Place to discuss the Theory of Relativity

[pervect]

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.

There is a potential for confusion here even with such a simple statement. You can't accelerate indefinitely with a constant coordinate acceleration, d^2x/dt^2, but you _can_ accelerate indefinitely with a constant proper acceleration (the sort an acceleromter mounted on a space-ship would measure, i.e. dv/dt, where v and t are measured from an instantaneously co-moving frame.

 

[Aer]

Have you read the sci.physics.faq entry on the topic?

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Assuming you did read it, did you regard it as non-definitive (in that it only made recommendations), or did you clasify it as "incomprehensible to a non-physicist"?

You seem to like that page a lot as I've seen you link it many times. However I must admit that I've done little more than skim over it as I don't find it to contain anything interesting. That is, there doesn't seem to be any real use for relativisitic mass and the uses that it is used for are valid only because the end result is the same whether you consider relativistic mass or invariant mass with kinetic energy. But the former can lead to non-physical situations as I've pointed out in a few threads so I would argue that the latter is the correct interpretation. Please point out any errors in this line of thinking.

 

[EnumaElish]

Have you read the sci.physics.faq entry on the topic?

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Assuming you did read it, did you regard it as non-definitive (in that it only made recommendations), or did you clasify it as "incomprehensible to a non-physicist"?

I read the Addendum. I understand relativistic mass is directional and I am okay with it. This makes perfect sense to me: relativistic mass results from velocity which is directional. I use the term "relativistic mass" while acknowledging its directional connotation.

 

[EnumaElish]

... However, if you wish to say that the constant acceleration is in the other ship's reference frame, then the acceleration felt by the ship accelerating is increasing (but note that this scenario is not physical as it would evenutally require the ship to exceed the speed of light). So as you can see, the interpretation that a constant increase in energy expendature, leads to a non-physical reality.

But, from the other ship's point of view, the first ship is not only maintaining a constant acceleration but increasing its relativistic mass as it gains speed. And surely, accelerating a relativistically more massive object would require more energy than accelerating (by the same amount) a relativistically less massive object, wouldn't it? In the limit, as the first ship's velocity approaches c, its relativistic mass will have approximated infinity. At that point it will require an approximately infinite amount of energy to accelerate it even a bit further.

 

[Aer]

But, from the other ship's point of view, the first ship is not only maintaining a constant acceleration but increasing its relativistic mass as it gains speed. And surely, accelerating a relativistically more massive object would require more energy than accelerating (by the same amount) a relativistically less massive object, wouldn't it?

This is not what is generally meant when something is said to constantly accelerate. However you may specify this condition if you so wish, but as I pointed out previously:

However, if you wish to say that the constant acceleration is in the other ship's reference frame, then the acceleration felt by the ship accelerating is increasing (but note that this scenario is not physical as it would evenutally require the ship to exceed the speed of light). So as you can see, the interpretation that a constant increase in energy expendature, leads to a non-physical reality.

(See, I did point it out previously) As I pointed out previously, this situation is not physical, pervect will testify to this as well.

There is a potential for confusion here even with such a simple statement. You can't accelerate indefinitely with a constant coordinate acceleration, d^2x/dt^2, but you _can_ accelerate indefinitely with a constant proper acceleration (the sort an acceleromter mounted on a space-ship would measure, i.e. dv/dt, where v and t are measured from an instantaneously co-moving frame.

See.

 

[EnumaElish]

This is not what is generally meant when something is said to constantly accelerate. However you may specify this condition if you so wish, but as I pointed out previously:
(See, I did point it out previously) As I pointed out previously, this situation is not physical, pervect will testify to this as well.
See.

I need to think it over. For us non-physicists, "relativistic mass" has an intuitive content that is difficult to reproduce with the use of equations alone.

I also need to take into consideration HallsOfIvy's

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.

Intuitively I detect some circularity when I put this quote along with the excerpt from pervect's post that you quoted ("You can't accelerate indefinitely with a constant coordinate acceleration"). HOI is saying you can't because of the rel. mass (RM) effect. Then Aer says yes, you can't, which proves, or is because of (or both), there is no RM. We are all saying you can't accelerate indefinitely, but arrive at diametrically opposed conclusions about what that implies in terms of RM.

Am I right to understand that the way you (Aer) would explain the proposition "you can accelerate forever and never reach c" is purely through time dilation & length contraction, there being no need for a "story" about expending an infinite amount of energy?

 

[Aer]

Am I right to understand that the way you (Aer) would explain the proposition "you can accelerate forever and never reach c" is purely through time dilation & length contraction, there being no need for a "story" about expending an infinite amount of energy?

No. An infinite amount of energy would be expended if you tried to reach c as you would never be able to do so (i.e. you would expend energy over an infinite amount of time) and not becuase mass increases.

 

[EnumaElish]

No. An infinite amount of energy would be expended if you tried to reach c as you would never be able to do so (i.e. you would expend energy over an infinite amount of time) and not becuase mass increases.

That is what I meant to say by "time dilation." But that's by an outside observer's definition of time, right? How does the ship's crew explain to themselves the fact that they've been burning up so much energy yet are still nowhere near the speed of light?

 

[Daminc]

How does the ship's crew explain to themselves the fact that they've been burning up so much energy yet are still nowhere near the speed of light?

Good question. That confuses me as well :)

 

[selfAdjoint]

How does the ship's crew explain to themselves the fact that they've been burning up so much energy yet are still nowhere near the speed of light?

Good question. That confuses me as well :)

Space command insists its crews all learn relativity, so they know what's happening.

 

[EnumaElish]

Space command insists its crews all learn relativity, so they know what's happening.

Okay, the crew set up a web conference with a relativity prof on Earth, who explains to the crew that they have been burning up all this energy in the hope of reaching lightspeed, but according to him (the prof) that's a futile attempt because, according to his measurements, the ship has been getting more and more massive in the direction of its movement. "That's why you have been burning up all this energy, but your acceleration, according to my measurements, has been declining gradually because of this extra mass you and your ship have put on lately" he explains. What is wrong with his explanation?

 

[Aer]

That is what I meant to say by "time dilation." But that's by an outside observer's definition of time, right? How does the ship's crew explain to themselves the fact that they've been burning up so much energy yet are still nowhere near the speed of light?

Simple, imagine headlines on the spaceship. No matter how much acceleration the ship has experienced, the crew would measure the speed of the light emitted from their headlights as c.

 

[EnumaElish]

Simple, imagine headlines on the spaceship. No matter how much acceleration the ship has experienced, the crew would measure the speed of the light emitted from their headlights as c.

Right, so why haven't they been gaining on light? (They ask.)

 

[Aer]

Okay, the crew set up a web conference with a relativity prof on Earth, who explains to the crew that they have been burning up all this energy in the hope of reaching lightspeed, but according to him (the prof) that's a futile attempt because, according to his measurements, the ship has been getting more and more massive in the direction of its movement.

The professor could not make this measurement. If you think he could, please explain exactly how he might make this measurement - that is explain exactly how the professor would measure the mass of the ship to be greater than if the ship was at rest.

"That's why you have been burning up all this energy, but your acceleration, according to my measurements, has been declining gradually because of this extra mass you and your ship have put on lately" he explains. What is wrong with his explanation?

The fact that he sees the acceleration of the ship decreasing does not mean that the force being exerted on the ship is decreasing. The force is measured in the frame of the object which is subjected to the force. Trying to measure the force in any other frame is what leads to the false notion that the ship is gaining mass as it's speed increases. The relativistic mass as measured by the professor is a non-physical attributed that only one in the professor's inertial reference frame would be able to attribute to the ship. It does not explain any fundamental aspect of what is going on with the ship's energy supplies.

 

[Aer]

Right, so why haven't they been gaining on light? (They ask.)

This question seems to indicate a lacking of any fundamental understanding of relativity.

 

[EnumaElish]

This question seems to indicate a lacking of any fundamental understanding of relativity.

Yeah, the crew are an uneducated bunch originally destined for Mars. En route, something went wrong with their decelerators so they have been "constantly" accelerating toward the speed of light for some "time" now.

 

[EnumaElish]

The fact that he sees the acceleration of the ship decreasing does not mean that the force being exerted on the ship is decreasing. The force is measured in the frame of the object which is subjected to the force. Trying to measure the force in any other frame is what leads to the false notion that the ship is gaining mass as it's speed increases.

Not just any mass, but relativistic mass in the direction of the ship's motion only. It is definitely not rest mass, it is relativistic mass (unrest mass, one might say).

The relativistic mass as measured by the professor is a non-physical attributed that only one in the professor's inertial reference frame would be able to attribute to the ship. It does not explain any fundamental aspect of what is going on with the ship's energy supplies.

Somewhat similar to this "false" notion of time that everyone outside the ship seems to have, for some unexplicable reason, isn't it?

 

[Aer]

Not just any mass, but relativistic mass in the direction of the ship's motion only. It is definitely not rest mass, it is relativistic mass (unrest mass, one might say).

As I've said before, you may use this concept to arrive at the same result, but it is incorrect to say that this method explains anything fundamental. In other words, to arrive at any conclusions that require specifically relativistic mass could not be considered a correct conclusion unless you prove the same conclusion using fundamentals.

Somewhat similar to this "false" notion of time that everyone outside the ship seems to have, for some unexplicable reason, isn't it?

There is no "false" notion of time by anyone either in the ship or outside the ship. I don't know where you are pulling this statement from.

 

[EnumaElish]

As I've said before, you may use this concept to arrive at the same result,

Thank you.

but it is incorrect to say that this method explains anything fundamental.

I concede being superficial.

In other words, to arrive at any conclusions that require specifically relativistic mass could not be considered a correct conclusion unless you prove the same conclusion using fundamentals.

Would you mind stating or pointing to a source for these fundamentals?

There is no "false" notion of time by anyone either in the ship or outside the ship. I don't know where you are pulling this statement from.

Why is it that there is no falsity of time but falsity of force, or of relativistic mass? That's where I was coming from, if you follow my meaning.

 

[pervect]

That is what I meant to say by "time dilation." But that's by an outside observer's definition of time, right? How does the ship's crew explain to themselves the fact that they've been burning up so much energy yet are still nowhere near the speed of light?

You'll need to specify the ships drive mechanism before we can give a detailed description of how the ship's crew accounts for the energy usage. If it's a rocket, they'll be complaining about how rockets are very inefficient at low velocities. If it's a light sail, they'll be complaining about the low momentum of the red-shifted light that is being shined on their lightsail (the light is redshifted because of their velocity) - and it's low intensity, for that matter (the latter takes a bit of math to demonstrate).


One thing that you should realize from Newtonian theory is that energy is a frame dependent quantity.

Another important point is that the ship's crews report of energy usage is just as valid as anyone else's account.

To be specific, in my frame of reference, my velocity is always zero, and so is my kinetic energy. The same holds true in relativity. In somoene else's frame of reference, I may be going at .9c, and have a lot of kinetic energy, in my own frame my kinetic energy is always zero. If I drop off a probe which matches my current velocity (a co-moving observer), I will find that my rocket ship accelerates at the normal and expected rate relative to the probe, no matter how fast I am going.

Imagine I am carrying a series of probes, and I drop them off regularly.

I drop off the first probe, and accelerate up to .1c with respect to it. I then drop the second probe, and accelerate up to .1c with respect to the second probe. My velocity with respect to the first probe now is NOT .2c, though -- it is 1% lower by the relativistic velocity addition formula (.1+.1)/(1.01). As I continue to accelerate and drop off probes, the discrepancy increases.

If I make a table, I get the following results. The probe numbering scheme is a bit different than I used in the text, it should be self-explanatory though.

probe velocity
curr 0
-1 .1
-2 .198
-3 .292
-4 .381
-5 .463
-6 .538
-7 .606
-8 .665
-9 .717
-10 .763
-11 .802

The result is, no matter how many probes I drop off, my velocity never reaches 'c'. Futhermore, I never, at any time, feel exceptionally heavy, I always measure my own density to be normal. Of course I am expending fuel like mad to reach these sorts of velocities, even with an idealized beam-core antimatter drive, one of the highest ISP (lowest fuel usage) rockets imaginable.

 

[EnumaElish]

The result is, no matter how many probes I drop off, my velocity never reaches 'c'. Futhermore, I never, at any time, feel exceptionally heavy, I always measure my own density to be normal.

Just like you measure your time to be normal, and if you're anything like an engineer worth the salt, know that there isn't anything particularly wrong with your engines. Thanks to this debate with Aer, I have been able to narrow down to the following question: why is it okay for everyone to have their own concept of time, but not okay to have different notions of an object's relativistic mass?

 

[Aer]

Just like you measure your time to be normal, and if you're anything like an engineer worth the salt, know that there isn't anything particularly wrong with your engines. Thanks to this debate with Aer, I have been able to narrow down to the following question: why is it okay for everyone to have their own concept of time, but not okay to have different notions of an object's relativistic mass?

Time dilation is a result of the postulates of special relativity. These postulates are the fundamentals. Relativistic mass is the result of attributing a mass to something from a frame other than the frame in which the force acts on the mass. In other words, according to a muon moving through the atmosphere at .998c, you have a relativistic mass approaching infinity. Now it doesn't make much sense to attribute this infinite mass to you does it? It is an attribute that one would say the muon sees and only the muon sees. I take the position that relativistic mass is useless because it explains nothing that isn't already explained in a fundamental way - using postulates.

 

[learningphysics]

The acceleration is measured by the object accelerating. Regardless of any acceleration that may have happened in the past (the ship may be moving at 0c, .5c, .9c, etc relative to another ship), according to the ship accelerating, in it's reference frame it is moving at 0c by definition. So the acceleration at any of the relative velocities listed above will be constant for a constant amount of expended energy. There is not an increase in the amount of expended energy to achieve a constant acceleration. However, if you wish to say that the constant acceleration is in the other ship's reference frame, then the acceleration felt by the ship accelerating is increasing (but note that this scenario is not physical as it would evenutally require the ship to exceed the speed of light). So as you can see, the interpretation that a constant increase in energy expendature, leads to a non-physical reality.

Both situations are equally non-physical. One involves the expenditure of an infinite amount of fuel over an infinite amount of time. The other involves an expenditure of an infinite amount of fuel for a finite amount of time.

 

[pervect]

It's much easier to keep mass as a scalar quantity (one that does not depend on direction) than to incorporate a concept of mass that varies with direction. The benefit gained by the additional complexity is minimal. So you wind up with a more complex formulation of mass that does not gain any significant computational advantage.

Other reasons are argued in the FAQ - they boil down to experience, experience with people becoming hopelessly confused by the concept of relativistic mass. I think the origin of this confusion is the aforementioned difficultiy of dealing with a mass that depends on direction, but it's hard to be positive about the source of confusion (it's too confused :-)).

By hopelessely confused I mean that said people become either unable to calculate the correct results to problems in relativity, or, even worse, that they calculate incorrect results and vehemently insist that their incorrect results are correct.

 

[learningphysics]

Time dilation is a result of the postulates of special relativity. These postulates are the fundamentals. Relativistic mass is the result of attributing a mass to something from a frame other than the frame in which the force acts on the mass. In other words, according to a muon moving through the atmosphere at .998c, you have a relativistic mass approaching infinity. Now it doesn't make much sense to attribute this infinite mass to you does it? It is an attribute that one would say the muon sees and only the muon sees. I take the position that relativistic mass is useless because it explains nothing that isn't already explained in a fundamental way - using postulates.

How would you describe the fact that the weight of the muon increases with increasing speed? Relativistic mass (or inertial mass) seems useful to me at least to be able to say that gravitational mass = inertial mass.

Invariant masses aren't additive... ie you can't take a system of say gas particles, add up their invariant masses... and say that that's the invariant mass of the entire gas. But you can add up relativistic masses of the particles and say that the total is the relativistic mass of the entire gas.

 

[Aer]

Both situations are equally non-physical. One involves the expenditure of an infinite amount of fuel over an infinite amount of time. The other involves an expenditure of an infinite amount of fuel for a finite amount of time.

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.

 

[Aer]

How would you describe the fact that the weight of the muon increases with increasing speed?

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

Relativistic mass (or inertial mass) seems useful to me at least to be able to say that gravitational mass = inertial mass.

Show experimental proof.

 

[EnumaElish]

Time dilation is a result of the postulates of special relativity. These postulates are the fundamentals.

What is a good source for me to look up these postulates?

Relativistic mass is the result of attributing a mass to something from a frame other than the frame in which the force acts on the mass.

Similar to relativistic time being the result of attributing a "stickiness" to a clock from a frame other than the frame in which the clock ticks.

In other words, according to a muon moving through the atmosphere at .998c, you have a relativistic mass approaching infinity.

Exactly.

Now it doesn't make much sense to attribute this infinite mass to you does it?

Define "sense." I am being relativistically facetious. If you see me smiling, then you are outside my frame.

It is an attribute that one would say the muon sees and only the muon sees.

No, if I see the muon then I see the muon.

I take the position that relativistic mass is useless because it explains nothing that isn't already explained in a fundamental way - using postulates.

What is a good source for me to look up these postulates?

 

[Aer]

What is a good source for me to look up these postulates?

Postulates of Special Relativity

The rest of your post is either stupid or brings up issues that I've already addressed, I'm not going to repeat myself.

Similar to relativistic time being the result of attributing a "stickiness" to a clock from a frame other than the frame in which the clock ticks.Exactly.Define "sense." I am being relativistically facetious. If you see me smiling, then you are outside my frame.No, if I see the muon then I see the muon.What is a good source for me to look up these postulates?

 

[EnumaElish]

Postulates of Special Relativity

The rest of your post is either stupid or brings up issues that I've already addressed, I'm not going to repeat myself.

I didn't mean to annoy you, Aer; sorry if I appear stubborn. (For me it is a fundamental trait, so it has nothing to do with you personally.) Thank you for the intellectual energy you have expended so far; we are getting somewhere, I promise. Thank you for the link, I will look it up.