Place to discuss the Theory of Relativity

[EnumaElish]

I looked up Aer's link. I see the 4 postulates are:
"Space and time form a 4-dimensional continuum".
"There exist global spacetime frames with respect to which unaccelerated objects move in straight lines at constant velocity".
"The speed of light c is a universal constant, the same in any inertial frame".
"The laws of physics are the same in any inertial frame, regardless of position or velocity".
Which of these statements conflict with the concept of "relativistic mass"? My uneducated guess is, none does.

My next question is, does "relativistic mass" add anything that is not already explained by these postulates? My uneducated answer is, if you had to explain relativity to someone like myself, it just might. I also hear pervect saying "it may also confuse people"; I am with you there. At this point I agree to make a tactical concession because of this (pedagogical) point, but am not yet ready to make a strategic retreat until and unless someone can show exactly which of the postulates is being violated by it.

 

[learningphysics]

You seem to equate infinity with non-physical. That is not the case. Infinitity is just an upper limit greater than the scope of what you are analyzing. A small amount of experience in the real world, rather than the theoretical world may help you realize this.

Define non-physical.

 

[learningphysics]

As measured by whom? The muon would not say that it's mass is increasing as we say it's speed is increasing

I was referring to weight (not mass) as measured by someone at rest on the Earth, while the muon is speeding.

Show experimental proof.

General relativity rests on gravitational mass being equal to inertial mass. I'm surprised that you're asking for proof. Anyway, Wikipedia lists a few experiments that showed no difference in the two:

http://en.wikipedia.org/wiki/Equivalence_principle#Tests_of_the_weak_equivalence_principle

 

[Aer]

Define non-physical.

Something that is physically impossible. Exceeding the speed of light is physcially impossible. If we assume a ship accelerates constantly as seen by the stationary Earth, then the ship would have to eventually exceed the speed of light in order to accelerate forever. Now you might wonder how this relates to relativistic mass (I assume so given what you posted below!) Relativistic mass is the mass of the said ship as measured in the Earth frame so that the Earth frame knows how much energy the ship most expend in or to have this constant accleration according to the Earth frame. So using this analysis you are going to say that the ship can exceed the speed of light - that is non-physical.

The normal interpretation of when someone says a ship accelerates at a constant rate is that the ship accelerates at a constant rate as seen by the ship's instantaneous inertial reference frame (i.e., the inertial reference frame of its instantaneous velocity). Now in this interpretation one does not use relativistic mass to calculate the energy expended to keep this constant acceleration. In fact the energy expended is constant for this case and the ship will never exceed the speed of light even if it accelerates for all eternity. This is an example of a physical situation.

I was referring to weight (not mass) as measured by someone at rest on the Earth, while the muon is speeding.



General relativity rests on gravitational mass being equal to inertial mass. I'm surprised that you're asking for proof. Anyway, Wikipedia lists a few experiments that showed no difference in the two:

http://en.wikipedia.org/wiki/Equivalence_principle#Tests_of_the_weak_equivalence_principle

Tell me how "These experiments demonstrate that all objects fall at the same rate when the effect of air resistance is either eliminated or negligible." relates to relativistic mass. You seem very confused.

 

[learningphysics]

Something that is physically impossible. Exceeding the speed of light is physcially impossible. If we assume a ship accelerates constantly as seen by the stationary Earth, then the ship would have to eventually exceed the speed of light in order to accelerate forever. Now you might wonder how this relates to relativistic mass (I assume so given what you posted below!) Relativistic mass is the mass of the said ship as measured in the Earth frame so that the Earth frame knows how much energy the ship most expend in or to have this constant accleration according to the Earth frame. So using this analysis you are going to say that the ship can exceed the speed of light - that is non-physical.

It is non-physical because it requires an infinite amount of energy.

The normal interpretation of when someone says a ship accelerates at a constant rate is that the ship accelerates at a constant rate as seen by the ship's instantaneous inertial reference frame (i.e., the inertial reference frame of its instantaneous velocity). Now in this interpretation one does not use relativistic mass to calculate the energy expended to keep this constant acceleration. In fact the energy expended is constant for this case and the ship will never exceed the speed of light even if it accelerates for all eternity. This is an example of a physical situation.

No it is not. To accelerate for all eternity, the ship needs an infinite amount of fuel. This is physically impossible.

Tell me how "These experiments demonstrate that all objects fall at the same rate when the effect of air resistance is either eliminated or negligible." relates to relativistic mass. You seem very confused.

What are you talking about? You wanted experiments that showed that inertial mass=gravitational mass. That's what I gave you.

 

[Aer]

It is non-physical because it requires an infinite amount of energy.

Wrong, the fact that it takes infinite amount of energy doesn't prevent you from assuming you have this infinite amount of energy. Prove that there is a finite amount of energy in the universe. Or, prove that there is no way possible to take energy from another universe and that there are not an infinite number of universes.

No it is not. To accelerate for all eternity, the ship needs an infinite amount of fuel. This is physically impossible.

As I said, prove that you cannot have an infinite amount of energy. Just because something is impossible practically doesn't prevent it theoretically.

What are you talking about? You wanted experiments that showed that inertial mass=gravitational mass. That's what I gave you.

I did not ask for any such thing, I asked you to prove that relativistic mass is in anyway related to this. Please check your definition of inertial mass

 

[EnumaElish]

the fact that it takes infinite amount of energy doesn't prevent you from assuming you have this infinite amount of energy. Prove that there is a finite amount of energy in the universe. Or, prove that there is no way possible to take energy from another universe and that there are not an infinite number of universes.

Aha! So, what you're saying Aer, is that if one had access to an infinite amount of energy then they could surpass the lightspeed provided that their only constraint was an infinite relativistic mass that was becoming a huge burden on them (and the rest of the physics worked Newtonianly). I don't see an infinite amount of energy boosting an infinite amount of relativistic mass to, or above, a definite speed (c). I don't see an infinite amount of energy pushing an infinite relativistic mass to any definite (in your vocabulary, "physical") speed at all. If I had to guess, I'd put my money on infinite relativistic mass winning against infinite energy; because relativistic mass is a function of velocity (first order) whereas reaching lightspeed is a matter of acceleration (second order). First order beats second order. But I'd be content with the answer being indeterminate.

 

[Aer]

Aha! So, what you're saying Aer, is that if one had access to an infinite amount of energy then they could surpass the lightspeed provided that their only constraint was an infinite relativistic mass that was becoming a huge burden on them (and the rest of the physics worked Newtonianly). I don't see an infinite amount of energy boosting an infinite amount of relativistic mass to, or above, a definite speed (c). I don't see an infinite amount of energy pushing an infinite relativistic mass to any definite (in your vocabulary, "physical") speed at all. If I had to guess, I'd put my money on infinite relativistic mass winning against infinite energy; because relativistic mass is a function of velocity (first order) whereas reaching lightspeed is a matter of acceleration (second order). First order beats second order. But I'd be content with the answer being indeterminate.

You are correct to say that the speed of light would never be exceeded, but in order for this to happen, the acceleration as measured by the Earth rest frame would have to deviate from constant thus rendering your relativistic mass useless. You are getting too hung up on infinities.

 

[EnumaElish]

You are correct to say that the speed of light would never be exceeded, but in order for this to happen, the acceleration as measured by the Earth rest frame would have to deviate from constant thus rendering your relativistic mass useless. You are getting too hung up on infinities.

Hold on -- how is it that c will never be exceeded in a Newtonly universe (except there is relativistic mass)? Suppose none of the 4 postulates hold. Also suppose relativistic mass \nearrow as v \nearrow. Under the circumstances, what is constraining v becoming > c, other than relativistic mass?

 

[Aer]

Hold on -- how is it that c will never be exceeded in a Newtonly universe (except there is relativistic mass)? Suppose none of the 4 postulates hold. Also suppose relativistic mass \nearrow as v \nearrow. Under the circumstances, what is constraining v becoming > c, other than relativistic mass?

I've never brought up a Newtonian universe as that would be completely absurd when dealing with velocities that approach anything near c. Relativistic mass IS NOT relativitity in a Newtonian universe - perhaps you need to read up more on the basics of special relativity.

 

[Doc Al]

I scanned this thread quickly and didn't see this point made: you can't just accelerate something indefinitely at a constant acceleration because the relativistic mass increases as speed increases. Since F= ma, in order to have constant acceleration with increasing mass, you would need to increase the force. As the speed nears c, the mass, and therefore force required to accelerate, goes to infinity.

Careful here. At relativistic speeds, F no longer equals ma, even if you replace m by the "relativistic mass". Assuming that the force and acceleration are in the same direction as the object's velocity, and that the acceleration a is that measured by an inertial observer who measures the object to be moving at speed v, the relationship would be:
F = m \gamma^3 a
where m is the usual invariant ("rest") mass. (m \gamma^3 is sometimes called the longitudinal mass.)

So, yes, as the speed increases it requires (greatly) increasing force to maintain a constant acceleration with respect to the inertial observer.

 

[learningphysics]

Wrong, the fact that it takes infinite amount of energy doesn't prevent you from assuming you have this infinite amount of energy. Prove that there is a finite amount of energy in the universe. Or, prove that there is no way possible to take energy from another universe and that there are not an infinite number of universes.

Well then why is exceeding the speed of light a non-physical situation? If one can possesses infinite amounts of energy, what prevents it.

I'm troubled by where this is going... infinity is not even a real number.

I did not ask for any such thing, I asked you to prove that relativistic mass is in anyway related to this. Please check your definition of inertial mass

Relativistic mass = inertial mass

 

[EnumaElish]

I've never brought up a Newtonian universe as that would be completely absurd when dealing with velocities that approach anything near c. Relativistic mass IS NOT relativitity in a Newtonian universe - perhaps you need to read up more on the basics of special relativity.

I am working on my reading list. In the meantime, just bear with me and assume a universe that is Newtonian in every aspect but relativistic mass. We know the universe isn't Newtonian (even I know that!), and what I am asking you to assume is absurd, non-physical, maybe even stupid. But I think I have a point to make. I will give you the benefit of an infinite supply of energy available instantly on demand. In such a universe, it would still be impossible to exceed the speed of light because of the relativistic mass effect. Every incremental amount of energy that the ship consumes would add to the ship's relativistic mass far more than it would add to the ship's velocity.

 

[Aer]

Relativistic mass = inertial mass

How wrong you are. Well, perhaps my knowledge of what relativistic mass is lacking. So I will challenge you to prove yourself correct in the statement Relativistic mass = inertial mass

 

[Aer]

I am working on my reading list. In the meantime, just bear with me and assume a universe that is Newtonian in every aspect but relativistic mass. We know the universe isn't Newtonian (even I know that!), and what I am asking you to assume is absurd, non-physical, maybe even stupid. But I think I have a point to make. I will give you the benefit of an infinite supply of energy available instantly on demand. In such a universe, it would still be impossible to exceed the speed of light because of the relativistic mass effect. Every incremental amount of energy that the ship consumes would add to the ship's relativistic mass far more than it would add to the ship's velocity.

I don't wish to subject myself to what I consider nonsense, prove to me that it is not nonsense and I'll reconsider.

 

[Janus]

Well then why is exceeding the speed of light a non-physical situation? If one can possesses infinite amounts of energy, what prevents it.

It takes an infinite amount of energy to reach the speed of light, exceeding it is another animal completely.

The equation for the total energy for an object(including the energy equivalnet of its rest mass) is:

E = \frac{Mc^2}{ \sqrt{1- \frac{v^2}{c^2}}}

Notice that if v>c, the bottom half of the equation becomes a squareroot of a negative number.

Meaning that the total energy of the object becomes non-physical.

 

[EnumaElish]

I am working on my reading list. In the meantime, just bear with me and assume a universe that is Newtonian in every aspect but relativistic mass. We know the universe isn't Newtonian (even I know that!), and what I am asking you to assume is absurd, non-physical, maybe even stupid. But I think I have a point to make. I will give you the benefit of an infinite supply of energy available instantly on demand. In such a universe, it would still be impossible to exceed the speed of light because of the relativistic mass effect. Every incremental amount of energy that the ship consumes would add to the ship's relativistic mass far more than it would add to the ship's velocity.

I don't wish to subject myself to what I consider nonsense, prove to me that it is not nonsense and I'll reconsider.

No, I freely admit it is nonsense. But it proves a point.

 

[Aer]

No, I freely admit it is nonsense. But it proves a point.

Nonsense is used to prove something other than nonsense?

 

[pervect]

Relativistic mass = inertial mass

Nooooooooooooooooooo!

 

[pervect]

I am working on my reading list. In the meantime, just bear with me and assume a universe that is Newtonian in every aspect but relativistic mass. We know the universe isn't Newtonian (even I know that!), and what I am asking you to assume is absurd, non-physical, maybe even stupid.

This doesn't give me any clear mental picture of what sort of "universe" you are talking about. Writing down a Lagrangian for this universe would be nice (perhaps it's too much to ask of you?)

By Lagrangian I mean the Lagrangain of a particle in potential V, i.e. for Newtonian mechanics

L(x,xdot) = .5*m*xdot^2 - V(x)

where V(x) is the potential.

Anyway, a little bit of thinking about what you might mean more or less convinces me that such a universe must have some sort of "preferred frame". I assume in your universe velocities add linearly. I think that this is what you mean by Newtonian, you want the Gallilean transform to be the transform between moving and non-moving coordinte systems.

x' = x-vt
t' = t

and not the Lorentz transform

x' = gamma*(x-vt)
t' = gamma*(t-vx/c^2)

Right?

Then this universe would have to be some sort of preferred frame that distinguishes high velocities, where it is difficult to accelerate, from low velocities, where it is not.

The point I've been trying to make is that it is the Lorentz transform itself that makes it impossible to exceed 'c' in relativity, and that "relativistic mass" is not needed to explain why it is impossible to exceed 'c'.

The Lorentz transform gives us a velocity addition formula by means of which one can add any fininte number of velocities less than 'c' and arrive at a velocity less than 'c'. Thus it becomes obvious that one is not going to exceed 'c' by means of acceleration.

[add]
It may be belaboring the obvious, but I want to point out that acceleration is just the process of accumulating velocity via addition

i.e. v(t+dt) = v(t) + a*dt

(using the Galiean transform, which makes velocities add linearly)

the relativistic version using the Lorentz transforms is

v(t+dt) = v(t) + (1-(v/c)^2)*a*dt

thus, the process of acceleration consists of adding incrementally to one's existing velocity.
[end add]

Thus it is obvious from the Lorentz transform and the velocity addition formula alone that one cannot accelerate to the velocity of 'c', the concept of relativistic mass is not needed.

 

[learningphysics]

It takes an infinite amount of energy to reach the speed of light, exceeding it is another animal completely.

The equation for the total energy for an object(including the energy equivalnet of its rest mass) is:

E = \frac{Mc^2}{ \sqrt{1- \frac{v^2}{c^2}}}

Notice that if v>c, the bottom half of the equation becomes a squareroot of a negative number.

Meaning that the total energy of the object becomes non-physical.

E is also undefined when v=c and the denominator is 0.

 

[learningphysics]

How wrong you are. Well, perhaps my knowledge of what relativistic mass is lacking. So I will challenge you to prove yourself correct in the statement Relativistic mass = inertial mass

It is not really proving... it's a matter of definition. I was using inertial mass as defined as p/v, where p is the relativistic momentum and v is velocity. This happens to be the definition of relativistic mass. In Rindler's "Introduction to Special Relativity" he calls p/v "relativistic inertial mass".

Anyway, I was able to find some lecture notes here and there using this definition of inertial mass.

http://physics.tamuk.edu/~hewett/ModPhy1/Unit1/SpecialRelativity/RelativeView/Mass/Mass.html

The comment about the spinning flywheel is one of the reasons I personally find relativistic mass helpful.

This prof says we can interpret the relativistic mass as inertial mass:
http://www.physics.hku.hk/~phys1303/Chap4.doc

The beginning of Section 7.1 here talks about the principle of equivalence and relativistic mass-energy
http://ankh-morpork.maths.qmul.ac.uk/~saha/teach/relativity/notes.pdf

 

[learningphysics]

Nooooooooooooooooooo!

Can you elaborate?

 

[EnumaElish]

(perhaps it's too much to ask of you?)

It is. (I'd hate to disappoint.)

Anyway, a little bit of thinking about what you might mean more or less convinces me that such a universe must have some sort of "preferred frame". I assume in your universe velocities add linearly.

I guess I am okay with both of these. Velocities add linearly so in principle one could exceed the speed of light but cannot because their "relativistic" mass keeps increasing with their velocity. They just cannot go on speeding up indefinitely.

acceleration is just the process of accumulating velocity via addition

i.e. v(t+dt) = v(t) + a*dt

Alternatively, a = x''(t), (I am guessing that these two definitions would be equivalent in this nonsense universe.)

Thus it is obvious from the Lorentz transform and the velocity addition formula alone that one cannot accelerate to the velocity of 'c', the concept of relativistic mass is not needed.

I agree that it is not necessary, but sufficient.

 

[EnumaElish]

Nonsense is used to prove something other than nonsense?

Yes, as in reductio ad absurdum.

 

[Aer]

Velocities add linearly so in principle one could exceed the speed of light but cannot because their "relativistic" mass keeps increasing with their velocity. They just cannot go on speeding up indefinitely.

Where were you educated? Lazy teachers would be better off not teaching their students anything rather than teaching them wrongly. SIGH

Alternatively, a = x''(t),

"Alternatively"?! assume v(t) = x'(t), then a(t)=x''(t) follows from the same equation. Maybe that is what you meant, but it sounds like you are saying that is an unrelated defintion.

 

[EnumaElish]

Where were you educated? Lazy teachers would be better off not teaching their students anything rather than teaching them wrongly. SIGH

I never had physics beyond HS, where relativity was not covered. Everything was Newtonian. I might add that I find it quite unbecoming (even a little unsettling) to disparage educators you don't even know.

"Alternatively"?! assume v(t) = x'(t), then a(t)=x''(t) follows from the same equation. Maybe that is what you meant, but it sounds like you are saying that is an unrelated defintion.

You should be pickier about the words you use. I'd say they are two independent definitions. I would never say they are unrelated. (Well, almost never.) See pervect's post #31 above, where he defines x''(t) as coordinate acceleration vs. v'(t) as proper acceleration. I am not a physicist, so I would only guess that there can be a difference between the two. To my uneducated understanding, that does not mean that the two are always different, only that they can be different.

 

[Aer]

I never had physics beyond HS, where relativity was not covered. Everything was Newtonian. I might add that I find it quite unbecoming (even a little unsettling) to disparage educators you don't even know.

To each his own... I recall having a few ignorant teachers in HS whom I still think would be better off spending their days out of the classroom and my HS was rated within the top 100 in the US when I attended.

You should be pickier about the words you use. I'd say they are two independent definitions. I would never say they are unrelated. (Well, almost never.) See pervect's post #31 above, where he defines x''(t) as coordinate acceleration vs. v'(t) as proper acceleration. I am not a physicist, so I would only guess that there can be a difference between the two. To my uneducated understanding, that does not mean that the two are always different, only that they can be different.

As I said, it seemed like you meant the other thing as I don't see the point of your response if that is what you initially meant.

 

[EnumaElish]

To each his own... I recall having a few ignorant teachers in HS whom I still think would be better off spending their days out of the classroom

Hell if I care. Just leave mine out of your comments. (Yeah, that's a hot button for me.)

My advice to you is to try to take responsibility for what you have become, or where you have ended up in, especially if you think you could have done better.

Having gotten this out of my chest, in what ways were your teachers ignorant? Do you mean technically, or culturally? Isn't blaming teachers (and anyone other than one's self) the easy way out? What about personal responsibility?

Don't your teachers deserve any credit for the fact that you can outsmart almost anybody in this forum?

 

[Aer]

Hell if I care. Just leave mine out of your comments. My advice to you is to try to take responsibility for what you have become, or where you have ended up in, especially if you think you could have done better.

What have I become? Am I evil for pointing out the short-comings in some educators? I never included all educators, in fact many of my HS teachers were a lot better teachers than some of the professors I had in college. However, I cannot say that I had any ignorant college professors - they were all appropriately knowledgeable in their respective fields which we'd all hope to be the case at the university level.