Question About Relativistic Acceleration

[Physicsguru]

Hello everyone,

I regard myself as the smartest man in the world, and I have two questions for everyone here:

Question 1: Is it possible to accelerate to the speed of light in 24 hours.

Yes or No?

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


Kind regards,

Guru

P.S.: The opening statement is to get the best minds here to criticize a line of reasoning, which leads to the conclusion that the answer is yes, not offend anyone.

:)

 

[jcsd]

No it is impossible in any frame for an object to accelerate from rest to c, any other line of reasoning that suggests otherwise is a priori wrong.

 

[Physicsguru]

No it is impossible in any frame for an object to accelerate from rest to c, any other line of reasoning that suggests otherwise is a priori wrong.

You failed to answer question two, the more important of the two questions.

Kind regards,

Guru

 

[dextercioby]

What do you mean he failed to answer the question??Maybe he didin't say specifically what theory forbids it (theory of relativity),but that was a good & correct answer...

Daniel.

 

[jcsd]

Any particle traveling at c has zero mass and any particle with zero mass travels at c (this is easily shown by examing the four momentum of particles that travel at c), so a massive particle can never travel at c and a massless particle always travels at c. This is a widely knoiw and basic result of relativity.

 

[Physicsguru]

What do you mean he failed to answer the question??Maybe he didin't say specifically what theory forbids it (theory of relativity),but that was a good & correct answer...

Daniel.

He answered question one, and he failed to answer question two.

Saying that the theory of relativity dictates the answer, is like saying the sky is green, because you read it in the Enquirer.

Kind regards,

Guru

 

[Physicsguru]

Any particle traveling at c has zero mass and any particle with zero mass travels at c (this is easily shown by examing the four momentum of particles that travel at c), so a massive particle can never travel at c and a massless particle always travels at c. This is a widely knoiw and basic result of relativity.

Firstly, how does knowing that any particle traveling at c has an inertial mass of zero imply that the answer to question one is no, and secondly, can you prove that any particle traveling at c has zero mass?

Kind regards,

Guru

 

[JesseM]

He answered question one, and he failed to answer question two.

Saying that the theory of relativity dictates the answer, is like saying the sky is green, because you read it in the Enquirer.

The difference is that there is an awful lot of evidence that relativity is correct in all its various predictions, including the equation for how energy increases with velocity, which implies an object with finite rest mass would need infinite energy to move at c.

Why don't you just explain your idea for how it is possible to reach the speed of light through acceleration, so people can criticize it?

 

[jcsd]

Firstly, how does knowing that any particle traveling at c has an inertial mass of zero imply that the answer to question one is no, and secondly, can you prove that any particle traveling at c has zero mass?

Kind regards,

Guru

Actually particles traveling at c don't strictly have zero 'inertial mass' (though some may argue what exactly inertial mass is), they do however have have a zero (rest) mass, the reason I mentioned this is to exclude the case of zero rest mass particles accelarting from rest to c.

The four moemntum of a particle is parallel to a particles worldline, this comes from the definition P = mU. The magnitude of the four moemntum is it's mass, if that mass is zero then the magnitude of the four momentum is non-zero and hence it is not a null vector which means the worldline is not null and the particle does not travel at c.

 

[Physicsguru]

Actually particles traveling at c don't strictly have zero 'inertial mass' (though some may argue what exactly inertial mass is), they do however have have a zero (rest) mass, the reason I mentioned this is to exclude the case of zero rest mass particles accelarting from rest to c.

The four moemntum of a particle is parallel to a particles worldline, this comes from the definition P = mU. The magnitude of the four moemntum is it's mass, if that mass is zero then the magnitude of the four momentum is non-zero and hence it is not a null vector which means the worldline is not null and the particle does not travel at c.

In question one, I made no reference to the kind of object being accelerated, be it particle or large body. For the sake of definiteness, let me rephrase question one as follows:

Question one: Is it possible to accelerate a large body from rest to the speed of light in 24 hours?


(As an aside, can you prove that the rest mass of any particle traveling at c, must be zero?)

 

[jcsd]

Whether the body is spatially extended or not makes no difference (plus all bodies are made of particles anyway).

I suppose you could have some hypothetical body of zero rets mass mving at less than c, but it woldn't have any phsyical properties as it has an enrgy of zero, so most people would be more inclined to call it empty space.

 

[JesseM]

(As an aside, can you prove that the rest mass of any particle traveling at c, must be zero?)

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.

 

[marlon]

Question one: Is it possible to accelerate a large body from rest to the speed of light in 24 hours?

It would take an infinite amount of time to accelerate a massive body to the speed of light.

The posts of JCSD are completely CORRECT.

regards
marlon

 

[Physicsguru]

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.

How do you respond to this:

P = mv = \frac{h}{\lambda}

Therefore:

m = \frac{h}{\lambda v}

Suppose that m=0, and v=c. Therefore:

0 = \frac{h}{\lambda c}

Therefore:

0 = \frac{1}{\lambda}

From which it follows that lambda is infinite. Since nothing can have an infinite wavelength, either not (m=0) or not (v=c). Since you are stipulating that v=c, it must be the case that not (m=0), contrary to your conclusion.

Regards,

Guru

 

[JesseM]

How do you respond to this:

P = mv = \frac{h}{\lambda}

This equation is not correct in relativity, where if m_0 is the rest mass, p = m_0 v/\sqrt{1 - v^2/c^2}

 

[dextercioby]

How do you respond to this:

P = mv = \frac{h}{\lambda}

Therefore:

m = \frac{h}{\lambda v}

Suppose that m=0, and v=c.

I'm afraid your line of argument is not correct.The first formula u posted (interpreted in the assumption m=0) would indicate that "m" is the rest mass and that the formula P=mv would be purely NONRELATIVISTIC.However,it's easy to see that in nonrelativistic physics the "m=0" does not make any sense (the concept of REST MASS doesn't make sense,as it is simply absolute)...


Daniel.

 

[Physicsguru]

This equation is not correct in relativity, where if m_0is the rest mass,

p = m_0 v/\sqrt{1 - v^2/c^2}

Let m0 = rest mass, and let M = relativistic mass. Let v = speed of center of mass, in some reference frame. let h = Planck's constant of nature, and let lambda denote 'wavelength.'

Definition: P= momentum = Mv

Therefore we have:

Mv = \frac{m_0v}{\sqrt{1-v^2/c^2}} = \frac{h}{\lambda}

I now ask you this, can the wavelength undergo length contraction or not?

Regards,

Guru

 

[JesseM]

Let m0 = rest mass, and let M = relativistic mass. Let v = speed of center of mass, in some reference frame. let h = Planck's constant of nature, and let lambda denote 'wavelength.'

Definition: P= momentum = Mv

Therefore we have:

Mv = \frac{m_0v}{\sqrt{1-v^2/c^2}} = \frac{h}{\lambda}

I now ask you this, can the wavelength undergo length contraction or not?

Regards,

Guru

the left and middle part of your equation becomes undefined if the rest mass is zero and the velocity is c. But sure, for a particle with nonzero rest mass moving at velocity less than c, the wavelength becomes smaller the higher its velocity.

 

[Physicsguru]

the left and middle part of your equation becomes undefined if the rest mass is zero and the velocity is c. But sure, for a particle with nonzero rest mass moving at velocity less than c, the wavelength becomes smaller the higher its velocity.

What is the formula for the wavelength in terms of velocity?

Kind regards,

Guru

 

[JesseM]

What is the formula for the wavelength in terms of velocity?

Kind regards,

Guru

For a particle moving at a velocity slower than light, it's just \lambda = (h\sqrt{1 - v^2/c^2})/m_0v. But this equation has no well-defined limit as you let m_0 approach 0 and let v approach c.

 

[dextercioby]

*For light waves:
\lambda=\frac{c}{\nu}
*For matter waves (de Broglie) associated to relativistic massive particles it can be deduced from the equality u posted...

What are u trying to prove/learn here?

Daniel.

 

[Physicsguru]

For a particle moving at a velocity slower than light, it's just \lambda = (h\sqrt{1 - v^2/c^2})/m_0v. But this equation has no well-defined limit as you let m_0 approach 0 and let v approach c.

Would a relativistic analysis yield the following formula:

\lambda = \lambda_0 \sqrt{1-v^2/c^2}

?

Regards,

Guru

 

[Physicsguru]

*For light waves:
\lambda=\frac{c}{\nu}
*For matter waves (de Broglie) associated to relativistic massive particles it can be deduced from the equality u posted...

What are u trying to prove/learn here?

Daniel.

In this post, I am interested in "matter waves," but in this "side issue" i am leaving things up to Jesse, since he is the individual who asserted that any particle which moves with speed c, has a rest mass of zero. That's why I am asking him a few questions, since he is the one who made the assertion.

As for what I am trying to prove/learn here, I am trying to learn whether or not anyone here knows whether or not it is possible to accelerate a large body from rest to the speed of light in 24 hours.

Kind regards,

Guru

 

[dextercioby]

Who's \lambda_{0} ?


Daniel.

 

[dextercioby]

As for what I am trying to prove/learn here, I am trying to learn whether or not anyone here knows whether or not it is possible to accelerate a large body from rest to the speed of light in 24 hours.

Kind regards,

Guru

Lemme join marlon & jcsd in telling you that accelerating a large body from rest to the speed of light in 24 hours is IMPOSSIBLE WITH THE PHYSICAL KNOWLEDGE MANKIND HAS PRODUCED BETWEEN 1905 AND 2005...

Daniel.

 

[JesseM]

Would a relativistic analysis yield the following formula:

\lambda = \lambda_0 \sqrt{1-v^2/c^2}

Is \lambda_0 supposed to be some sort of "rest wavelength"? That doesn't make sense, because as you can see by examining the equation for the DeBroglie wavelength \lambda = h/p, the wavelength goes to infinity as the momentum goes to zero.

 

[JesseM]

For a particle moving at a velocity slower than light, it's just \lambda = (h\sqrt{1 - v^2/c^2})/m_0v. But this equation has no well-defined limit as you let m_0 approach 0 and let v approach c.

Actually come to think of it I'm not completely sure that this equation is correct, because it's mixing an equation from relativity, p = m_0 v / \sqrt{1 - v^2/c^2}, with an equation from nonrelativistic QM, \lambda = h/p. Does anyone know if the equation for the DeBroglie wavelength also makes sense in relativistic QM/quantum field theory?

 

[russ_watters]

To put it more simply, you're using the Newtonian physics equation for momentum in a way that it was never intended and quite simply doesn't work (those are two separate flaws in your line of reasoning): it only works for objects with mass and it only works at low velocity.

edit: that equation is irrelevant anyway. Your question asks about accelerating an object with mass (presumably...) to C. Acceleration of a massive object to C has been predicted theoretically and proven experimentally to be impossible. And objects without mass (photons) do not "accelerate to c."

 

[jcsd]

In this post, I am interested in "matter waves," but in this "side issue" i am leaving things up to Jesse, since he is the individual who asserted that any particle which moves with speed c, has a rest mass of zero. That's why I am asking him a few questions, since he is the one who made the assertion.

As for what I am trying to prove/learn here, I am trying to learn whether or not anyone here knows whether or not it is possible to accelerate a large body from rest to the speed of light in 24 hours.

Kind regards,

Guru

1) matter waves are uninteresting in this context as if you treat them as classical plane waves then they are incompatible with both relativity and infact non-relativstic mechanics. That is to say you cannot treat them as actual waves and always expect to get meaningful results especially within relativity. In this case it is esepcially unintersing as soon as you consider the effects of time dialtion/length contraction on matter waves I don't see how you cannot get the wrong answer if you naively treat them ason the same footing as classical EM waves rather than giving them the fall QM treatment.

2) I have already shown that a particle that moves with speed c (i.e. has a null worldline) has a rest mass of zero

3) It's already been shown that in any frmae thta it is impossible to accelerate a particle (or indeed any body) from rest to c within any finite period of time.

 

[Physicsguru]

Here is where I was going with this. Suppose that:

\lambda = \lambda_0 \sqrt{1-v^2/c^2}

Therefore, the following equation would be a true statement:

Mv = \frac{m_0v}{\sqrt{1-v^2/c^2}} = \frac{h}{\lambda_0 \sqrt{1-v^2/c^2} }

From which it would follow that:

Mv = m_0v = \frac{h}{\lambda_0 }

Suppose now, that v=c. Therefore, it would follow that:

m_0c = \frac{h}{\lambda_0 }

Since not (c=0), it would therefore follow that:

m_0 = \frac{h}{c \lambda_0 }

Now, suppose that if v=c then m_0=0. It therefore follows that:

0 = \frac{h}{c \lambda_0 }

Since wavelength cannot be infinite, it therefore follows that Planck's constant is equal to zero, and that's known to be false. Therefore, it is not the case that if v=c then m_0=0.

Therefore, granted that v=c, it necessarily follows that not(m_0=0), which is the contrary of the assertion that if the speed of a particle is c, then it necessarily has a zero rest mass.

Obviously, you must end up disagreeing with some step which I have made, so I now ask you, which one?

Regards,

Guru

 

[russ_watters]

Mv = \frac{m_0v}{\sqrt{1-v^2/c^2}} = \frac{h}{\lambda_0 \sqrt{1-v^2/c^2} }

Obviously, you must end up disagreeing with some step which I have made, so I now ask you, which one?

Step 2, above, is false, for reasons already stated.

 

[Physicsguru]

Step 2, above, is false, for reasons already stated.

Russ, Energy=hf, therefore h has units of Kg m^2/s. Therefore, h divided by a quantity with units of length has units of classical momentum. How can you simply dismiss setting Mv equal to \frac{h}{\lambda}? You have said they are unequal, but how do you know that?

Kind regards,

Guru

 

[JesseM]

Here is where I was going with this. Suppose that:

\lambda = \lambda_0 \sqrt{1-v^2/c^2}

It was already pointed out to you that this equation makes no sense--what is \lambda_0? If you know that p=0 exactly (which in classical mechanics is what is meant by an object's rest frame), then the DeBroglie wavelength \lambda is infinite.

 

[Physicsguru]

It was already pointed out to you that this equation makes no sense--what is \lambda_0? If you know that p=0 exactly (which in classical mechanics is what is meant by an object's rest frame), then the DeBroglie wavelength \lambda is infinite.

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."

Kind regards,

Guru

 

[russ_watters]

Russ, Energy=hf, therefore h has units of Kg m^2/s. Therefore, h divided by a quantity with units of length has units of classical momentum. How can you simply dismiss setting Mv equal to \frac{h}{\lambda}? You have said they are unequal, but how do you know that?

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.

For the experimentation, well, there are lots of examples. Particle accelerators, for a start.

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

 

[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.