His proper speed
ramps up without limit?
I'm self taught in this subject, and have a question.
A traveler in a closed vehicle can deduce velocity using
an accelerometer. What if he simply burns energy without
limit, and continuously accelerates? His proper speed
ramps up without limit? When does the c limit kick in?
This issue arises in Bell's spaceship paradox, does it not?
The inertial observer sees the ships maintain a constant
separation, while both accelerate. The occupants within
feel a constant proper acceleration, what's the limit on their
proper velocity? What do they see when they look out the window?
MarkMark-T do not listen to Dono. Instead of the enigma of proper velocity, concentrate all your efforts on the enigma of proper and coordinate RELATIVE velocity. That is where all of relativity's dead bodies are buried. Become proficient in that subject
On September 25, 2023, Mark-T wrote:
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
On September 25, 2023, Dono. wrote:
On September 25, 2023, Mark-T wrote:
His proper speed ramps up without limit?
Err, no.Then it approaches c. And that's what the traveler sees, when he looks
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
out the window?
I can't find that equation in Einstein's 1905 paper. Is there
a derivation somewhere?
A traveler in a closed vehicle can deduce velocity using an
accelerometer. What if he simply burns energy without limit, and continuously accelerates? His proper speed ramps up without limit?
When does the c limit kick in?
This issue arises in Bell's spaceship paradox, does it not?
The inertial observer sees the ships maintain a constant separation,
while both accelerate. The occupants within feel a constant proper acceleration, what's the limit on their proper velocity?
What do they see when they look out the window?
On 9/25/23 3:50 PM, Mark-T wrote:
A traveler in a closed vehicle can deduce velocity using an
accelerometer. What if he simply burns energy without limit, and
continuously accelerates? His proper speed ramps up without limit?
When does the c limit kick in?
The accelerometer he carries displays his proper acceleration. An object
with constant proper acceleration executes "hyperbolic motion". That is, relative to any inertial frame (this is SR) its trajectory is a
hyperbola, which asymptotically approaches c as time increases without
bound. This, of course, is a highly unrealistic scenario, as it requires
an infinite amount of energy....
Note also that in physics, "proper" means "in the rest frame of the
object in question". So an object's proper speed and proper velocity are identically zero, making them useless. (Some poorly worded and/or crank websites use those terms in nonstandard ways.)
[In astronomy, "proper velocity" has a very different,
and useful, meaning.]
This issue arises in Bell's spaceship paradox, does it not?
No. The same analysis applies.
The inertial observer sees the ships maintain a constant separation,
while both accelerate. The occupants within feel a constant proper
acceleration, what's the limit on their proper velocity?
Their proper velocity remains zero. Their velocity relative to their
initial inertial frame is a hyperbola that asymptotically approaches c.
What do they see when they look out the window?
That depends in detail on what is located outside their window.
Tom Roberts
I'm self taught in this subject, and have a question.
A traveler in a closed vehicle can deduce velocity using
an accelerometer. What if he simply burns energy without
limit, and continuously accelerates? His proper speed
ramps up without limit? When does the c limit kick in?
This issue arises in Bell's spaceship paradox, does it not?
The inertial observer sees the ships maintain a constant
separation, while both accelerate. The occupants within
feel a constant proper acceleration, what's the limit on their
proper velocity? What do they see when they look out the window?
MarkTheir speed continues to increase continuously without limit. There is no cosmic speed limit of c. If you look out the window you won't be hoodwinked by the relativists.
On Monday, September 25, 2023 at 1:50:32 PM UTC-7, Mark-T wrote:
A traveler in a closed vehicle can deduce velocity using anTheir speed continues to increase continuously without limit. There
accelerometer. What if he simply burns energy without limit, and
continuously accelerates? [...]
is no cosmic speed limit of c.
On September 26, Dono. wrote:
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
Then it approaches c. And that's what the traveler sees, when he looks
out the window?
Yes. Asymptotically.
And an external observer sees him accelerate at rate a, the same reading
as his accelerometer?
Ignore patdolan , he's an imbecile.
I'll take your word on it. But suppose he contradicts your assertion,
how should I proceed?
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
Then it approaches c. And that's what the traveler sees, when he looks
out the window?
Yes. Asymptotically.
Ignore patdolan , he's an imbecile.
On Wednesday, September 27, 2023 at 4:43:17 PM UTC-7, Mark-T wrote:Mark-T, mark how they flee in terror before me. You would do well to become my disciple.
On September 26, Dono. wrote:
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
Then it approaches c. And that's what the traveler sees, when he looks >> out the window?
Yes. Asymptotically.
And an external observer sees him accelerate at rate a, the same reading as his accelerometer?
Ignore patdolan , he's an imbecile.
I'll take your word on it. But suppose he contradicts your assertion,Reference a university textbook... pretty much any one of them will refute anything Dolan has to say...
how should I proceed?
On Wednesday, September 27, 2023 at 4:46:40 PM UTC-7, Paul Alsing wrote:
On Wednesday, September 27, 2023 at 4:43:17 PM UTC-7, Mark-T wrote:
On September 26, Dono. wrote:
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
Then it approaches c. And that's what the traveler sees, when he looks
out the window?
Yes. Asymptotically.
And an external observer sees him accelerate at rate a, the same reading as his accelerometer?
Ignore patdolan , he's an imbecile.
I'll take your word on it. But suppose he contradicts your assertion, how should I proceed?Reference a university textbook... pretty much any one of them will refute anything Dolan has to say...
Mark-T, mark how they flee in terror before me. You would do well to become my disciple.
On September 26, Dono. wrote:
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
Then it approaches c. And that's what the traveler sees, when he looks
out the window?
Yes. Asymptotically.
And an external observer sees him accelerate at rate a, the same reading
as his accelerometer?
Ignore patdolan , he's an imbecile.
I'll take your word on it. But suppose he contradicts your assertion,
how should I proceed?
Mark
Ignore patdolan , he's an imbecile.
I'll take your word on it. But suppose he contradicts your assertion,
how should I proceed?
Reference a university textbook... pretty much any one of them will refute anything Dolan has to say...
Mark-T, mark how they flee in terror before me. You would do well to become my disciple.
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Then it approaches c. And that's what the traveler sees, when he looks
out the window?
Yes. Asymptotically.
And an external observer sees him accelerate at rate a, the same reading
as his accelerometer?
You haven't specified what you mean by "external observer" -- is he moving along with the ship, is he stationary wrt the ship at t = 0, or what?
A traveler in a closed vehicle can deduce velocity using an
accelerometer. What if he simply burns energy without limit, and
continuously accelerates? His proper speed ramps up without limit?
When does the c limit kick in?
The accelerometer he carries displays his proper acceleration. An object
with constant proper acceleration executes "hyperbolic motion". That is, relative to any inertial frame (this is SR) its trajectory is a
hyperbola, which asymptotically approaches c as time increases without
bound.
Note also that in physics, "proper" means "in the rest frame of the
object in question". So an object's proper speed and proper velocity are identically zero, making them useless.
What do they see when they look out the window?
That depends in detail on what is located outside their window.
On September 28, 2023, Gary Harnagel wrote:
And an external observer sees him accelerate at rate a, the same reading as his accelerometer?
You haven't specified what you mean by "external observer" -- is he moving along with the ship, is he stationary wrt the ship at t = 0, or what?
The observer is stationary, relative to the ship at t=0.
Does he see the ship accelerate at the same rate as the
accelerometer reading?
Accounting for length contraction, if necessary.
Mark
On September 26, Dono. wrote:
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
Then it approaches c. And that's what the traveler sees, when he looks
out the window?
Yes. Asymptotically.And an external observer sees him accelerate at rate a,
as his accelerometer?
Ignore patdolan , he's an imbecile.I'll take your word on it. But suppose he contradicts your assertion,
how should I proceed?
On Wednesday, September 27, 2023 at 4:43:17 PM UTC-7, Mark-T wrote:
On September 26, Dono. wrote:
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
Then it approaches c. And that's what the traveler sees, when he looks >> out the window?
This is "coordinate " acceleration. dr/dtYes. Asymptotically.And an external observer sees him accelerate at rate a,
the same reading
as his accelerometer?This is "proper" acceleration, dr/d\tau. They are not the same. You really need to read a book or take a class.
Ignore patdolan , he's an imbecile.
I'll take your word on it. But suppose he contradicts your assertion,
how should I proceed?
At your own risk. Listening to imbeciles will only confuse you .
On Wednesday, September 27, 2023 at 4:43:17 PM UTC-7, Mark-T wrote:
On September 26, Dono. wrote:
His proper speed ramps up without limit?
Err, no.
v=at/sqrt(1+{at/c)^2)
Read on hyperbolic motion.
Then it approaches c. And that's what the traveler sees, when he looks >> out the window?
This is "coordinate " acceleration. d^2r/dt^2Yes. Asymptotically.And an external observer sees him accelerate at rate a,
the same reading
as his accelerometer?This is "proper" acceleration, d^2r/d\tau^2. They are not the same. You really need to read a book or take a class.
Ignore patdolan , he's an imbecile.I'll take your word on it. But suppose he contradicts your assertion,
how should I proceed?
At your own risk. Listening to imbeciles will only confuse you .
On September 26, 2023, Tom Roberts wrote:
A traveler in a closed vehicle can deduce velocity using an
accelerometer. What if he simply burns energy without limit, and
continuously accelerates? His proper speed ramps up without
limit? When does the c limit kick in?
The accelerometer he carries displays his proper acceleration. An
object with constant proper acceleration executes "hyperbolic
motion". That is, relative to any inertial frame (this is SR) its
trajectory is a hyperbola, which asymptotically approaches c as
time increases without bound.
I don't get this hyperbolic thing. I can draw a hyperbola on a
blank sheet of paper. I don't know what a hyperbolic velocity is.
The traveler drives along a straight highway. Where's the
hyperbola?
Note also that in physics, "proper" means "in the rest frame of the
object in question". So an object's proper speed and proper
velocity are identically zero, making them useless.
So if he computes his velocity, as he watches his accelerometer,
it's meaningless?
The observer is stationary, relative to the ship at t=0. Does he see
the ship accelerate at the same rate as the accelerometer reading?
On 9/25/23 3:50 PM, Mark-T wrote:
A traveler in a closed vehicle can deduce velocity using anThe accelerometer he carries displays his proper acceleration.
accelerometer. What if he simply burns energy without limit, and continuously accelerates? His proper speed ramps up without limit?
When does the c limit kick in?
Note also that in physics, "proper" means
[In astronomy, "proper velocity" has a very different,
and useful, meaning.]
On 9/28/23 4:36 PM, Mark-T wrote:
On September 26, 2023, Tom Roberts wrote:
A traveler in a closed vehicle can deduce velocity using an
accelerometer. What if he simply burns energy without limit, and
continuously accelerates? His proper speed ramps up without limit?
When does the c limit kick in?
The accelerometer he carries displays his proper acceleration. An
object with constant proper acceleration executes "hyperbolic
motion". That is, relative to any inertial frame (this is SR) its
trajectory is a hyperbola, which asymptotically approaches c as time
increases without bound.
I don't get this hyperbolic thing. I can draw a hyperbola on a
blank sheet of paper. I don't know what a hyperbolic velocity is.
Given inertial frame S with coordinates (x,t), and a traveler starting
from rest in S at x=0,t=0 with constant proper acceleration a along the
x axis, the velocity u of the traveler relative to S for \tau>=0 is:
u(\tau) = c*tanh(a*\tau/c)
where \tau is the traveler's proper time with \tau=0 when the
acceleration begins. Note that u(0) = 0, and as \tau -> \infinity,
u(\tau) -> c.
The traveler drives along a straight highway. Where's the hyperbola?
In the velocity relative to S as a function of \tau.
Note also that in physics, "proper" means "in the rest frame of the
object in question". So an object's proper speed and proper velocity
are identically zero, making them useless.
So if he computes his velocity, as he watches his accelerometer,
it's meaningless?
No he just has to be careful about what he is doing, and use the
relativistic equations. tis includes understanding to which inertial
frame his calculation applies.
The observer is stationary, relative to the ship at t=0. Does he see
the ship accelerate at the same rate as the accelerometer reading?
Let the observer be at rest in S (see above). Since a single observer
cannot observe the traveler's acceleration, let me use the inertial
frame S and its (x,t) coordinates to measure it. For the traveler:
at t=0: d^2x/dt^2 = a
for t>0: 0 < d^2x/dt^2 < a
as t->\infinity: d^2x/dt^2 -> 0.
On 9/28/2023 11:51 PM, Tom Roberts wrote:
On 9/28/23 4:36 PM, Mark-T wrote:
On September 26, 2023, Tom Roberts wrote:
A traveler in a closed vehicle can deduce velocity using an
accelerometer. What if he simply burns energy without limit, and
continuously accelerates? His proper speed ramps up without limit?
When does the c limit kick in?
The accelerometer he carries displays his proper acceleration. An
object with constant proper acceleration executes "hyperbolic
motion". That is, relative to any inertial frame (this is SR) its
trajectory is a hyperbola, which asymptotically approaches c as time
increases without bound.
I don't get this hyperbolic thing. I can draw a hyperbola on a
blank sheet of paper. I don't know what a hyperbolic velocity is.
Given inertial frame S with coordinates (x,t), and a traveler starting
from rest in S at x=0,t=0 with constant proper acceleration a along the
x axis, the velocity u of the traveler relative to S for \tau>=0 is:
u(\tau) = c*tanh(a*\tau/c)
where \tau is the traveler's proper time with \tau=0 when the
acceleration begins. Note that u(0) = 0, and as \tau -> \infinity,
u(\tau) -> c.
The traveler drives along a straight highway. Where's the hyperbola?
In the velocity relative to S as a function of \tau.
Note also that in physics, "proper" means "in the rest frame of the
object in question". So an object's proper speed and proper velocity
are identically zero, making them useless.
So if he computes his velocity, as he watches his accelerometer,
it's meaningless?
No he just has to be careful about what he is doing, and use the relativistic equations. tis includes understanding to which inertial
frame his calculation applies.
The observer is stationary, relative to the ship at t=0. Does he see
the ship accelerate at the same rate as the accelerometer reading?
Let the observer be at rest in S (see above). Since a single observer cannot observe the traveler's acceleration, let me use the inertial
frame S and its (x,t) coordinates to measure it. For the traveler:
at t=0: d^2x/dt^2 = a
for t>0: 0 < d^2x/dt^2 < a
as t->\infinity: d^2x/dt^2 -> 0.
Thank you, Tom, for your patient explanations, even if it's "pearls
before swine" for 95% of the posters here. A few of us learn from them.
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