t expect to be able to see extremely redshifted images of interesting ancient objects near the event horizons of black holes.

 

I’ve a wild idea that black holes might be usable to build telescopes with tremendous power, and a weak kind of “time travel” ability (see “An exotic variation” in the 5823).

[jungjedi]

Since anything passing the event horizon of a black hole remains there infinitely (when viewed by a distant observer, from time dilation) does this imply that one would be able to see everything ever pulled into the hole (although redshifted)?

 

i think information about anything approuching a black hole would be smeared out over a region of of the black hole known as the swartzchild radius

[androstan1234]

The orbital period of a particle (or the most dense portion of a wave-packet) that moves with constant angular velocity increases if the particle is in uniform translation.

 

Each cycle of the wavicle sends a signal which we count as a clock tick.

 

Any questions?

[Little Bang]

Back to the original question

 

Most people would say that the mass of the Earth causes it's gravitational field and the field causes the time dilation.

 

Consider, an observer in space at rest WRT a clock (A) on the surface of the Earth. A clock (:) further out in space on a line parallel with the observer and the clock on Earth. Clock B is under one gee of acceleration away from the Earth. The observer will see the same time dilation for B as he does for A. So time dilation is an affect of acceleration and not mass?

Edited August 15, 2010 by Little Bang
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[CraigD]

Welcome to hypography, androstan! :)

The orbital period of a particle (or the most dense portion of a wave-packet) that moves with constant angular velocity increases if the particle is in uniform translation.

...

Any questions?

Yes. What’s your source for this claim? :QuestionM

 

The orbital period for a body with constant angular speed [math]\omega[/math] is by definition [math]T = \frac{2\pi}{\omega}[/math], regardless of the velocities of the body or of its center of revolution. I can’t see how, by their simple definitions, [math]\omega[/math] can change without [math]T[/math] also changing.

Consider, an observer in space at rest WRT a clock (A) on the surface of the Earth. A clock (B) further out in space on a line parallel with the observer and the clock on Earth. Clock B is under one gee of acceleration away from the Earth. The observer will see the same time dilation for B as he does for A.

Though it’s correct that, according to relativity’s equivalence principles, gravitation and equivalent acceleration are indistinguishable. The observer will see the same time dilation for B as he does for A only for the instant that A and B have zero relative velocity.

 

As B accelerates, its velocity relative to the observer will differ from that of A, and the total time dilation observed will differ according to their relative velocity time dilation.

So time dilation is an affect of acceleration and not mass?

Gravitational time dilation results either from difference in gravitational potential – how “deep in a gravity well” a clock is relative to another – or acceleration, which is indistinguishable within a point-sized lab from gravitational potential. Because, as best we know now, gravitational potential is always due to mass, we can reasonable, though indirectly, say that time dilation is an affect of both mass and/or acceleration.

[androstan1234]

Welcome to hypography, androstan! :)

 

 

Yes. What’s your source for this claim? :QuestionM

 

 

The orbital period for a body with constant angular speed [math]omega[/math] is by definition [math]T = frac{2pi}{omega}[/math], regardless of the velocities of the body or of its center of revolution. I can’t see how, by their simple definitions, [math]omega[/math] can change without [math]T[/math] also changing.

 

Thanks for the welcome CraigD.

 

That formula is correct for a nontranslating circularly rotating system with Euclidean axioms. However, if you assume the system is moving uniformly and apply Galilean relativity to it, you'll find that the orbital period must increase.

 

You can rationalize this by realizing that circular rotation that suddenly begins to translate "to the right" is now undergoing ellipsoidal rotation wherein the "smaller radius" of the ellipse is equal to the previous circle's radius.

 

Also, when you employ Galilean relativity, you'll find that the orbital period increases by exactly the Lorentz factor, assuming Euclidean axioms.

 

Though it’s correct that, according to relativity’s equivalence principles, gravitation and equivalent acceleration are indistinguishable. The observer will see the same time dilation for B as he does for A only for the instant that A and B have zero relative velocity.

 

 

As B accelerates, its velocity relative to the observer will differ from that of A, and the total time dilation observed will differ according to their relative velocity time dilation.

 

 

Gravitational time dilation results either from difference in gravitational potential – how “deep in a gravity well” a clock is relative to another – or acceleration, which is indistinguishable within a point-sized lab from gravitational potential. Because, as best we know now, gravitational potential is always due to mass, we can reasonable, though indirectly, say that time dilation is an affect of both mass and/or acceleration.

[C. michael Turner]

Anyone got any ideas of how and why time dilation occurs?

 

The fact that it does happen is fine but why exactly? I tried google but couldn't up with anything.

 

Any help appreciated.

You are looking for the mechanism that makes it understandable. Yes I know and here it is first as a metaphor. Imagine that you are trying to enter a crowded threater as the movie is over and and as you are trying to enter, everyone is exiting. The process is slow because you encounter resistance vs entering an empty theater. In the same way time is slowed in denser generated gravitational fields then your own generated gravitational field. By approaching a denser field your field is retarded from the mass to energy transfer from all magnetic field decay into a gravitational field. So dense fields while synchronizing with less dense fields retard the conversion of matter to gravitational wave decay and thus dialate time for the less dense field.

This explains a lot more too and I have copyrighted the entire explaination. This site allows copyrighted information as long as it is your own. This is mine. It explains how time, space and gravity are actions of matter decay via the gravitational wave from each piece of substance,potential energy, other that space itself, the endpoint of decay.

1). Matter and energy decay creating space and time is the statis of change

2). Gravitational wavefront formation explains dark matter and the backaction of wavefront formation explains gravity and the limits in the quantum world. The speed of light is a constant because the measuring frame is always the controlling point as the light synchronizes with the denser field. The measuring reference frame is dictating the limits of light speed always. As easy and maybe controversial as it sounds, it is correct and answers your question with a solid answer that is easy to understand.

----Michael Turner

[HydrogenBond]

One way to infer an answer, is to consider the situations where time dilation occurs. If we increase mass density we get more time dilation via general relativity. The second situation is via velocity and special relativity. The common link is mass/energy (two side of the same coin), with gravity/mass and velocity/energy. With SR the more energy as velocity we add, the more time dilation. With GR the more mass we add, the more the time dilation. So time dilation increases with increasing mass/energy.

 

If you look at refrigeration, foods last longer in the fridge. The fresh hamburger may last a day on the counter but a week in the fridge. The refrigeration cycle removes energy, however the refrigeration cycle requires energy to work. This suggests that time dilation is not only connected to mass/energy but this mass/energy is used to remove energy. The more mass /energy we have, the more energy we have to remove energy, causing everything in the time dilation fridge to last longer without spoilage.

 

Unlike a fridge that only removes thermal energy to chill the food, time dilation fridge removes all forms of energy to preserve all states of matter. Even nuclear hamburgers can last a longer time in the time dilation fridge. This not only shows the equivalence of mass/energy but the equivalency of all physical states. This points to a unified concept or where mass/energy can chill all physical states at the same time.