# Thread: Maximum speed of light, maximum speed of causality

1. I stumbled on a cool PBS Spacetime video on this. I like the term "maximum speed of causality".

This got me to think about accelerated objects as seen from an inertial frame. If I understood this correctly a force accelerating an object first affects only the "point of impact" and then later on the rest of the body of the accelerated object as the effect travels through the body at c.

One question popped into mind. Consider a long spaceship accelerates with its' rear "thruster". Say the spaceship is 1.0 light seconds long and stationary relative to our inertial observer. Then the spaceship begins the acceleration, first the rear accelerates and then the front accelerates 1.0 seconds later. If the acceleration was a pulsed acceleration (short bursts), each pulse then first accelerates the rear.

So the question that occurred to me was:
If the front begins accelerating later, does it experience somehow a higher acceleration than the rear?

2.

3. Originally Posted by grandi
I stumbled on a cool PBS Spacetime video on this. I like the term "maximum speed of causality".

This got me to think about accelerated objects as seen from an inertial frame. If I understood this correctly a force accelerating an object first affects only the "point of impact" and then later on the rest of the body of the accelerated object as the effect travels through the body at c.
It propagates through the body at the speed sound in the material, not at the speed of light. (That is why it is "maximum speed of causality" and not "speed of causality".)

If the front begins accelerating later, does it experience somehow a higher acceleration than the rear?
Not sure why it should. It might depend on the structure and material, if that allows it to build up a larger pressure wave or something. Otherwise it is just the same acceleration but delayed.

4. Originally Posted by Strange
Originally Posted by grandi
I stumbled on a cool PBS Spacetime video on this. I like the term "maximum speed of causality".

This got me to think about accelerated objects as seen from an inertial frame. If I understood this correctly a force accelerating an object first affects only the "point of impact" and then later on the rest of the body of the accelerated object as the effect travels through the body at c.
It propagates through the body at the speed sound in the material, not at the speed of light. (That is why it is "maximum speed of causality" and not "speed of causality".)

If the front begins accelerating later, does it experience somehow a higher acceleration than the rear?
Not sure why it should. It might depend on the structure and material, if that allows it to build up a larger pressure wave or something. Otherwise it is just the same acceleration but delayed.
If from the stationary observer's point of view the rear is at all times going faster than the front, then the "rear would travel past the front". So I guess there is some limit to the body compressing which then causes the front to "jerk" forward?

5. A force applied to one end of a non-rigid body will compress it, at the same time as imparting acceleration. So the front end moves a bit later and the time difference is equivalent to the degree to which the body is compressed. Also if the force is applied suddenly, there will be a pressure wave that may move through the body, rebound from the far end and travel back to the end where the force is applied. So the far end may oscillate relative to the end where the force is.

I would not be surprised to learn that this happens in space rockets, to a sufficient extent that engineers have to plan for it in some way. Dywyddyr may be able to comment.

6. Originally Posted by grandi
If the front begins accelerating later, does it experience somehow a higher acceleration than the rear?
If a spring is in constant acceleration such that it maintains its equilibrium length at all times, then the rear of the spring (relative to the direction of acceleration) has a greater acceleration than the front of the spring. This is a consequence of relativistic length-contraction.

7. Originally Posted by KJW
Originally Posted by grandi
If the front begins accelerating later, does it experience somehow a higher acceleration than the rear?
If a spring is in constant acceleration such that it maintains its equilibrium length at all times, then the rear of the spring (relative to the direction of acceleration) has a greater acceleration than the front of the spring. This is a consequence of relativistic length-contraction.
I'd expect that to be true for the beginning of the acceleration. But at some point the front must jerk forward (greater acceleration) so that it reaches the same speed as the rear. Right?

Exchemist, lets assume the acceleration is subtle and constant to keep the situation simple...

8. Originally Posted by grandi
Consider a long spaceship accelerates with its' rear "thruster". Say the spaceship is 1.0 light seconds long and stationary relative to our inertial observer. Then the spaceship begins the acceleration, first the rear accelerates and then the front accelerates 1.0 seconds later. If the acceleration was a pulsed acceleration (short bursts), each pulse then first accelerates the rear.

So the question that occurred to me was:
If the front begins accelerating later, does it experience somehow a higher acceleration than the rear?
A problem with this question as it stands is that it requires knowledge of the material properties of spaceship, and that relativity alone is insufficient.

9. Originally Posted by KJW
Originally Posted by grandi
Consider a long spaceship accelerates with its' rear "thruster". Say the spaceship is 1.0 light seconds long and stationary relative to our inertial observer. Then the spaceship begins the acceleration, first the rear accelerates and then the front accelerates 1.0 seconds later. If the acceleration was a pulsed acceleration (short bursts), each pulse then first accelerates the rear.

So the question that occurred to me was:
If the front begins accelerating later, does it experience somehow a higher acceleration than the rear?
A problem with this question as it stands is that it requires knowledge of the material properties of spaceship, and that relativity alone is insufficient.
Can we at least determine that the front must jerk forward regardless of the material? Less stiff material the greater the jerk?

10. Originally Posted by grandi
Originally Posted by KJW
If a spring is in constant acceleration such that it maintains its equilibrium length at all times, then the rear of the spring (relative to the direction of acceleration) has a greater acceleration than the front of the spring. This is a consequence of relativistic length-contraction.
I'd expect that to be true for the beginning of the acceleration. But at some point the front must jerk forward (greater acceleration) so that it reaches the same speed as the rear. Right?
No. I'm talking about something different from your original question, but something that needs to be understood about accelerated objects. Note that I was taking about a spring that is in constant acceleration and maintaining its equilibrium length, but without specifying how that is accomplished.

11. Originally Posted by KJW
Originally Posted by grandi
Originally Posted by KJW
If a spring is in constant acceleration such that it maintains its equilibrium length at all times, then the rear of the spring (relative to the direction of acceleration) has a greater acceleration than the front of the spring. This is a consequence of relativistic length-contraction.
I'd expect that to be true for the beginning of the acceleration. But at some point the front must jerk forward (greater acceleration) so that it reaches the same speed as the rear. Right?
No. I'm talking about something different from your original question, but something that needs to be understood about accelerated objects. Note that I was taking about a spring that is in constant acceleration and maintaining its equilibrium length, but without specifying how that is accomplished.
But if some inertial observer is looking at the spring and at all times the rear has greater acceleration, then by definition the rear must fly past the front. That wouldn't make any sense. Doesn't the acceleration have to stabilise?

12. Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
Originally Posted by KJW
If a spring is in constant acceleration such that it maintains its equilibrium length at all times, then the rear of the spring (relative to the direction of acceleration) has a greater acceleration than the front of the spring. This is a consequence of relativistic length-contraction.
I'd expect that to be true for the beginning of the acceleration. But at some point the front must jerk forward (greater acceleration) so that it reaches the same speed as the rear. Right?
No. I'm talking about something different from your original question, but something that needs to be understood about accelerated objects. Note that I was taking about a spring that is in constant acceleration and maintaining its equilibrium length, but without specifying how that is accomplished.
But if some inertial observer is looking at the spring and at all times the rear has greater acceleration, then by definition the rear must fly past the front. That wouldn't make any sense. Doesn't the acceleration have to stabilise?
One thing I neglected to mention: that the constant acceleration referred to is in the frame-of-reference of the accelerated spring. In the frame-of-reference of an inertial observer, both ends of the spring asymptotically approach the speed-of-light.

However, note that in the frame-of-reference of the spring, every part of the spring is at rest relative to every other part of the spring (the spring maintains its equilibrium length). The rear of the spring is time-dilated relative to the front of the spring. It should be noted that the maximum possible constant acceleration of the front of the spring is c2/L (where L=length of the spring). In this case, the rear of the spring would be at the event horizon of the accelerated frame-of-reference, and the acceleration of the rear of the spring would be infinite.

13. Originally Posted by KJW
Originally Posted by grandi
But if some inertial observer is looking at the spring and at all times the rear has greater acceleration, then by definition the rear must fly past the front. That wouldn't make any sense. Doesn't the acceleration have to stabilise?
One thing I neglected to mention: that the constant acceleration referred to is in the frame-of-reference of the accelerated spring. In the frame-of-reference of an inertial observer, both ends of the spring asymptotically approach the speed-of-light.

However, note that in the frame-of-reference of the spring, every part of the spring is at rest relative to every other part of the spring (the spring maintains its equilibrium length). The rear of the spring is time-dilated relative to the front of the spring. It should be noted that the maximum possible constant acceleration of the front of the spring is c2/L (where L=length of the spring). In this case, the rear of the spring would be at the event horizon of the accelerated frame-of-reference, and the acceleration of the rear of the spring would be infinite.
Isn't it so that neither end will actually reach the speed of light (despite getting closer and closer) in the inertial observer's frame? So the rear end would always move at a greater speed in that frame.

14. Originally Posted by grandi
Isn't it so that neither end will actually reach the speed of light (despite getting closer and closer) in the inertial observer's frame?
That's what "asymptotically approach the speed-of-light" means.

Originally Posted by grandi
So the rear end would always move at a greater speed in that frame.
Yes. As the spring gets faster, its length contracts in the frame-of-reference of the inertial observer, thus the rear has to travel faster than the front to produce the length contraction.

15. Originally Posted by KJW
Originally Posted by grandi
Isn't it so that neither end will actually reach the speed of light (despite getting closer and closer) in the inertial observer's frame?
That's what "asymptotically approach the speed-of-light" means.

Originally Posted by grandi
So the rear end would always move at a greater speed in that frame.
Yes. As the spring gets faster, its length contracts in the frame-of-reference of the inertial observer, thus the rear has to travel faster than the front to produce the length contraction.
In the inertial observer's frame after the acceleration starts, if the speed of the rear is at all times greater than the front's and the the acceleration affects the rear first and then later the front - this means that in terms of linear speed in the observer's frame the rear would travel past the front. And it would happen quite quickly as well.

This would be quite simple to quantify, wouldn't it?

16. Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
Isn't it so that neither end will actually reach the speed of light (despite getting closer and closer) in the inertial observer's frame?
That's what "asymptotically approach the speed-of-light" means.

Originally Posted by grandi
So the rear end would always move at a greater speed in that frame.
Yes. As the spring gets faster, its length contracts in the frame-of-reference of the inertial observer, thus the rear has to travel faster than the front to produce the length contraction.
In the inertial observer's frame after the acceleration starts, if the speed of the rear is at all times greater than the front's and the the acceleration affects the rear first and then later the front - this means that in terms of linear speed in the observer's frame the rear would travel past the front. And it would happen quite quickly as well.

This would be quite simple to quantify, wouldn't it?
I was talking about a spring that has a constant acceleration over all time.

17. Originally Posted by KJW
Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
Isn't it so that neither end will actually reach the speed of light (despite getting closer and closer) in the inertial observer's frame?
That's what "asymptotically approach the speed-of-light" means.

Originally Posted by grandi
So the rear end would always move at a greater speed in that frame.
Yes. As the spring gets faster, its length contracts in the frame-of-reference of the inertial observer, thus the rear has to travel faster than the front to produce the length contraction.
In the inertial observer's frame after the acceleration starts, if the speed of the rear is at all times greater than the front's and the the acceleration affects the rear first and then later the front - this means that in terms of linear speed in the observer's frame the rear would travel past the front. And it would happen quite quickly as well.

This would be quite simple to quantify, wouldn't it?
I was talking about a spring that has a constant acceleration over all time.
I have a proposal:
That spring in constant acceleration suddenly becomes visible to an inertial observer. The observer then begins to measure it. First the spring appears to have length s, which then decreases linearly as the observer observes the rear travel faster than the front.

If that is the case... Is it? Does the rear at all times travel faster than the front in the inertial observer's frame?

18. Originally Posted by grandi
Originally Posted by KJW
I was talking about a spring that has a constant acceleration over all time.
I have a proposal:
That spring in constant acceleration suddenly becomes visible to an inertial observer. The observer then begins to measure it. First the spring appears to have length s, which then decreases linearly as the observer observes the rear travel faster than the front.

If that is the case... Is it? Does the rear at all times travel faster than the front in the inertial observer's frame?
Who said the length decreases linearly? The length decreases due to length contraction, and can only decrease to zero as the speed approaches the speed of light.

19. Originally Posted by KJW
Originally Posted by grandi
Originally Posted by KJW
I was talking about a spring that has a constant acceleration over all time.
I have a proposal:
That spring in constant acceleration suddenly becomes visible to an inertial observer. The observer then begins to measure it. First the spring appears to have length s, which then decreases linearly as the observer observes the rear travel faster than the front.

If that is the case... Is it? Does the rear at all times travel faster than the front in the inertial observer's frame?
Who said the length decreases linearly? The length decreases due to length contraction, and can only decrease to zero as the speed approaches the speed of light.
I suppose no one. If we are now in the inertial observer's frame observing what they are observing. The rear is travelling faster than the front. Is the rear travelling increasingly faster than the front as the acceleration continues?

20. Originally Posted by grandi
Is the rear travelling increasingly faster than the front as the acceleration continues?
No, both front and rear asymptotically approach the speed-of-light. Keep in mind that in the frame-of-reference of the spring, the length of the spring remains constant over all time.

21. Originally Posted by KJW
Originally Posted by grandi
Is the rear travelling increasingly faster than the front as the acceleration continues?
No, both front and rear asymptotically approach the speed-of-light. Keep in mind that in the frame-of-reference of the spring, the length of the spring remains constant over all time.
But the rear is travelling faster than the front as seen from any inertial frame, right?

22. Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
Is the rear travelling increasingly faster than the front as the acceleration continues?
No, both front and rear asymptotically approach the speed-of-light. Keep in mind that in the frame-of-reference of the spring, the length of the spring remains constant over all time.
But the rear is travelling faster than the front as seen from any inertial frame, right?
Not in the inertial frame-of-reference in which the spring is at instantaneous rest. But bear in mind that the speed-of-light is the speed-of-light in all inertial frames-of-reference. What point are you trying to make?

23. Originally Posted by KJW
Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
Is the rear travelling increasingly faster than the front as the acceleration continues?
No, both front and rear asymptotically approach the speed-of-light. Keep in mind that in the frame-of-reference of the spring, the length of the spring remains constant over all time.
But the rear is travelling faster than the front as seen from any inertial frame, right?
Not in the inertial frame-of-reference in which the spring is at instantaneous rest. But bear in mind that the speed-of-light is the speed-of-light in all inertial frames-of-reference. What point are you trying to make?
The point is that from an inertial observer's perspective the rear of the spring will travel faster than the front. From that perspective the rear will also accelerate more if acceleration is absolute.

Also, isn't the rear of the spring in a different non-inertial frame than the front of the spring at all times?

24. Originally Posted by grandi
The point is that from an inertial observer's perspective the rear of the spring will travel faster than the front. From that perspective the rear will also accelerate more if acceleration is absolute.
That's what I've been saying. From the beginning, I've said that the rear has a greater acceleration than the front.

Originally Posted by grandi
Also, isn't the rear of the spring in a different non-inertial frame than the front of the spring at all times?
Yes, the frame-of-reference of the rear of the spring has a greater acceleration than the frame-of-reference of the front of the spring.

25. Originally Posted by KJW
Originally Posted by grandi
The point is that from an inertial observer's perspective the rear of the spring will travel faster than the front. From that perspective the rear will also accelerate more if acceleration is absolute.
That's what I've been saying. From the beginning, I've said that the rear has a greater acceleration than the front.

Originally Posted by grandi
Also, isn't the rear of the spring in a different non-inertial frame than the front of the spring at all times?
Yes, the frame-of-reference of the rear of the spring has a greater acceleration than the frame-of-reference of the front of the spring.
And thus from an inertial observer's perspective the rear must be travelling faster than the front. Even if there was no acceleration the rear would pass the front and leave the front far behind . But now the rear is accelerating even more than the front so the rear will pass the front even quicker. As seen by an inertial observer.

26. The equation of motion of the front of the spring in an inertial frame-of-reference is:

x2 - c2 t2 = c4/aF2

The equation of motion of the rear of the spring in the same inertial frame-of-reference is:

x2 - c2 t2 = c4/aR2

The length of the spring is:

c2/aF - c2/aR

An interesting feature of the equation of motion of a constantly accelerated object is that it is invariant to Lorentz transformations about the origin. This means that for all straight lines that passes through the origin, the distance in spacetime between the points of intersection with the equations of motion will be the same (satisfying the maintaining of equilibrium length of the spring at all times).

27. This is just another lame attempt by an idiot1to "disprove" relativity. It shouldn't be in Physics...

1. Read his other thread his motivation is obvious, as is inability to be educated.

28. Originally Posted by PhDemon
This is just another lame attempt by an idiot1to "disprove" relativity. It shouldn't be in Physics...

1. Read his other thread his motivation is obvious, as is inability to be educated.
Huh? How is my point not getting across...

Let's try a super simple experiment with race cars.. We have cars A and B stationary on an extremely long straight so that B is from A 1000 miles to the right. Both cars accelerate to the left with the exact same constant acceleration (10 m/s?) without stopping the acceleration.

First B starts accelerating and closing to A.
Then exactly 1.0 seconds later A starts accelerating and trying to get away from B.

B started first but a long way out and both have the exact same acceleration. Will B ever catch A?

29. The evidence his here in your forum posts, you are a waste of our time...

30. Originally Posted by PhDemon
The evidence his here in your forum posts, you are a waste of our time...
You don't care about my specific point?

Well... Then I guess I can spare you the trouble of doing the calculations. B will indeed catch A and leave A far behind. That is the nature of acceleration, it is nonlinear. That was my point.

31. No, because it is made by a moron with an agenda. Your pose of "just asking questions" is dishonest. Your are a hardened crank, a troll or a combination of the two... You are starting with the premise of "I don't understand relativity, so it must be wrong". This is flawed, the only problem is between your ears... In your last thread this was patiently explained, you ignored it, and now you are reintroducing your misconceptions in a new thread. Stop it you twat.

32. Originally Posted by PhDemon
No, because it is made by a moron with an agenda. Your pose of "just asking questions" is dishonest. Your are a hardened crank, a troll or a combination of the two... You are starting with the premise of "I don't understand relativity, so it must be wrong". This is flawed, the only problem is between your ears...
How could asking questions ever be dishonest?

Science is made by asking questions. The better questions, the better science.

33. Not when you already think you know the answer despite all evidence and reason to the contrary. Trash please. I can't be bothered with you. Life's to short to try and educate the terminally stupid...

34. Originally Posted by grandi
Let's try a super simple experiment with race cars.. We have cars A and B stationary on an extremely long straight so that B is from A 1000 miles to the right. Both cars accelerate to the left with the exact same constant acceleration (10 m/s?) without stopping the acceleration.

First B starts accelerating and closing to A.
Then exactly 1.0 seconds later A starts accelerating and trying to get away from B.

B started first but a long way out and both have the exact same acceleration. Will B ever catch A?
Irrelevant. I've given the equations of motion for the front and rear points of the spring and these two hyperbolic curves do not intersect.

35. Originally Posted by PhDemon
Not when you already think you know the answer despite all evidence and reason to the contrary. Trash please. I can't be bothered with you. Life's to short to try and educate the terminally stupid...
Well I don't know the answer to the original question. I figured there must be some sort of variation of acceleration in the front. There must be something to compensate the rear travelling faster than the front. I'm not the expert here so that's why I am asking..

36. Originally Posted by KJW
Originally Posted by grandi
Let's try a super simple experiment with race cars.. We have cars A and B stationary on an extremely long straight so that B is from A 1000 miles to the right. Both cars accelerate to the left with the exact same constant acceleration (10 m/s?) without stopping the acceleration.

First B starts accelerating and closing to A.
Then exactly 1.0 seconds later A starts accelerating and trying to get away from B.

B started first but a long way out and both have the exact same acceleration. Will B ever catch A?
Irrelevant. I've given the equations of motion for the front and rear points of the spring and these two hyperbolic curves do not intersect.
What does that mean for the inertial observer? If the observer takes measurements, will they show the rear travelling faster than the front?

37. Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
Let's try a super simple experiment with race cars.. We have cars A and B stationary on an extremely long straight so that B is from A 1000 miles to the right. Both cars accelerate to the left with the exact same constant acceleration (10 m/s?) without stopping the acceleration.

First B starts accelerating and closing to A.
Then exactly 1.0 seconds later A starts accelerating and trying to get away from B.

B started first but a long way out and both have the exact same acceleration. Will B ever catch A?
Irrelevant. I've given the equations of motion for the front and rear points of the spring and these two hyperbolic curves do not intersect.
What does that mean for the inertial observer? If the observer takes measurements, will they show the rear travelling faster than the front?
Yes, but the rear will not overtake the front.

38. Originally Posted by KJW
Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
Let's try a super simple experiment with race cars.. We have cars A and B stationary on an extremely long straight so that B is from A 1000 miles to the right. Both cars accelerate to the left with the exact same constant acceleration (10 m/s?) without stopping the acceleration.

First B starts accelerating and closing to A.
Then exactly 1.0 seconds later A starts accelerating and trying to get away from B.

B started first but a long way out and both have the exact same acceleration. Will B ever catch A?
Irrelevant. I've given the equations of motion for the front and rear points of the spring and these two hyperbolic curves do not intersect.
What does that mean for the inertial observer? If the observer takes measurements, will they show the rear travelling faster than the front?
Yes, but the rear will not overtake the front.
Isn't speed a linear concept? Will the observer always measure the rear travel faster than the front?

39. Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
What does that mean for the inertial observer? If the observer takes measurements, will they show the rear travelling faster than the front?
Yes, but the rear will not overtake the front.
Will the observer always measure the rear travel faster than the front?
I have already answered that question. I've given the equations of motion. I can't do any more than that.

Originally Posted by grandi
Isn't speed a linear concept?
What does that mean?

40. Well I don't know the answer to the original question. I figured there must be some sort of variation of acceleration in the front. There must be something to compensate the rear travelling faster than the front. I'm not the expert here so that's why I am asking..
But when your questions are answered you ignore it, and come back with"yeah but" and ask another stupid question...

From the other above post it is evident you have a classic inability to be educated... Dumb as a rock...

41. Originally Posted by PhDemon
You see, a classic inability to be educated... Dumb as a rock...
I take offense at that characterisation.

-- Rock

42. Ok, how do feel about as dumb as a bag of hammers, or thicker than three short planks

43. Originally Posted by PhDemon
Ok, how do feel about as dumb as a bag of hammers, or thicker than three short planks
Much better, though you might be hearing from the hammers shortly.

44. Originally Posted by grandi
Then exactly 1.0 seconds later A starts accelerating and trying to get away from B.
1.0 seconds in which frame of reference? A? B? The original starting point?

45. Originally Posted by grandi
[Isn't speed a linear concept?
I'm not sure what you mean by that. But I suspect the answer is no.

46. Originally Posted by Strange
Originally Posted by grandi
Then exactly 1.0 seconds later A starts accelerating and trying to get away from B.
1.0 seconds in which frame of reference? A? B? The original starting point?
As with the first post we have our inertial observer. First all three are at rest.

47. Originally Posted by Strange
Originally Posted by grandi
[Isn't speed a linear concept?
I'm not sure what you mean by that. But I suspect the answer is no.
As seen by the inertial observer the moving object's location changes linearly. With acceleration it changes nonlinearly.

Relativistic velocity addition is of course nonlinear.

48. Originally Posted by KJW
Originally Posted by grandi
Let's try a super simple experiment with race cars.. We have cars A and B stationary on an extremely long straight so that B is from A 1000 miles to the right. Both cars accelerate to the left with the exact same constant acceleration (10 m/s?) without stopping the acceleration.

First B starts accelerating and closing to A.
Then exactly 1.0 seconds later A starts accelerating and trying to get away from B.

B started first but a long way out and both have the exact same acceleration. Will B ever catch A?
Irrelevant. I've given the equations of motion for the front and rear points of the spring and these two hyperbolic curves do not intersect.
This is not actually irrelevant.

If you consider the situation in the first post. The inertial observer will observe the rear travel faster than the front. If both front and rear have the same acceleration it means that the rear would at all times travel faster than the front in the inertial observer's frame and would have to pass the front. This is why I asked if there is some variance in the acceleration causally propagated to the front.

49. Originally Posted by grandi
If you consider the situation in the first post.
You can't consider the situation in the first post until you understand the situation with the spring in constant acceleration. And even if you do understand the situation with the spring in constant acceleration, the situation in the first post may still be too difficult.

50. Originally Posted by KJW
Originally Posted by grandi
Also, isn't the rear of the spring in a different non-inertial frame than the front of the spring at all times?
Yes, the frame-of-reference of the rear of the spring has a greater acceleration than the frame-of-reference of the front of the spring.
Actually, if either or both ends of the spring relinquish their status as determiner of the origin and scale of the frame-of-reference, then both the rear and front of the spring can share the same non-inertial frame-of-reference. In particular, they both share the same notion of simultaneity.

It should be noted that the notion that the rear of the spring is faster than the front of the spring depends on the notion of simultaneity, and it is the inertial observer's notion of simultaneity for which the rear of the spring is faster than the front of the spring. If one considers the spring's notion of simultaneity (which is the same for all points along the spring), then the two ends of the spring have the same speed relative to the inertial observer (though we are taking the speed of the front of the spring at a different time in the inertial frame-of-reference to the speed of the rear of the spring).

51. Originally Posted by grandi
If both front and rear have the same acceleration it means that the rear would at all times travel faster than the front in the inertial observer's frame and would have to pass the front.
Obviously not. If it is a rigid object then the rear must always be behind the front.

And, when you consider relativistic speed addition, it is obvious why it doesn't happen.

But, as you have previously demonstrated that you are unable (or unwilling?) to understand even the most basic principles behind special relativity, I am not surprised you have confused yourself with this.

52. Originally Posted by KJW
Originally Posted by grandi
If you consider the situation in the first post.
You can't consider the situation in the first post until you understand the situation with the spring in constant acceleration. And even if you do understand the situation with the spring in constant acceleration, the situation in the first post may still be too difficult.
Sure, it appears that you have a grander understanding of the initial problem..

Let me try to understand your view in more detail. I'll put some simple numbers on the table. Say that the acceleration of the ship is 10000 m/s^2.

Here's what I gather happens in the stationary observer's frame:
- at t=0s both ends of the ship are stationary
- at t=1s the rear is travelling at 10000 m/s and the front is stationary
- at t=2s the rear is travelling at 20000 m/s and the front at 10000 m/s
- at t=3s the rear is travelling at 30000 m/s and the front at 20000 m/s
- at t=1000 the rear is travelling at 1000000 m/s and the front at 990000 m/s

So to me it seems that the distance between the front and the back is constantly changing at 10000 m/s at all times while the constant acceleration occurs.

Is this correct, or do you have some other way of describing the change of the distance between the front and the rear as seen by the inertial observer?

53. Originally Posted by KJW
Originally Posted by grandi
If you consider the situation in the first post.
You can't consider the situation in the first post until you understand the situation with the spring in constant acceleration. And even if you do understand the situation with the spring in constant acceleration, the situation in the first post may still be too difficult.
On the other hand, one could consider a non-relativistic version of the situation in the first post, where the propagation speed of the effects of the force is much less than the speed-of-light, and the acceleration produced by the force is very small resulting in velocities of the object being much less than the speed-of-light.

54. Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
If you consider the situation in the first post.
You can't consider the situation in the first post until you understand the situation with the spring in constant acceleration. And even if you do understand the situation with the spring in constant acceleration, the situation in the first post may still be too difficult.
Sure, it appears that you have a grander understanding of the initial problem..

Let me try to understand your view in more detail. I'll put some simple numbers on the table. Say that the acceleration of the ship is 10000 m/s^2.

Here's what I gather happens in the stationary observer's frame:
- at t=0s both ends of the ship are stationary
- at t=1s the rear is travelling at 10000 m/s and the front is stationary
- at t=2s the rear is travelling at 20000 m/s and the front at 10000 m/s
- at t=3s the rear is travelling at 30000 m/s and the front at 20000 m/s
- at t=1000 the rear is travelling at 1000000 m/s and the front at 990000 m/s

So to me it seems that the distance between the front and the back is constantly changing at 10000 m/s at all times while the constant acceleration occurs.

Is this correct, or do you have some other way of describing the change of the distance between the front and the rear as seen by the inertial observer?
First you need to consider what happens in the frame of the ship. At some the read starts to accelerate, the compression wave moves through the ship at the speed of sound for the material of the ship and reaches the front of the ship. after some period of "ringing" the length of the ship will settle down to a slightly compressed state compared than that which it had before the acceleration began. Assuming the magnitude of the acceleration remains unchanged, the length of the ship and distance between front and back remains unchanged.
From the inertial frame, the compression also propagates forward, though with different timing than as measured from the ship. Now after the "ringing" ends, the inertial frame will continue to see the distance between front and back as decreasing due to length contraction. While the ship measures the distance as unchanging, the intertial frame measures the ship as a whole having an increasing velocity, and thus getting shorter due to length contraction. But he will also measure the acceleration of the ship as decreasing. the closer the ship gets to the speed of light, the slower it will approach it. And just like the fact that the ship can get closer and closer to c but never reach it, the distance between the ends of the ship can get closer and closer to zero but never reach it. The back of the ship can get closer and closer to the front but will never catch it, and the difference in speeds between front and back will not be a constant for the inertial observer.

55. Originally Posted by Janus
Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
If you consider the situation in the first post.
You can't consider the situation in the first post until you understand the situation with the spring in constant acceleration. And even if you do understand the situation with the spring in constant acceleration, the situation in the first post may still be too difficult.
Sure, it appears that you have a grander understanding of the initial problem..

Let me try to understand your view in more detail. I'll put some simple numbers on the table. Say that the acceleration of the ship is 10000 m/s^2.

Here's what I gather happens in the stationary observer's frame:
- at t=0s both ends of the ship are stationary
- at t=1s the rear is travelling at 10000 m/s and the front is stationary
- at t=2s the rear is travelling at 20000 m/s and the front at 10000 m/s
- at t=3s the rear is travelling at 30000 m/s and the front at 20000 m/s
- at t=1000 the rear is travelling at 1000000 m/s and the front at 990000 m/s

So to me it seems that the distance between the front and the back is constantly changing at 10000 m/s at all times while the constant acceleration occurs.

Is this correct, or do you have some other way of describing the change of the distance between the front and the rear as seen by the inertial observer?
First you need to consider what happens in the frame of the ship. At some the read starts to accelerate, the compression wave moves through the ship at the speed of sound for the material of the ship and reaches the front of the ship. after some period of "ringing" the length of the ship will settle down to a slightly compressed state compared than that which it had before the acceleration began. Assuming the magnitude of the acceleration remains unchanged, the length of the ship and distance between front and back remains unchanged.
From the inertial frame, the compression also propagates forward, though with different timing than as measured from the ship. Now after the "ringing" ends, the inertial frame will continue to see the distance between front and back as decreasing due to length contraction. While the ship measures the distance as unchanging, the intertial frame measures the ship as a whole having an increasing velocity, and thus getting shorter due to length contraction. But he will also measure the acceleration of the ship as decreasing. the closer the ship gets to the speed of light, the slower it will approach it. And just like the fact that the ship can get closer and closer to c but never reach it, the distance between the ends of the ship can get closer and closer to zero but never reach it. The back of the ship can get closer and closer to the front but will never catch it, and the difference in speeds between front and back will not be a constant for the inertial observer.
Ah, the situation in the inertial frame of reference is not simple...

What if the ship was accelerated by some device in the inertial frame; using a large laser beam, kind of like a solar sail type of thing but in a much larger scale. Acceleration would be much less, maybe 10 m/s^2. Would the acceleration of the ship remain constant as seen in the inertial frame?

56. Originally Posted by grandi
Originally Posted by Janus
Originally Posted by grandi
Originally Posted by KJW
Originally Posted by grandi
If you consider the situation in the first post.
You can't consider the situation in the first post until you understand the situation with the spring in constant acceleration. And even if you do understand the situation with the spring in constant acceleration, the situation in the first post may still be too difficult.
Sure, it appears that you have a grander understanding of the initial problem..

Let me try to understand your view in more detail. I'll put some simple numbers on the table. Say that the acceleration of the ship is 10000 m/s^2.

Here's what I gather happens in the stationary observer's frame:
- at t=0s both ends of the ship are stationary
- at t=1s the rear is travelling at 10000 m/s and the front is stationary
- at t=2s the rear is travelling at 20000 m/s and the front at 10000 m/s
- at t=3s the rear is travelling at 30000 m/s and the front at 20000 m/s
- at t=1000 the rear is travelling at 1000000 m/s and the front at 990000 m/s

So to me it seems that the distance between the front and the back is constantly changing at 10000 m/s at all times while the constant acceleration occurs.

Is this correct, or do you have some other way of describing the change of the distance between the front and the rear as seen by the inertial observer?
First you need to consider what happens in the frame of the ship. At some the read starts to accelerate, the compression wave moves through the ship at the speed of sound for the material of the ship and reaches the front of the ship. after some period of "ringing" the length of the ship will settle down to a slightly compressed state compared than that which it had before the acceleration began. Assuming the magnitude of the acceleration remains unchanged, the length of the ship and distance between front and back remains unchanged.
From the inertial frame, the compression also propagates forward, though with different timing than as measured from the ship. Now after the "ringing" ends, the inertial frame will continue to see the distance between front and back as decreasing due to length contraction. While the ship measures the distance as unchanging, the intertial frame measures the ship as a whole having an increasing velocity, and thus getting shorter due to length contraction. But he will also measure the acceleration of the ship as decreasing. the closer the ship gets to the speed of light, the slower it will approach it. And just like the fact that the ship can get closer and closer to c but never reach it, the distance between the ends of the ship can get closer and closer to zero but never reach it. The back of the ship can get closer and closer to the front but will never catch it, and the difference in speeds between front and back will not be a constant for the inertial observer.
Ah, the situation in the inertial frame of reference is not simple...

What if the ship was accelerated by some device in the inertial frame; using a large laser beam, kind of like a solar sail type of thing but in a much larger scale. Acceleration would be much less, maybe 10 m/s^2. Would the acceleration of the ship remain constant as seen in the inertial frame?
If the power source for the laser beam remained constant then the acceleration would be seen to decrease with time.
if you try to maintain a constant acceleration, then you have to keep increasing the power supplied to the laser.
As the ship increases in speed, its kinetic energy as measured in the inertial frame increases by the equation:

KE = mc^2(1/sqrt(1-v^2/v^2)-1)

So for example, the additional energy per kg of ship mass needed to go from 0.1c to 0.2 c is ~1.4e15 joules, and the energy needed to go from 0.2c to 0.3c is ~2.5e15 joules or 1.8 times more. The energy needed to go from 0.8c to 0.9c is 5.16e16 joules, or 40 times that needed to go from 0.1c to 0.2c
It gets even worse as you go from 0.9c towards c. So it would take 132 times as much energy to go from 0.98c to 0.99c than it did to go from 0.1c to 0.2c.

Put another way, the same energy that increases the ship speed to 0.2c from 0.1c, would only accelerate you up to 0.9014c from 0.9c

The amount of energy needed increases towards infinity as the ship speed approaches c.

57. Originally Posted by Janus
Originally Posted by grandi
Ah, the situation in the inertial frame of reference is not simple...

What if the ship was accelerated by some device in the inertial frame; using a large laser beam, kind of like a solar sail type of thing but in a much larger scale. Acceleration would be much less, maybe 10 m/s^2. Would the acceleration of the ship remain constant as seen in the inertial frame?
If the power source for the laser beam remained constant then the acceleration would be seen to decrease with time.
if you try to maintain a constant acceleration, then you have to keep increasing the power supplied to the laser.
As the ship increases in speed, its kinetic energy as measured in the inertial frame increases by the equation:

KE = mc^2(1/sqrt(1-v^2/v^2)-1)

So for example, the additional energy per kg of ship mass needed to go from 0.1c to 0.2 c is ~1.4e15 joules, and the energy needed to go from 0.2c to 0.3c is ~2.5e15 joules or 1.8 times more. The energy needed to go from 0.8c to 0.9c is 5.16e16 joules, or 40 times that needed to go from 0.1c to 0.2c
It gets even worse as you go from 0.9c towards c. So it would take 132 times as much energy to go from 0.98c to 0.99c than it did to go from 0.1c to 0.2c.

Put another way, the same energy that increases the ship speed to 0.2c from 0.1c, would only accelerate you up to 0.9014c from 0.9c

The amount of energy needed increases towards infinity as the ship speed approaches c.
So it sounds like it is possible to design an experiment where the ship is accelerated with a laser beam from the stationary inertial frame and by adjusting the power of the beam the acceleration as seen in the inertial frame is always constant.
To keep the situation simple, this should be possible. Right?

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