Question About Relativistic Acceleration

[jcsd]

Yes infact even if you assume your approach is correct (which it is not see the De Broglie paradox) JesseM's answer is entriely sufficent when v = c lambda_0 has no possible meaning.

 

[Physicsguru]

Ok, we are digressing from the central point of this thread. I thought about it last night, and I didn't actually ask question one, as I fully intended. Let me re-ask both questions:

Question 1: Is it possible to accelerate a body with living beings inside, from rest to the speed of light in 24 hours, such that they remain alive?

Question 2: If the answer to question one is yes, why is it yes; and if the answer to question one is no, why is it no?

P.S. As for whether or not particles moving at speed c have a zero rest mass or not, I would just as soon leave that for another thread.

Kind regards,

Guru

 

[JesseM]

How have you drawn the conclusion that the equation makes no sense? I agree with you, that without an interpretation for $$\lambda_0$$, the equation will never "make sense."

Because putting a little 0 in subscript usually means the quantity is evaluated in the particle's rest frame. If that's not what you mean, then please supply the meaing of $$\lambda_0$$.

 

[Physicsguru]

Because putting a little 0 in subscript usually means the quantity is evaluated in the particle's rest frame. If that's not what you mean, then please supply the meaing of $$\lambda_0$$.

That is exactly how I would interpret $$\lambda_0$$ in that formula. So why would that interpretation be meaningless? Also, please note that I do not wish to digress from the main question, which seems to be happening. I never meant for this question to be about particles, I meant for it to be about large bodies accelerating with living occupants inside.

Kind regards,

Guru

 

[JesseM]

Ok, we are digressing from the central point of this thread. I thought about it last night, and I didn't actually ask question one, as I fully intended. Let me re-ask both questions:

Question 1: Is it possible to accelerate a body with living beings inside, from rest to the speed of light in 24 hours, such that they remain alive?

Given that people have already answered "no" for the case of any object with nonzero rest mass, I think you can figure out what our answer to this one would be.

Question 2: If the answer to question one is yes, why is it yes; and if the answer to question one is no, why is it no?

As I said before:

Because the energy of an object with rest mass $$m_0$$ moving at velocity $$v$$ is $$E = m_0 c^2 / \sqrt{1 - v^2 / c^2}$$...if $$m_0$$ is nonzero, then as $$v$$ approaches $$c$$, the energy approaches infinity.

 

[JesseM]

That is exactly how I would interpret $$\lambda_0$$ in that formula. So why would that interpretation be meaningless?

Because if p=0, $$\lambda$$ is infinite.

Also, please note that I do not wish to digress from the main question, which seems to be happening. I never meant for this question to be about particles, I meant for it to be about large bodies accelerating with living occupants inside.

Macro-objects have a DeBroglie wavelength too, it's still given by the formula $$\lambda = h/p$$

 

[Physicsguru]

JesseM, you are making an error, and rather than prattle on, let me ask the main question again:

Question: Is it possible for a large body to accelerate from rest to the speed of light in 24 hours, in such a way that the occupants remain alive for the duration of the trip?

Unless you know for certain that the relativistic energy formula is correct, you cannot use that formula to arrive at certainty as to the possibility or impossibility of the scenario I am asking about. I do not agree that the relativistic energy formula is correct.

Regards,

Guru

 

[JesseM]

JesseM, you are making an error

perhaps you should point it out then.

Unless you know for certain that the relativistic energy formula is correct

I don't know it for certain. Likewise, I don't know for certain that the Earth is round. But there is plenty of evidence for both theories. Do you have an alternate theory that can explain all the observations that are used to support relativity, but which predicts a different formula for the relation between energy and velocity?

 

[Physicsguru]

perhaps you should point it out then. I don't know it for certain. Likewise, I don't know for certain that the Earth is round. But there is plenty of evidence for both theories. Do you have an alternate theory that can explain all the observations that are used to support relativity, but which predicts a different formula for the relation between energy and velocity?

Yes I do, and it involves a temperature term, but forget about that formula. My question in this thread is meant to be taken as, "what if you don't know for certain that E=Mc^2, but you want to try to answer this question with certainty, can you do it?" That's sort of what I'm after here. This question is actually intended to be a GIGANTIC mental challenge, not another "oh I will just tell him it goes against relativity so he's wrong" thread.

Kind regards,

Guru

 

[JesseM]

Yes

Kind regards,

Guru

Well, lay it on me, baby! Do you think your theory could make correct quantitative predictions about all the experiments listed here, for example? Could you predict the number of http://www.prestoncoll.ac.uk/cosmic/muoncalctext.htm ?

 

[JesseM]

My question in this thread is meant to be taken as, "what if you don't know for certain that E=Mc^2, but you want to try to answer this question with certainty, can you do it?"

No, it is impossible to be certain of anything in science, including the roundness of the earth. But if you want to answer the question with a high level of confidence, just do lots of experiments to test that the energy formula (along with other basic formulas in relativity like the time dilation formula) is in fact correct.

 

[Physicsguru]

This thread is not about a new theory of energy, it's about a real answer to an answerable question.

Is it, or isn't is possible to accelerate living beings from rest to the speed of light in 24 hours, such that they remain alive for the duration of the trip?

You are so entangled in relativistic effects, you have forgotten about the greatest impediment to the answer being yes, which is that they will be crushed by the g-forces long before coming even close to c. I would think you must deal with that issue at some point.

Kindest regards,

Guru

 

[JesseM]

You are so entangled in relativistic effects, you have forgotten about the greatest impediment to the answer being yes, which is that they will be crushed by the g-forces long before coming even close to c. I would think you must deal with that issue at some point.

g-forces only depend on acceleration, not on velocity (this is true in Newtonian mechanics as well as relativity). So if I accelerate at $$9.8 m/s^2$$ throughout the trip, I will feel earth-type-gravity the whole time, even as I get arbitrarily close to the speed of light.

 

[Physicsguru]

g-forces only depend on acceleration, not on velocity. So if I accelerate at $$9.8 m/s^2$$ throughout the trip, I will feel earth-type-gravity the whole time, even as I get arbitrarily close to the speed of light.

Ok, well this is a start. Suppose, as you say, that you accelerate at $$9.8 m/s^2$$ throughout the trip, how long will it take you to reach the speed of light? (Is your answer anywhere near 24 hours?)

Regards,

Guru

 

[JesseM]

Ok, well this is a start. Suppose, as you say, that you accelerate at $$9.8 m/s^2$$ throughout the trip, how long will it take you to reach the speed of light? (Is your answer anywhere near 24 hours?)

Infinite time. Acceleration doesn't work the same way in relativity that it does in Newtonian mechanics, your velocity at time t in a given frame won't just be (acceleration rate)*(time since your velocity was zero in that frame). See Acceleration in Special Relativity.

 

[Physicsguru]

Like I said before, we know they are unequal from both theory and experimentation. For the theory, Newton did not intend for momentum to be used that way when he wrote his momentum equation, and Einstein didn't intend for it to be used that way when he wrote his part. You're mixing classical mechanics with Relativity. In addition, it is well known that classical mechanics is flawed.

How is classical mechanics flawed?

Why do you think that simply having the same units makes them equal?

I don't think that they are equal, but I do think that they are proportional.

Kind regards,

Guru

 

[Physicsguru]

Infinite time. Acceleration doesn't work the same way in relativity that it does in Newtonian mechanics, your velocity at time t won't just be (acceleration rate)*(time since your velocity was zero).

Let me try this a different way JesseM. Suppose that you are in a ship which is accelerating at 9.8 m/s^2. If you start from rest, how fast will your ship be moving after 24 hours?

Regards,

Guru

 

[JesseM]

Let me try this a different way JesseM. Suppose that you are in a ship which is accelerating at 9.8 m/s^2. If you start from rest, how fast will your ship be moving after 24 hours?

24 hours according to the onboard clock, or according to clocks in the inertial frame that the ship started out at rest in?

 

[jcsd]

Physics guru the answer to you question s have been given, is this thread going anywhere? The only challenge I see are your misconceptions onn relativity.
As for accelartion if you mean extrinsic acceleration (i.e. the coordinate accelartion as measured form some inertial frame) then it is impossible to maintain an extrinsic accelartion of 9.8 m/s^2 indefintely as you soon find the force required to keep up that accelartion is infinite. If you mean intrinsic acceleration, then yes you can maintin an instrinsic accelartion of 9.81 m/s^2 indefintely, but you will never reach a velocity of c or greater in any inertial frame.

 

[Physicsguru]

24 hours according to the onboard clock, or according to clocks in the inertial frame that the ship started out at rest in?

Give the answer in both frames.

(I would also suggest that you cover both cases case 1) relativity correct, case 2) relativity incorrect).

Regards,

Guru

 

[Physicsguru]

Physics guru the answer to you question s have been given, is this thread going anywhere? The only challenge I see are your misconceptions onn relativity.
As for accelartion if you mean extrinsic acceleration (i.e. the coordinate accelartion as measured form some inertial frame) then it is impossible to maintain an extrinsic accelartion of 9.8 m/s^2 indefintely as you soon find the force required to keep up that accelartion is infinite. If you mean intrinsic acceleration, then yes you can maintin an instrinsic accelartion of 9.81 m/s^2 indefintely, but you will never reach a velocity of c or greater in any inertial frame.

JCSD the answer is not as simple as the question appears. To put this another way, no one is addressing the question in an epistemologically correct manner, since no one is actually certain that E=Mc^2. This is supposed to be a hard question, which eventually leads to the Meissner effect, but this thread is nowhere near that point yet.

Regards,

Guru

 

[quantumdude]

JCSD the answer is not as simple as the question appears.

Yes, it is. According to the best information we have, it is not possible to accelerate any massive object to a speed of c in any finite amount of time.

To put this another way, no one is addressing the question in an epistemologically correct manner, since no one is actually certain that E=Mc^2.

You're asking the members of this Forum to make a scientific prediction. No such prediction is ever certain. Furthermore, no one is relying on E=mc². That equation describes a particle at rest. The respondents to your question are referring to relativistic kinematics.

But in any case, we are as sure of both E=mc² and of relativistic kinematics as we are of anything else in science.

This is supposed to be a hard question, which eventually leads to the Meissner effect, but this thread is nowhere near that point yet.

Why don't you just make your point?

 

[jcsd]

No it's a rather simplistic question that has alreday been answered and as for the relevance of the Meissner effect I really can't see where you're going. If you think there is something being missed it is best you actually say what it is rather than leading everyone on a wild goose chase as the answer already given is undeniably corrcet (within the context of relativty, if you're talking baout any other context then why post it in this forum?) so if you've got another answer you have made a mistake.

 

[JesseM]

Give the answer in both frames.

(I would also suggest that you cover both cases case 1) relativity correct, case 2) relativity incorrect).

OK, you can see the equations for velocity as a function of time (both proper time and coordinate time) for constant acceleration according to relativity on http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html page. For onboard time T, the equation is:
$$v = c*tanh(aT/c)$$
It's easier to evaluate this equation if you use units of years and light-years instead of meters and seconds, since c=1 in these units; the page mentions that an acceleration of $$9.8 m/s^2$$ is approximately equal to $$1.03 lyr/yr^2$$. Meanwhile, 1 day = 1/365 years, or about 0.00274 years, so aT/c will be about 0.00282 in these units. Here is a graphing calculator applet that can do the tanh function--in this case, if I type tanh(0.00282) and click the "Eval" button, I get back a number which is still approximately equal to 0.00282, I guess because tanh(x) is close to x when x is close to zero. So, this means that after 24 hours of onboard time, the velocity would be about 0.00282c.

For time in the reference frame where the velocity is being measured, the equation given is:
$$v = at/\sqrt{1 + (at/c)^2}$$
So, with a = 1.03 and t=0.00274, this will also be very close to 0.00282c. I guess you'd need a significantly larger time or acceleration for there to be any noticeable difference.

As for covering the case 2), "relativity incorrect", there would of course be an infinite number of possible answers depending on what alternate theory you choose. For example, one of these theories would be that anyone who accelerates at 1G for exactly 24 hours is instantly transported away from our universe and into smurfworld, where they live smurfilly ever after moving at velocity smurf. Did you have a specific theory in mind?

 

[Physicsguru]

No it's a rather simplistic question that has alreday been answered and as for the relevance of the Meissner effect I really can't see where you're going. If you think there is something being missed it is best you actually say what it is rather than leading everyone on a wild goose chase as the answer already given is undeniably corrcet (within the context of relativty, if you're talking baout any other context then why post it in this forum?) so if you've got another answer you have made a mistake.

The question isn't simplistic at all. No one here has been handling accelerating reference frames very well.

Regards,

Guru

 

[jcsd]

The question isn't simplistic at all. No one here has been handling accelerating reference frames very well.

Regards,

Guru

You don't need to use accelerated frames here (if you are talking about accelerated frames you need to specifcally say so), infact I've specifcally been careful to always make it clear thta I'm talking about inertial frames only as bodies can have coordinate speeds of greater than c in non-inertial frames (that fact is pretty trivial).

 

[quantumdude]

You don't need to use accelerated frames here (if you are talking about accelerated frames you need to specifcally say so),

I think he means the rocket, which is accelerating.

 

[jcsd]

I think he means the rocket, which is accelerating.

that's what I thought possibly, but by defintion the coordinate speed of the accelarted rocket in it's own frame is zero (it's intrinsic accelartion is it's accelartion relative to it's momentarily comoving inertial frame, however the mometarily comoving inertial frame is different at each instant).

 

[Physicsguru]

24 hours according to the onboard clock, or according to clocks in the inertial frame that the ship started out at rest in?

Give me the answer in both frames.

Regards,

Guru

 

[JesseM]

Give me the answer in both frames.

I already did--did you miss my post on the last page?

 

[Physicsguru]

I already did--did you miss my post on the last page?

Yes I did miss it, and I just went back and read it, and of course you arrived at what I expected... namely that you would need a far larger acceleration to be anywhere near c, after 24 hours.

So now, let me ask you this. What would the rate of accleration have to be, in order for you to be near the speed of light after one day?

 

[JesseM]

So now, let me ask you this. What would the rate of accleration have to be, in order for you to be near the speed of light after one day?

Just solve the two equations I gave for a and you should be able to find the answer. Have a stab at it yourself, and if you have trouble I'll help you out.

 

[Physicsguru]

Just solve the two equations I gave for a and you should be able to find the answer. Have a stab at it yourself, and if you have trouble I'll help you out.

It's a trivial problem.

initial speed=0
final speed = 299792458 m/s
t = 24 hours = 24*3600 seconds

Vf=Vi + at

299792458 = a 24*3600

a = 299792458/(24*3600) m/s^2

Guru

 

[JesseM]

It's a trivial problem.

initial speed=0
final speed = 299792458 m/s
t = 24 hours = 24*3600 seconds

Vf=Vi + at

No, this equation would only be correct in Newtonian physics. Like I said before, in relativity your velocity after accelerating from rest for time t is not at. I meant you should try solving the equations I gave in my previous post for a to see how this works in relativity.

 

[ZapperZ]

It's a trivial problem.

initial speed=0
final speed = 299792458 m/s
t = 24 hours = 24*3600 seconds

Vf=Vi + at

299792458 = a 24*3600

a = 299792458/(24*3600) m/s^2

Guru

This calculation, of course, isn't valid. It's one of the traps a good physics instructor, teaching a class in SR, would lay onto the students.

To be able to use that kinematical equation, one has made an explicit assumption that the force (or dp/dt) applied to the object is a constant. But we know this isn't true in the observer's reference frame (the one who is observiing and measuring this vf and vi). As the velocity of the object increases, the observer is also seeing an increase in the mass (relativistic mass) of the object. Thus, to maintain a constant acceleration, the applied force has to increase. Immediately, that simply, first-year kinematic equation is no longer valid. And if, instead, one maintains that constant force, then the acceleration is no longer a constant (again due to the increasing mass) and you again can't use that kinematical equation.

Zz.