Quick quiery?

[Damo2600]

If accelerating momentum does in fact slow down time then wouldn't decelerating momentum speed up time?

 

;)

[Buffy]

Yes, but its only giving you back what it took away when you accellerated in the first place...

 

Cheers,

Buffy

[Damo2600]

I see. So accelerating slows time. Decelerating speeds time and moving at a constant speed would not, I'm assuming, speed nor slow time?

 

Damo

[Damo2600]

If I accelerate and time slows, when I stop accelerating faster, at a constant speed time is going at a constant slower speed to time as it would if I were stationary? ;)

 

Damien

[Damo2600]

This makes sense. If however I accelerate starting at 1mm/hour slowly gaining speed for ten years until I reach 200km per hour. Time is steadily decreasing in momentum. Now if at ten years I decelerate at the same rate I accelerated time would speed up it's momentum and I would return to a stationary time frame with no time dilation at all. According to the theory of relativity only when the acceleration increases then remains constant would there be time dilation when you return to a stationary time frame.

 

Does this make sense?

[Damo2600]

Hi,

If I may repeat the mental experiment with a second point

 

There are two cars. I am driving one and Buffy is driving the other and we travel along the same road which is straight.

 

I accelerate starting at 1mm/hour slowly gaining speed for ten years until I reach 200km per hour. Time is steadily decreasing in momentum. Now if at ten years I decelerate at the same rate I accelerated time would speed up it's momentum and I would return to a stationary time frame with no time dilation at all.

 

Buffy accelerates starting at 1mm/hour slowly gaining speed for five years until she reaches 100km per hour. Time is steadily decreasing in momentum and now has level off at a constant slower speed. Now if at fifteem years she decelerates at the same rate she accelerated. Time would speed up it's momentum and she would return to a stationary time frame with some time dilation.

 

In general relativity we would reach the same finish point at the same time and our clocks should match (i.e. if we sycronised them before the experiment). According to special relativity (if I understand this correctly) Buffy and I should reach the same destination at the same time (I think). Although according to Buffy's clock my clock would have been going faster.

 

Have I got his right so far?

 

Damien

[Damo2600]

Sorry to reply to my own posts. I hope this isn't against the rules Tormod.

 

Now considering the experiment I have described:

 

At the ten year mark before I begin my deceleration my time dilation would be much greater than Buffy's. This is because my time kept getting slower where as Buffy's leveled off five years ago. This can't mean that my time dilation is twice that of Buffy's. If Tormod, in a third car, had of accelerated from 1mm/s to 100km/s over ten years then my time dilation would equal twice his time dilation.

 

Any problems so far?

 

At this point Tormod and Buffy are driving next to each other, right?

 

If Tormod levels off his aceleration then he would be driving next to Buffy?

[Damo2600]

I see the problem our average speeds are not equal. So we would not reach the same destination at the same time (I think). So at 7.5 years I would need to decelerate for 5 years from 150km/s down to 50km/s. Then at 12.5 years I would acelerate from 50km/s to 100/kms over the next 2.5 years. The rest of the trip I would be driving next to Buffy.

 

I don't own a car so don't blame me if I don't know how they work. LOL

 

Damien

[Damo2600]

What I see as strange is that Buffy and I travel the same distance at the same average speed. We would arrive at the same time however Buffy would experience time dilation and I would not.

 

Could ANYONE help me out with this?

 

Damien

[Buffy]

It makes no sense, but I think you've given yourself the right answers. Here's a summary:

We both start at point A. I go to point B accellerating and decellerating evenly up to 50% of the speed of light. You do some crazy quilt accelerating decellerating, but basically we both head straight for point B. Two possible outcomes:

1. We both arrive at the same time, and our watches will both agree because we've done in aggregate the same amount of accellerating and decellerating.
   
2. One of us arrives first, which means that relative to the other observer the person who arrived first accellerated/decellerated/travelled faster than the other person, and the person who travelled faster will see 11:00 on their watch while the slower person will see 11:05.
   

This is basically equivalent to the experiment with two moving towers I described above.

 

Cheers,

Buffy

[Damo2600]

You are messing with my head then. Either you are not trying to understand the situation properly or you do not know the answer.

 

You said that if you travel in a plane for long enough the atomic clock will have time dilation. In my example I forgot to mention that we are also syncronised, time wise, with a stationary observer. If your atomic clock thing is correct either we don't really know how atomic clocks work or Buffy in the car should experience time dilation and I should not. Since I accelerated and decelerated evenly my time dilation should increase and decrease evenly.

 

Your time dilation increases to a point then maintains a constant slower time dilation and then your time dilation decreases. So your acceleration and deceleration cancel each other out. Right? However there is a point in the middle where your time dilation maintains a constant speed. This time dilation has not been accounted for. Right?

 

All my time has been accounted for whereas yours has not.

 

We are travelling at an equal 'average' speed over an equal distance for an equal amount of time. So in general relativity we should arrive at the same time and our clocks should equal the stationary observers clock.

 

However in special relativity I'm not completely sure what is happening. My clock should equal the clock that is stationary. You however should experience time dilation so when we meet up either our clock won't match or our arrival times are different. Which is it?

 

If your time is going at an equal slower speed than mine and the stationary observer, then, your clock is doing something completely wierd. Your clock HAS TO(!!!!), and I mean HAS TO(!!!!), be lying to you for some reason i.e. if special relativity is telling us the truth.

 

That means during the period you travel at 100kms/s for ten years this is not really the speed you are doing. (?????????????????????????)

 

Damien

 

Damien

[Buffy]

What you're missing is what you left out of your earlier posts. No matter what, our clocks will be much earlier than the stationary observer. What I'm having trouble following in your argument is why you think that you would have time dilation cancelled out and I would not: if we went the same distance at the same average speed our clocks would be the same. Again, the only thing we can do is measure the relative settings of clocks. There's no "absolute time" although we can refer to a "stationary" observer, but that is only within an agreed upon local reference frame, and we need to get back to the stationary observer to really agree on the distance travelled and what the time is on each other's clocks. Also, as soon as you start talking about three observers in different locations, you end up starting to see "simultaneity differences" since different observers in different locations travelling at different speeds will see remote events happining in different orders!

 

This is a big topic, far more than just litle ol' me can explain textually, and there are many many books that cover basic explanations of special relativity to arbitrary levels of detail. Here's a couple of web sites that offer some basic explanations of Special Relativity and they have bibliographies as well for further info:

 

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

http://physics.about.com/b/a/014032.htm

http://science.howstuffworks.com/relativity.htm

http://casa.colorado.edu/~ajsh/sr/sr.shtml

http://home.earthlink.net/~spencerdoolin/relativity/wavereflect.htm

And for some fun:

http://www.fnal.gov/pub/ferminews/santa/

 

Cheers,

Buffy

[Damo2600]

No Buffy. You said that if the acceleration increases the time dilation increases. The reverse is true if you decelerate. So I made the assumption that if I did both evenly there would be no time dilation. Can I make the further point that the entire journey takes place around a circumference that is equal to the journey length? This way the two observers return to the stationary observer.

 

I don't see how this would affect the mental experiment in any way.

 

Now you are suggesting that there is only time dilation compared to the stationary observer if the moving observer is travelling at a constant speed. This is the conclusion I am making considering the example you gave of the atomic clock in an air plane. It's acceleration and deceleration cancel each other out. The period of time the plane is travelling at a constant rate is the period where the time dilation occurs. So when the plane lands the time dilation of the atomic clock is different to the atomic clock that is stationary.

 

I'm creating the experiment based on your comments so I'm supposing that you can help me sort out the problem.

 

Thanks Damien

[Buffy]

No Buffy. You said that if the acceleration increases the time dilation increases. The reverse is true if you decelerate. So I made the assumption that if I did both evenly there would be no time dilation. Can I make the further point that the entire journey takes place around a circumference that is equal to the journey length? This way the two observers return to the stationary observer.

 

Now you are suggesting that there is only time dilation compared to the stationary observer if the moving observer is travelling at a constant speed. This is the conclusion I am making considering the example you gave of the atomic clock in an air plane. It's acceleration and deceleration cancel each other out. The period of time the plane is travelling at a constant rate is the period where the time dilation occurs. So when the plane lands the time dilation of the atomic clock is different to the atomic clock that is stationary.

"Cancel out" only happens if both observers are accellerating and moving and move back to meet: when they get to the meeting place, their clocks will match because they travelled the same distance and left and arrived simultaneously. HOWEVER, the stationary observer will see that the clocks of both travelers HAVE slowed down. Its not as if decelleration causes a "negative dilation" its that the perceived dilation of that the two moving observers see in the OTHER moving observer "disappears" if they both travel the same distance with simultaneous start and finish.

 

Another clarification on the meanings of speed and accelleration: Accelleration is necessary for an observer to reach speeds close to the speed of light *within his own frame of reference* (if there's no accelleration, there's no "movement within his reference frame"). The effects of time dilation are not a simple linear function--this is an oversimplification usually glossed over in discussions of SR, but dilation is proportional to the average *speed* over a given distance, including accelleration and decelleration. Its not that decelleration produces "negative dilation" its that the dilation decreases.

 

Cheers,

Buffy

[Damo2600]

Hi Buffy,

 

The original qestion I asked in this thread is following:

 

"If accelerating momentum does in fact slow down time then wouldn't decelerating momentum speed up time?"

 

You agreed with this and stated

 

"Yes, but its only giving you back what it took away when you accellerated in the first place..."

 

My assumption from this is that if I accelerate at a certain rate, around the circumference of the earth for example, and when I get half way around the globe I, by ceasing acceleration, begin to decelerate symetrically to the rate I accelerated my clock should, therefore, be the same as the observer that is stationary to the start point.

 

The 'time slowing' that occured during my acceleration should be returned to me at an equal rate upon deceleration. So there is no time dilation at the end of the journey. Is this correct or not?

 

Damien

[Damo2600]

Hi Everyone,

 

Can anyone assist me with the previous post? Does the deceleration time dilation cancel out equal acceleration? Or are the two time dilations unequal? or does deceleration not impact on the time dilation caused by acceleration?

 

I must point out however that I am not obligating anyone to provide an answer, I am just simply asking if anyone would mind spending time to reply to my post. If I don't state this I may be misconstrued.

 

Damien

[Buffy]

"If accelerating momentum does in fact slow down time then wouldn't decelerating momentum speed up time?" You agreed with this and stated "Yes, but its only giving you back what it took away when you accellerated in the first place..."

The 'time slowing' that occured during my acceleration should be returned to me at an equal rate upon deceleration. So there is no time dilation at the end of the journey. Is this correct or not?

You misunderstood what I was referring to: What you get back is only the *rate change* compared to the stationary observer, i.e. when you decellerate to stationary compared to the stationary observer, he no longer sees time dilation on your clock. Again, its not "making up the time" if it were, then Special Relativity would be wrong. Your last sentance is correct insofar as "there is no time dilation" once you're stationary with respect to the other observer, but your clock is still going to be behind his because your time was dilated compared to his during the trip.

 

Cheers,

Buffy