Two Easy Questions: Mass & Speed Limit of C

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In summary, the conversation discusses the concept of the 'speed limit' of the universe and whether or not an object can reach the speed of light with a finite force applied from within its inertial frame. It is mentioned that the speed limit of c holds true in special relativity, but there is no proof that it holds true in all cases. The speaker suggests a special case where an object with a constant proper acceleration could potentially reach the speed of light with a finite amount of energy. However, the other person in the conversation argues that this is not possible and gives examples to support their argument. The conversation ends with the conclusion that there is no clear example to support the speaker's suggestion.
  • #1
epkid08
264
1
(1) From the length contraction equation, would [tex](L\sqrt{1-(v/c)^2} )^3[/tex] give the coordinate volume of an object?



Here's the mass equation:
[tex]M=\frac{m_0}{\sqrt{1-(v/c)^2}}[/tex]
My second question is ultimately about the 'speed limit' of the universe.

As seen by an observer, an object's mass will approach infinity as its velocity approaches c. From this we can say that, as seen by an observer, it will take a force equal to infinity to accelerate the object to c, and because it's impossible for anything to apply that force, we say that the speed limit of the universe is c.

For the most part this makes perfect sense. As seen by an observer, an object approaching a velocity of c would experience the fallowing: length approaching zero, time approaching infinity, mass approaching infinity etc. This can be easily visualized, as something approaches c, it escapes more and more light, and in theory, if it reached c, the object would vanish, in turn revealing a zero length, infinite time, and a questionably visualized infinite mass.

But what about the proper variables? They don't change with an increase in velocity. Mass, time, and length, by definition, don't change in the object's inertial frame. The object keeps its own rest mass. This is my main point as the 'speed limit' was initially set because the object's coordinate mass approaches infinity, but now I'm saying that an object's mass doesn't change in its inertial frame. That being said, I think it's obvious that the energy required for an object to accelerate itself to c, is in fact finite. Keep in mind, it's very important that the force be applied from within the object's inertial frame. If the force was applied from outside of the frame, it would take an infinite force for the object to reach c.

The speed limit of c holds very true in special relativity. In theory, an observer will NEVER see an object traveling at or faster than c, for more than one reason. To be honest, I see no proof that the speed limit of c holds true in all cases. Obviously there is no proof that faster than light travel is possible, but even if it was very possible, we still wouldn't be able to observe that.

To conclude, in theory, an object can reach the speed of light or greater with a finite force applied to itself from within its inertial frame.

(2) Why wouldn't this statement be true?

(whether or not we know how to initiate the above bolded phrase, doesn't change the theoretical case)
 
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  • #2
1. No, you don't take 1/gamma to the third power, since the length contraction is just in one direction.

2. I can't make sense of the bolded phrase. What would it mean to apply a force within the inertial frame? It sounds like you're going to pull your own hair or something. If you mean that you're going to do something that gives you a constant proper acceleration, that's not enough to get you to reach the speed of light.
 
  • #3
Fredrik said:
1. No, you don't take 1/gamma to the third power, since the length contraction is just in one direction.

2. I can't make sense of the bolded phrase. What would it mean to apply a force within the inertial frame? It sounds like you're going to pull your own hair or something. If you mean that you're going to do something that gives you a constant proper acceleration, that's not enough to get you to reach the speed of light.

I'm not sure what exactly what the bolded phrase would consist of, but that's not my point. I'll try to make a clear example here.

We say you can't accelerate an object to c because the relativistic mass demands a force of infinity to do so. But what if the mass I wanted to accelerate wasn't relativistic at all, if I could "somehow" accelerate myself, it would only take a finite amount of energy to reach c. In this special case, I am my own observer so my rest mass is constant to me, and thus requiring finite energy.

I'm just trying to show that in theory, nothing (yet), stops an object in its inertial frame from obtaining a velocity of c in this way.
 
  • #4
epkid08 said:
That being said, I think it's obvious that the energy required for an object to accelerate itself to c, is in fact finite.
This statement does not make any sense whatsoever.

epkid08 said:
To conclude, in theory, an object can reach the speed of light or greater with a finite force applied to itself from within its inertial frame.
Sorry, but more nonsense.

A rocket with a constant thrust will never reach the speed of light with respect to another object. Not even in the limit because the hyperbolic velocity addition function does in fact have no limit.
 
  • #5
It's not just that I don't know how to accomplish what you're suggesting. It's that I don't know what you're suggesting. I don't think there's any way to make sense of it.

What if I e.g. run behind you and give you a push once per second according to your clock. Even if we ignore the practical problems and how out of shape I am, you would still at best approximate the world line of an object with constant proper acceleration, and constant proper acceleration is definitely not enough to reach c.
 
  • #6
Fredrik said:
It's not just that I don't know how to accomplish what you're suggesting. It's that I don't know what you're suggesting. I don't think there's any way to make sense of it.

What if I e.g. run behind you and give you a push once per second according to your clock. Even if we ignore the practical problems and how out of shape I am, you would still at best approximate the world line of an object with constant proper acceleration, and constant proper acceleration is definitely not enough to reach c.

That's not even close to a proper example of the special case I'm suggesting, and neither is the rocket example.

There is no clear example that we could grasp, I already admitted that. Trying to find an example may or may not be hopeless.

If applied a constant force per time on a rock, its acceleration would drop as its velocity approached c. That's an example of a force from outside of the inertial frame of an object, and becuase it's from outside of the inertial frame, we must use relativistic mass transformation to calculate the mass. If we are bounded to using the relativistic mass tansformation, then we no object with rest mass greater than 0 will ever travel at c or faster. So ask yourself, when are we not bounded to using the relativistic mass transformation? The answer is, when you are the object, when you are in the inertial frame, when you are observing yourself. Being the object in the inertial frame, we don't use the relativistic mass transformation, we use a simple m_0 = M.

This is where you are getting confused. Because you are the object in the inertial frame, and you are supposed to be applying a force, you need to "somehow" apply a force to yourself. (what ever that means, I could be very possibly using the wrong words to describe; there is no example of this thus far)

So, as you "apply a force to yourself" per time, you gain acceleration, and because your mass is not relative to your velocity, the amount of energy needed to accelerate you to c or more is finite.

[tex]E=M_c*c^2[/tex]
M_c signifies that the mass is constant for all v.
 
  • #7
Please note: while the acceleration can be viewed from your frame only, velocity only exists when viewed between two frames. You can't escape the fact that you'll always measure your velocity to be below C.
 
  • #8
epkid08 said:
you need to "somehow" apply a force to yourself.
The big problem here is much more fundamental than the speed limit of c. If I understand you correctly your idea expressed here violates the conservation of momentum, one of the most fundamental laws of the universe.

If you want to invent a magical universe where momentum is not conserved then you are certainly free to decide that in your fantasy-land c won't be a limiting speed either.
 
  • #9
epkid08 said:
That's not even close to a proper example of the special case I'm suggesting, and neither is the rocket example.

There is no clear example that we could grasp, I already admitted that. Trying to find an example may or may not be hopeless.
As I said, the problem isn't to find an example, it's to properly define what you would like to find an example of, and your attempts to do that don't make sense.

epkid08 said:
you need to "somehow" apply a force to yourself.
We seem to be back to pulling our own hair. (But internal forces cancel according to Newton's 3rd, as I'm sure you know).
 
  • #10
It sounds like the OP is thinking about "proper velocity", not relative velocity. Proper velocity is momentum/mass, so it it not limited to c. There's plenty of info on the net about proper velocity, but for most purposes, it's not very useful.

Al
 
  • #11
I have never heard of the term "proper velocity". Wouldn't that always be 0?
 
  • #12
DaleSpam said:
I have never heard of the term "proper velocity". Wouldn't that always be 0?

:smile:

i think it would be, Dale.
 
  • #13
DaleSpam said:
I have never heard of the term "proper velocity". Wouldn't that always be 0?

No. It's momentum/mass, or proper acceleration times proper time. Or, If I travel to a star 10 ly away at 0.8c rel. velocity, I stop at star and divide rest distance by elapsed time on my clock to get (average) proper velocity. In this case, 1.33c is my (average) proper velocity. It's only useful in some cases if it isn't misused. Another way to look at it is, I left Earth 7.5 yrs ago, now I'm 10 ly from earth, at rest with earth, 10 ly/7.5 yr is 1.33c.

There is plenty of info about it on the net, but it's normally not very relevant.

Al
 
  • #14
russ_watters said:
You can't escape the fact that you'll always measure your velocity to be below C.

True, but you're forgetting that the only time an object is observable is when its traveling at less than c. So the time that I was traveling at c, I wouldn't have been able to be measured, and so yes, at every point at which I could have been observed, it would read less than c.
Fredrik said:
We seem to be back to pulling our own hair. (But internal forces cancel according to Newton's 3rd, as I'm sure you know).

Very true, but as I said before, it's not an example of what I'm talking about, as I am not focused on making examples at this point. A few ideas could possibly involve light, but let's not get into personal theories.
DaleSpam said:
The big problem here is much more fundamental than the speed limit of c. If I understand you correctly your idea expressed here violates the conservation of momentum, one of the most fundamental laws of the universe.

If you want to invent a magical universe where momentum is not conserved then you are certainly free to decide that in your fantasy-land c won't be a limiting speed either.

At this point it is just a theoretical case that's completely true. Given that we can "apply a constant force to our self", it would only take a finite amount of energy to accelerate oneself to c.

As far as violating the conservation of momentum, I haven't even suggested an example yet, so you can't really assume so.

One possible idea to get around this, off the top of my head, is some collision with light in a way where energy is transferred to you, but because the light's rest mass is zero, the negative 'action' that is demanded by the conservation of momentum would cancel out, therefore holding the conservation of momentum. (please do not quote this example)

Bolded phrase is my main point of this topic.
 
  • #15
epkid08 said:
Given that we can "apply a constant force to our self", it would only take a finite amount of energy to accelerate oneself to c.

There's no theoretical limit to how much or how long you can accelerate. You could accelerate at 500 G for 10,000,000 yrs. No problem. Your velocity relative to any other mass in the universe will still be measured to be < c.

Al
 
  • #16
epkid08 said:
At this point it is just a theoretical case that's completely true. Given that we can "apply a constant force to our self", it would only take a finite amount of energy to accelerate oneself to c.
Sure. As I said above, if you are going to throw one law out the window you may as well throw the rest out too. Just don't kid yourself that you are discussing anything other than fiction.

epkid08 said:
As far as violating the conservation of momentum, I haven't even suggested an example yet, so you can't really assume so. .
It is not an assumption, if you apply a force to yourself which causes you to accelerate then momentum is not conserved. That is the nice thing about conservation laws: the specific example doesn't matter.
 
  • #17
Al68 said:
There is plenty of info about it on the net, but it's normally not very relevant.
Interesting. You are right, I looked up the wikipedia http://en.wikipedia.org/wiki/Proper_velocity" [Broken] page. That is a really unfortunate name for this concept, it seems to have nothing to do with the usual things associated with the term "proper". Specifically, it is not invariant, and it is not a property measurable in an object's rest-frame.

Thanks Al, it is nice to know that I can learn something even in the silliest threads!
 
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  • #18
Al68 said:
There's no theoretical limit to how much or how long you can accelerate. You could accelerate at 500 G for 10,000,000 yrs. No problem. Your velocity relative to any other mass in the universe will still be measured to be < c.

Al

I already stated that when velocity is able to be measured, it will always be less than c. You are not thinking of this in the correct way. I'll use a relativistic example in attempt to show you.

First of all, we assume that the object is able to apply a force to onself, therefore 'dodging' the relativistic mass equation.

Observer's frame

[tex]t_1[/tex]:An observer witnesses an object increasing its velocity in an unknown manner.

[tex]t_2[/tex]:The object's velocity is approaching c. The object's mass, as viewed by the observer, is seemingly approaching infinity, as well as the other transformations.

[tex]t_3[/tex]:The observer clocks the object at a velocity slightly less than c, and witnesses it decelerate.Object's inertial frame

[tex]t_1[/tex]:The object starts to accelerate, somehow harnessing a force from with its inertial frame, while still upholding the conservation of momentum.

[tex]t_2[/tex]:The object's velocity approaches c, and upon a finite amount of time, the object reaches c, and possibly continues to accelerate. And remember, there is nothing wrong with this, its mass does not approach infinity to the force that was applied to the object, because the force was part of the inertial frame.

[tex]t_{2 + vt}[/tex]:The object maintains its velocity for a period t, then decelerates to a speed under c.

[tex]t_3[/tex]:The object is now traveling at a speed less than c.To conclude, yes you are correct, the observer never observed the object reaching c.
 
  • #19
epkid08 said:
[tex]t_2[/tex]:The object's velocity approaches c, and upon a finite amount of time, the object reaches c, and possibly continues to accelerate. And remember, there is nothing wrong with this, its mass does not approach infinity to the force that was applied to the object, because the force was part of the inertial frame.
This is crackpottery.
 
  • #20
MeJennifer said:
This is crackpottery.

Given the circumstances, which by no means has been disproven thus far, it is true. Whether or not a clear example exists is the question, I've already made suggestions towards one.

The concept itself is really not hard to understand. The proper properties of an object i.e. length, time, mass etc., does not change with velocity. From this we can say that it takes a finite amount of energy for the object to reach c, given that the force is 'proper' in and of it self, which is the hardest part to conceptualize.
 
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  • #21
DaleSpam said:
Sure. As I said above, if you are going to throw one law out the window you may as well throw the rest out too. Just don't kid yourself that you are discussing anything other than fiction.

That is generally the belief of conjectures, until of course, they're proven.
 
  • #22
Hello epkid08.

I may misunderstand what you are trying to say but if you are saying you must apply a force to yourself then it will not work. To every action there is an equal and opposite reaction and so unless you throw some of your bits away from you then movement by such an applied force is impossible. This is of course the principle of rocket propulsion.


As you should well know from the very basics that SR says in your own frame some properties of an object such as length do not change with velocity. But length does change when viewed by another observer moving relative to yourself. It is not just an optical illusion. If you are disputing this then you are disagreeing with SR which of course you are perfectly entitled to do, but at least tell us your objections to the theory.

Matheinste.
 
  • #23
You have not yet said what you mean by "apply a constant force to ourself".

I am reminded of the old (joke) experiment in which you have a boat with mast and sail and an electric fan on the stern. Is that the kind of thing you mean? Do you understand why I said "joke"?
 
  • #24
epkid08 said:
[tex]t_1[/tex]:The object starts to accelerate, somehow harnessing a force from with its inertial frame, while still upholding the conservation of momentum.
Then you are talking about a rocket, which is clearly limited to v<c.
 
  • #25
epkid08 said:
To conclude, in theory, an object can reach the speed of light or greater with a finite force applied to itself from within its inertial frame.

I think you've forgotten the following: Your "inertial speed", your speed relative to yourself, will be zero. Imagine an empty universe, with you traveling in it. What would your velocity be? You've got nothing to compare your velocity with.

This is why what you are proposing, doesn't work: If you somehow manage to get the universe to ignore "every force has an opposite", and have an object accelerate itself, it would appear, from the inertial reference point, that any planet "behind you" is accelerating away. The more you force yourself to go faster, the faster it appears that the planet is moving away from you. However, because of general relativity, the rate of increase in velocity slows.

In essence, my point is that velocity must be measured from another reference frame. You cannot "feel" that you are moving at high rates of speed.
 
  • #26
epkid08 said:
Object's inertial frame

[tex]t_1[/tex]:The object starts to accelerate, somehow harnessing a force from with its inertial frame, while still upholding the conservation of momentum.

[tex]t_2[/tex]:The object's velocity approaches c, and upon a finite amount of time, the object reaches c, and possibly continues to accelerate. And remember, there is nothing wrong with this, its mass does not approach infinity to the force that was applied to the object, because the force was part of the inertial frame.
Once again, an object cannot measure a velocity with respect to itself. So that part is just nonsense.

There is only one velocity and it is the velocity wrt the observer.

I'm guessing you're thinking that the spaceship is applying its engines, feeling a force, and applying f=ma to calculate its speed independent of the observer. It just plain doesn't work that way. As soon as he looks out his window and sees the observer, he realizes that that speed calculation is giving him the wrong answer.
 
  • #27
DaleSpam said:
I have never heard of the term "proper velocity". Wouldn't that always be 0?

Maybe an argument can be made that proper velocity is the same as 4-velocity, which exists independently of its coordinates in any particular frame.

epkid08 seems to be misguided, though.
 
  • #28
This is a good point to end this thread, which has left the realm of accepted physics.
 

1. What is the mass of C?

C is a symbol for the element carbon, which has a standard atomic weight of 12.01 atomic mass units (amu). Therefore, the mass of C is approximately 12.01 amu.

2. What is the speed limit of C?

The speed limit of C refers to the speed of light, which is approximately 299,792,458 meters per second. This is often denoted as 'c' in scientific equations and is considered to be the fastest possible speed in the universe.

3. How is the mass of C determined?

The mass of C is determined by measuring the atomic mass of carbon atoms. This is done using a mass spectrometer, which separates and measures the different isotopes of carbon present in a sample.

4. Can anything travel faster than the speed of C?

According to the theory of relativity, nothing can travel faster than the speed of light. This is considered to be a fundamental physical limit in our universe.

5. How does the speed of C affect the behavior of objects?

The speed of light plays a crucial role in determining the behavior of objects in the universe. It is the maximum speed at which information, energy, and matter can travel. It also affects the perception of time and space, as objects moving at high speeds experience time dilation and length contraction.

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