Movement requires energy

[5614]

I know it's wrong, but I still don't understand why!

 

Keep it simple, which part of this is wrong and why...

 

We travel through the 4th dimension at c

 

Time dilation means that time is varied depending on that frames velocity relative to others in the 3 spatial dimensions.

 

So for example if I were travelling really fast relative to you then time would pass at a different rate for me than it would for you.

 

For this difference in time there's a difference in distance travelled in the 4th dimension, which requires a velocity change and energy blah blah, I know this part is wrong, I think the rest is right though, I just want to understand WHY, keep it simple!

 

Time dilation is a derived result for inertial (nonaccelerating) frames.

OK, so an inertial frame requires no energy if there's no opposing forces, which there isn't in time, fine... but at the moment I can imagine two objects moving at different speeds in spatial dimensions, which means they have different speeds in the time dimension... I think the problem is me visualising frames passing through time at different speeds, which is when acceleration and energy come into it.

 

Time dilation is derived for inertial frames..... I still see time passing differently for different frames which requires a varying velocity through the 4th dimension.

[Tom Mattson]

For this difference in time there's a difference in distance travelled in the 4th dimension' date=' which requires a velocity change and energy blah blah, I know this part is wrong, I think the rest is right though, I just want to understand WHY, keep it simple!

 

I did explain why, and I did keep it simple: Time dilation simply does not necessitate velocity changes! It is a result derived for nonaccelerating frames.

 

Instead of me trying to explain this to you, why don't you explain to me why you think time dilation does require velocity changes, and therefore energy?

[5614]

OK, I'm going down the road and am overtaken by a car.

 

I know that just as that car is going faster than me down the road, due to time dilation he is going slower than me through time.

 

However if he suddenly broke hard and came to a standstill then I would overtake him [on the road], due to time dilation, now I'm going faster than him, I'm going slower through time than him.

 

It is this "him going slower through time, then me going slower through time" which leads me to visualise a time line and me and him going down it at different rates.

 

OK, so they're inertial frames, so are you saying that there's no acceleration, it is an instaneous jump from speed x to speed y? But speed is continuous, it's not discrete, so can it jump from x to y... surely it goes through all the points in between, which would be acceleration.

[BlackHole]

Time dilation is the result of mass-energy conservation. When mass is accelerated toward light speed, physical processes slow down due to mass-energy conservation. Therefore clocks run slower.

[5614]

If you imagine the 4th dimension as a line and we are moving along it.... when clocks run slower does that not go to us moving slower through the 4th dimension, slower along that line?

 

When you say no, why?!?

 

(You see I know I'm wrong, I sadly just can't understand why)

[BlackHole]

Do you mean a fourth spatial dimension or a temporal dimension? I imagine space-time as an abstract 4-dimensional sphere but motion takes place only through the three spatial dimensions.

 

Kind regards

[Tom Mattson]

However if he suddenly broke hard and came to a standstill then I would overtake him [on the road]' date=' due to time dilation, now I'm going faster than him, I'm going slower through time than him.

[/quote']

 

But since you are inertial the whole time, there is no reason whatsoever to say that you are moving faster than he is. In fact, there is no reason for you to say that you are moving at all! When you say "I would overtake him" you are talking about what is observed from the perspective of an observer on the road, or in the other car. From your perspective, the other car whizzed by you in the opposite direction. For you, there is no change in the rate at which you move through time.

[Kygron]

...inertial...

...acceleration...

 

I think the definition of time dilation is getting in the way of the understanding. I think 5614 would like to hear reasoning within the full GR theory. Well, at least that's what I would like to hear when I read this thread

[5614]

But since you are inertial the whole time, there is no reason whatsoever to say that you are moving faster than he is. In fact, there is no reason for you to say that you are moving at all! When you say "I would overtake him" you are talking about what is observed from the perspective of an observer on the road, or in the other car. From your perspective, the other car whizzed by you in the opposite direction. For you, there is no change in the rate at which you move through time.

OK, well, lets say I'm moving at 50%c, he's moving at 60%c (that's when he overtakes me).... but then he brakes to 20%c (now I catch up and overtake him).

 

OK, so if it were just me and the other guy (no 3rd frame) all I'd know is that he's travelling 10%c faster than me, and then he's going 30%c in the opposite direction.

 

He's changed velocity relative to me,

 

So his speed through time has changed.

 

So even if my rate through time hasn't changed, his has, someone's has.

[Tom Mattson]

So even if my rate through time hasn't changed, his has, someone's has.

 

Right. And to do that he had to apply a force to do the work necessary to change his velocity. In other words, he expended energy, just as one would expect. So this should answer your orignial question: Movement does not require energy. Changing one's state of motion does.

[Tom Mattson]

I think 5614 would like to hear reasoning within the full GR theory. Well, at least that's what I would like to hear when I read this thread

 

There's really no reason to complicate things by going into GR. SR is perfectly capable of handling accelerated motion.

[5614]

Right. And to do that he had to apply a force to do the work necessary to change his velocity. In other words, he expended energy, just as one would expect. So this should[/i'] answer your orignial question: Movement does not require energy. Changing one's state of motion does.

Ohhhh, so it comes back to the "the same kinetic energy pushing us in x direction across a spatial dimension that is also pushing us in y direction across the time dimensions?" OK, cool, all sorted then... I dunno, I read that and it just clicked and all fell into position.... thanks a lot!!!

 

My only other question is, Tom, you say: "dilation is a derived result for inertial frames" So my question is what happens when you are accelerating? I mean, for example, I'm moving at 50%c and accelerating at 1%c/s^2 and you are moving at 40% and acclerating at 5%c/s^2.... the point is that you are moving slower, but will inevitably overtake me.

 

Is the only difference between this and 'normal' examples of time dilation (where everyone is inertial) that you'd have to 'freeze time' and take a specific speed to calculate time dilation and that because it is continually changing it would only apply to that instance?

 

Or basically, you say time dilation is for inertial frames, what happens to accelerating frames?

 

(And thanks again!)

[Tom Mattson]

My only other question is' date=' Tom, you say: "dilation is a derived result for inertial frames" So my question is what happens when you are accelerating?

.

.

.

Or basically, you say time dilation is for inertial frames, what happens to accelerating frames?

 

Your questions are difficult to answer what with LaTeX being broken. I am going to refer you to the following page of a free online relativity textbook. It has the Lorentz transformation for accelerated motion. Chewing on this should keep you busy for a while!

 

http://www.geocities.com/zcphysicsms/chap5.htm#BM5_4

 

(And thanks again!)

 

No problemo!

[Kygron]

There's really no reason to complicate things by going into GR. SR is perfectly capable of handling accelerated motion.

 

This is an aside, but since the original discussion is closing up...

 

If SR can handle accelerated motion, then what's the use of having GR?? Or, better, when do you need to start taking GR principles into account?