The Underlying Problem With Some Science Is Interpretation.

[A-wal]

I can follow some of that but not to the point that I could do it myself.

 

What does d represent?

 

How do you from this

By simple algebraic manipulation, we solve this expression for v²:

 

[math]\frac { { v }^{ 2 } }{ { c }^{ 2 } } =\quad 1-{ \left( \frac { { m }_{ o } }{ m }  \right)  }^{ 2 }[/math]

 

And:

 

[math]{ v }^{ 2 }=\quad { c }^{ 2 }\left\lceil 1-{ \left( \frac { { m }_{ o } }{ m }  \right)  }^{ 2 } \right\rceil[/math]

to this?

Next, we need to use a bit of calculus to differentiate the expression for v² with respect to m:

 

[math]d{ v }^{ 2 }=\quad 2{ c }^{ 2 }\left( \frac { { m }_{ o }^{ 2 } }{ { m }^{ 3 } }  \right) dm[/math]

 

[A-wal]

The postulate is that the speed of light is the same in all inertial frames. The speed limit is derived from that but a better way of looking at it is that no object can move at or over the speed of light relative to any other object in their frame of reference, therefore no object can move at or over twice the speed of light relative to any other object in any reference frame.

That's wrong as well because the angular velocities of objects can be anything. So the actual rule is:

 

The distance between any observer and any other object can't change at or faster than the speed of light in the inertial frame of reference of the observer and therefore the distance between any two objects can't change at or faster than twice the speed of light in any inertial frame of reference.

[sluggo]

A-wal #131

It's restricted to anything under 2c because they can only move at anything less than 1c relative to that frame (relative to an object at rest in that frame). Objects can only move at under c relative to an observer but can move at anything under 2c relative to each other in the reference frame of a third observer.

 

You omitted the last line.

"There is no mass moving faster than light!"

The spatial separation or gap, is not an object, so it can change at any arbitrary rate.

There is no violation of faster than light.

example: A laser rotating at 1 degree/second, would produce a light spot moving across the surface of the moon at 1.7c. given an array of reflectors on the surface. The spot has no mass.

OceanBreeze #132

You seem to be catching on that your velocity of 1.5c is meaningless. So, let me ask you this, you are sitting in your lab frame and the two objects (call them protons) are approaching each other at the relativistic velocity of 0.96c. Do you agree that is the velocity they will collide with each other?

The .96 value is what is measured in the frame of each particle. The closing speed as measured in the lab is 1.50. With a separation of  x, each particle requires (x/2)/.75 = x/1.50 sec to travel 1/2 distance. Their motion is simultaneous. The gap closes at a rate of 1.50.

OceanBreeze #133

 

 

What you are referring to is the gap velocity of two very distant objects where there is no restriction on the rate of expansion of space, because the local velocity in the vicinity of the objects still obeys the speed limit of c. There is no restriction at all on how fast space can expand, but that has nothing to do with this discussion. No mention has been made about how far apart the objects are. As long as they are in the same locality, they cannot move apart faster than c.

It's not about expansion of space, but the rate of changing separation. Relative to an observer who measures the speed of each as .75, the gap is increasing at 1.50. The gap is not growing as in an "expanding universe". It's just including more of the existing space. Just as you would take out a wall to enlarge your kitchen. without making the house bigger.  Within SR the c restriction for objects with mass is universal regardless of distance. A gap has no mass. The issue of faster than light is due to misinterpreting gap/closing speed as an object speed.

 

[A-wal]

A-wal #131

 

You omitted the last line.

"There is no mass moving faster than light!"

The spatial separation or gap, is not an object, so it can change at any arbitrary rate.

There is no violation of faster than light.

example: A laser rotating at 1 degree/second, would produce a light spot moving across the surface of the moon at 1.7c. given an array of reflectors on the surface. The spot has no mass.

OceanBreeze #132

Not at any rate, only anything under 2c. Objects can only move under c relative to an object at rest in any frame so objects that aren't in the observers frame can move relative to each other at anything under 2c because they can move anything under 1c in opposite directions from the observers reference frame.

 

The laser example isn't applicable because it's an effect, not an object. The photons are still moving at c. The spot can move at any velocity because it's not a 'thing', it's a continuous stream of things (photons).

 

The .96 value is what is measured in the frame of each particle. The closing speed as measured in the lab is 1.50. With a separation of  x, each particle requires (x/2)/.75 = x/1.50 sec to travel 1/2 distance. Their motion is simultaneous. The gap closes at a rate of 1.50.

But the objects themselves are moving at 1.5 relative to each other in the frame of the observer positioned equally between them. This rule covers everything:

 

The distance between any observer and any other object can't change at or faster than the speed of light in the inertial frame of reference of the observer and therefore the distance between any two objects can't change at or faster than twice the speed of light in any inertial frame of reference.

[OceanBreeze]

This debate just doesn’t want to go away, does it? The funny thing is, there is no need to argue at all since people are talking about entirely different things and confusing themselves needlessly.

 

There are no less than Four different types of velocities being discussed here, and needlessly being argued about, because we are getting them all mixed up!

 

I will try my best to identify the four different types, and try to put all the disagreement to rest:

 

1). The laser beam crossing the face of the moon is an example of Phase Velocity, and indeed this can move at virtually any velocity at all because nothing, not even photons, are moving across the face of the moon as FTL speed. It is the same as spinning around in a circle and seeing how fast the stars are moving around you. There is no inertial reference frame, and nothing is moving faster than light and it has nothing at all to do with relativity.

 

Here is what Wikipedia says:

If a laser beam is swept quickly across a distant object, the spot of light can move faster than c, although the initial movement of the spot is delayed because of the time it takes light to get to the distant object at the speed c. However, the only physical entities that are moving are the laser and its emitted light, which travels at the speed c from the laser to the various positions of the spot. Similarly, a shadow projected onto a distant object can be made to move faster than c, after a delay in time.[42] In neither case does any matter, energy, or information travel faster than light.[43

 

 

The second type of velocity I want to discuss is the Metric Expansion of Space:

In this type of motion, two objects that are located at cosmological distances from each other, can be moving apart at a velocity that is not limited by special relativity, and only depends on the rate of expansion of space between them and can be many multiples of the speed of light.

 

Again, Wikipedia:

Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity. Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons.

 

 

A third type of velocity (and one we have had some disagreements on) is happens when two objects with mass, either moving apart or moving towards one another, each with a velocity that is an significant fraction of c, as measured by an observer who is at rest between them.

 

I mostly agree with A-wal’s last statement: "The distance between any observer and any other object can't change at or faster than the speed of light in the inertial frame of reference of the observer and therefore the distance between any two objects can't change at or faster than twice the speed of light in any inertial frame of reference".

 

Unfortunately, that is not a Rule in relativity, as he says. Of course, he can prove me wrong by providing a link to this rule, if he has one.

 

My objection, however subtle it may be, is that the velocity of 2c he is getting is not the sort of velocity that is used in any relativistic equations. It is OK to use the velocity of 2c outside of the context of relativity, but not within relativity itself.

That may be hard to accept, but that is the only correct way of thinking about it. I have checked around the Internet and, as you might expect, we are not the first people to disagree on this point.

 

The best resolution of the question I have found anywhere is this one:

 

To illustrate what relativity is really limiting, let's look at a different case. Let's say, instead of photons, we have particles being emitted from the light bulb. Although they aren't allowed to move at the speed of light, they can move very close to it, so close that we'll just say that they're moving at c (the speed of light). Now, from our point of view, opposing particles are moving apart from one another at about twice the speed of light, and that's perfectly alright, because neither one of them is individually moving faster than c. The real tricky part comes when you ask how things appear from the point of view of one of the particles. Since, from our point of view, it seems that they're moving apart at nearly 2c, you would think that each particle would "see" the other moving away at this same velocity. Not so. In fact, relativity says that there is no point of view from which you can see something moving faster than c, so something has to be different from the point of view of these moving particles. In turns out that they both experience "time dilation", meaning their clocks run slower than ours, so they don't measure the other particle to be moving away from them at faster than the speed of light.

 

 

The follow up post by JTBell is what I like best:

 

To make this explicit here, we're dealing with two different kinds of velocities. The equations of relativity always deal with the velocity of an object as measured by a specific observer, or more precisely, in a specific inertial reference frame. The velocity in the first part of the above example is a different kind of velocity. We didn't measure that velocity "directly"; we inferred it from the difference in the velocities of the two objects, as measured by us. People often call this a "separation velocity" or "closing velocity" depending on whether which direction the objects are moving. Classically, the separation or closing velocity of two objects as measured by a third observer equals the velocity of either object as measured by the other one (ignoring signs). In relativity this is not true. To get the velocity of either object as measured by the other one, from the velocities of the two objects as measured by the third observer, you have to use the relativistic velocity-addition formula.

There's nothing fundamentally wrong with the separation velocity. Sometimes it's a perfectly sensible quantity to use. It's just not the kind of velocity that the relativistic transformation equations apply to.

 

 

So, in addition to the two types of velocities already mentioned, we have separation velocity (or closing velocity) which is not used in relativity, and we have relativistic velocities, which are added according to the relativistic transformation equations.

 

In summary, Four different types of velocities:

1). Phase velocity.

2). Velocity due to metric expansion of space.

3) Separation or Closing velocities, which are added algebraically and are not use in relativity.

4) Relativistic velocities that are added according to relativistic velocity addition.

 

That is as explicit as I can get, with references. If anyone still wants to argue, you will have to argue among yourselves as I have no more to say on this.

 

 

 

 

 

 

 

 

 

[OceanBreeze]

I can follow some of that but not to the point that I could do it myself.

 

What does d represent?

 

How do you from this

to this?

 

d is the differential operator which appears when taking the derivative of an expression.

 

The explanation is a bit involved if you are not familiar with basic calculus.

 

I will try and give you a more detailed reply later, In the meantime, you might want to read an introductory article on calculus. I think you will like it, seeing that you like physics. You really cannot get a good grasp of physics without some calculus. Velocity is the derivative of position, and acceleration is the derivative of velocity and there are many many other similar relationships throughout physics. You will like it, I assure you, once you get the general idea.

[A-wal]

I mostly agree with A-wal’s last statement: "The distance between any observer and any other object can't change at or faster than the speed of light in the inertial frame of reference of the observer and therefore the distance between any two objects can't change at or faster than twice the speed of light in any inertial frame of reference".

 

Unfortunately, that is not a Rule in relativity, as he says. Of course, he can prove me wrong by providing a link to this rule, if he has one.

It's a rule of nature, not of a specific paper. It is a rule of relativity, whether or not it happens to be explicitly mentioned in The Special Theory Of Relativity.

 

My objection, however subtle it may be, is that the velocity of 2c he is getting is not the sort of velocity that is used in any relativistic equations. It is OK to use the velocity of 2c outside of the context of relativity, but not within relativity itself.

That may be hard to accept, but that is the only correct way of thinking about it.

That only works if you only take into account the velocities of objects that are in motion relative to the observer, in other words one object's velocity relative to a specific frame of reference. It doesn't work as soon as you include the velocity of a second object relative to that frame of reference, in other words the velocity of two objects relative to each other from the perspective of a third object (the observer who is by definition at rest in that frame of reference).

 

By omitting velocities between 1c and 2c you're omitting no less than half of the relative velocities allowed by nature. All frames are equally valid and the same rules apply to all of them. In the particle accelerator example the two particles collide at well over 1c and the energy released by two atoms with their mass in the lab frame will agree that their collision speed was over 1c in the lab's frame because in the lab's frame they were moving towards each other faster than the speed of light (but each moving under the speed of light relative to the lab).

 

The velocities of anything up to 2c apply to relativistic velocities as long as it's the relativistic velocity of objects that doesn't include the observer. Objects can move at any velocity under 1c relative to an observer and at anything under 2c relative to each other from the perspective a third object and the physics of relative motion will still apply.

 

So, in addition to the two types of velocities already mentioned, we have separation velocity (or closing velocity) which is not used in relativity, and we have relativistic velocities, which are added according to the relativistic transformation equations.

It's not that it isn't part of relativity, it's that the velocity addition formula doesn't apply unless you change the inertial frame of the observer. That's the point I've being trying to make, that you never apply the velocity addition formula to objects that are in motion unless you move to the frame of reference of one of those objects.

[OceanBreeze]

It's a rule of nature, not of a specific paper. It is a rule of relativity, whether or not it happens to be explicitly mentioned in The Special Theory Of Relativity.

 

Bah, Humbug!

If it is "not explicitly mentioned" in special relativity (and it isn't) then it is not a rule of special relativity.

 

I just sense that you want to be right about this, no matter what, so I am going to have to insist you do as Craig says:

 

"As our site rules state, you should always provide links or references backing up the claims you make in your posts. This not only makes our site easier to read, it will force you to research your ideas, and hopefully prevent you from making obvious mistakes and harbor obvious misconceptions"

 

Hopefully, this will force you to research your ideas and stop harboring this very common misconception.

 

I will abide by the rules, as usual, and provide my sources to back up everything I say here.

 

Here is the scenario you are talking about:

 

The speed of light is the speed limit of the universe, so it follows that no observer will see any other observer approaching or receding at a speed greater than c. But what if observers A and B are both moving toward each other with speeds approaching c as seen by an external observer? How will A and B measure their relative speeds? This is an example of Einstein velocity addition. In the calculation below, velocities to the right are taken as positive.

 

 

A common resistance to the speed limit is to suggest that you just accelerate two different objects to more than half of the speed of light and point them toward each other, giving a relative speed greater than c. But that doesn't work! Time and space are interwoven in such a way that no one observer ever sees another object moving toward them at greater than c. The Einstein velocity addition deals with the transformation of velocities, always yielding a relative velocity less than c. It doesn't agree with your common sense, but it appears to be the way the universe works.

 

 

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/ltrans.html#c5

 

 

That only works if you only take into account the velocities of objects that are in motion relative to the observer, in other words one object's velocity relative to a specific frame of reference. It doesn't work as soon as you include the velocity of a second object relative to that frame of reference, in other words the velocity of two objects relative to each other from the perspective of a third object (the observer who is by definition at rest in that frame of reference).

 

By omitting velocities between 1c and 2c you're omitting no less than half of the relative velocities allowed by nature. All frames are equally valid and the same rules apply to all of them. In the particle accelerator example the two particles collide at well over 1c and the energy released by two atoms with their mass in the lab frame will agree that their collision speed was over 1c in the lab's frame because in the lab's frame they were moving towards each other faster than the speed of light (but each moving under the speed of light relative to the lab).

 

 

Please read all of the above, including the link. I repeat the key phrase below:

The speed of light is the speed limit of the universe, so it follows that no observer will see any other observer approaching or receding at a speed greater than c.

 

No observer, no exceptions, will ever see any other observer approaching or receding greater than c. In the case of two other observers, Einstein's velocity addition formula must be used within Special Relativity.

 

 

The velocities of anything up to 2c apply to relativistic velocities as long as it's the relativistic velocity of objects that doesn't include the observer. Objects can move at any velocity under 1c relative to an observer and at anything under 2c relative to each other from the perspective a third object and the physics of relative motion will still apply.

 

It's not that it isn't part of relativity, it's that the velocity addition formula doesn't apply unless you change the inertial frame of the observer. That's the point I've being trying to make, that you never apply the velocity addition formula to objects that are in motion unless you move to the frame of reference of one of those objects.

 

 

If you are adding velocities and getting a result greater than c, you are not working with special relativity.

 

You are making up your own rules to convince yourself you are right, when you are clearly and definitively wrong.

 

You are no longer arguing with me, but with every source that deals with SR. How does that make you feel? I think you are smarter than that.

[exchemist]

The fallacy here would seem to be the idea that an "observer" is somehow necessary for the speed limit of c to apply. This is wrong of course, but I find it interesting that this is not the first time I have seen this error on this forum. 

 

I wonder if this is a byproduct of quantum woo, which seems to be terribly fashionable. The notion seems to be that there is something subjective about physics, in that an act of observation by a conscious entity somehow changes what happens. This is a false idea.  

[OceanBreeze]

The fallacy here would seem to be the idea that an "observer" is somehow necessary for the speed limit of c to apply. This is wrong of course, but I find it interesting that this is not the first time I have seen this error on this forum. 

 

 

 

To be fair to A-wal, he seems to be saying something similar but not quite as far-fetched as the observer effect in quantum woo. He is saying that the presence of a third observer in his own IRF allows for measurement of velocities greater than c. He understands that both moving observers will measure their velocity with respect to each other as less than c. He also understands that the third observer will measure the velocity of each of the moving observers with respect to him, as less than c.

 

Where he goes wrong is in thinking that the third observer can measure the closing velocities of the two moving observers as greater than c. He can’t!

 

This is something that SR does not allow! The third observer can only measure the velocities between him and the moving observers one at a time, he has no means of measuring the relative velocities between them, with reference to himself. So he measures the velocity of A, with respect to himself, as 0.8c. Now he measures the velocity of B with respect to himself, as 0.7 c.

In order to compute the relative velocity between A and B, he must use Einstein’s velocity addition formula giving the result as 0.9615c:

 

A-wal infers that he can  add the velocities intuitively, getting 1.5 c, which is fine for some applications, as I told him before. I have no objection to him doing this at all. What I object to is his claim that this is a valid way to add velocities under SR. It is not permitted under SR where the maximum possible velocity is c.

 

When working with SR it is necessary to forget about intuition and Galilean velocity addition, no matter how difficult it may be to let go of.

 

I wonder if this is a byproduct of quantum woo, which seems to be terribly fashionable. The notion seems to be that there is something subjective about physics, in that an act of observation by a conscious entity somehow changes what happens. This is a false idea.  

 

 

Oh well, quantum woo is quantum poo and there is a lot of that out there, not only on this forum. Now I can’t use a mirror when shaving because the razor is never where I think I see it. No wonder I get razor nicks!

[exchemist]

To be fair to A-wal, he seems to be saying something similar but not quite as far-fetched as the observer effect in quantum woo. He is saying that the presence of a third observer in his own IRF allows for measurement of velocities greater than c. He understands that both moving observers will measure their velocity with respect to each other as less than c. He also understands that the third observer will measure the velocity of each of the moving observers with respect to him, as less than c.

 

Where he goes wrong is in thinking that the third observer can measure the closing velocities of the two moving observers as greater than c. He can’t!

 

This is something that SR does not allow! The third observer can only measure the velocities between him and the moving observers one at a time, he has no means of measuring the relative velocities between them, with reference to himself. So he measures the velocity of A, with respect to himself, as 0.8c. Now he measures the velocity of B with respect to himself, as 0.7 c.

In order to compute the relative velocity between A and B, he must use Einstein’s velocity addition formula giving the result as 0.9615c:

 

A-wal infers that he can  add the velocities intuitively, getting 1.5 c, which is fine for some applications, as I told him before. I have no objection to him doing this at all. What I object to is his claim that this is a valid way to add velocities under SR. It is not permitted under SR where the maximum possible velocity is c.

 

When working with SR it is necessary to forget about intuition and Galilean velocity addition, no matter how difficult it may be to let go of.

 

 

Oh well, quantum woo is quantum poo and there is a lot of that out there, not only on this forum. Now I can’t use a mirror when shaving because the razor is never where I think I see it. No wonder I get razor nicks!

Thanks for the clarification: not as bad as I feared, then.  

[CraigD]

I think the essence of confusion around statement like

Objects can only move at under c relative to an observer but can move at anything under 2c relative to each other in the reference frame of a third observer.

Comes from considering quantities like “the rate of change of distance between 2 bodies moving relative to a third as measured by the third” as speeds, when speed is properly the scalar of the rate of change of position of a single body in a specific inertial frame ([math]v = \left | \frac{\Delta D}{\Delta t} \right |[/math]).

 

Though “the distance between 2 bodies” is a well-defined quantity, it isn’t a position ([math]D[/math]), so its rate of change isn’t a speed ([math]v[/math]).

 

There are many well-defined quantities with dimension length (L) that have rate of changes (which, like speed, have dimension L T^-1) greater than the speed of light. The sum of the speed of all the cars and truck on the road right now, for example, is about 100 c. Few people would find this confusing, because it’s so obviously due to there being so many cars and trucks in the world, but it’s essentially the same confusion as with A-wal’s scenario.

 

Then there are false speeds that come from considering the change in position of things that aren’t bodies, such as a bright spot illuminated by a narrow beam of light, a situation known as the lighthouse paradox. We’ve seen several people claim here at hypography that this paradox invalidates special relativity. It doesn’t, obviously, but this shows that people can be confused by quantities with the dimension of speed that aren’t truly speeds.

[A-wal]

Bah, Humbug!

If it is "not explicitly mentioned" in special relativity (and it isn't) then it is not a rule of special relativity.

Okay I'll make this perfectly clear because their seems to be some confusion:

SR = Special relativity, as in the effects of relative motion in nature.

TSTOR = The Special Theory Of Relativity, a specific scientific paper that deals with the same subject.

 

What I'm talking about is SR, not TSTOR which only deals with the velocity of objects relative to the observer. I'm talking about the velocity of other objects relative to each other from the perspective of the observer, something that TSTOR doesn't go into.

 

I just sense that you want to be right about this, no matter what, so I am going to have to insist you do as Craig says:

 

"As our site rules state, you should always provide links or references backing up the claims you make in your posts. This not only makes our site easier to read, it will force you to research your ideas, and hopefully prevent you from making obvious mistakes and harbor obvious misconceptions"

 

Hopefully, this will force you to research your ideas and stop harboring this very common misconception.

This isn't about wanting to be right. I'd openly admit to being wrong if that was the case. I like knowing I was wrong, it means I've learned something.

 

There's no need to back up my claims because everything I've said is in accordance with standard theory. It's a very silly rule anyway: No opinions my be expressed on this forum unless you can show that those opinions have been previously expressed by others before you and accepted by the scientific community.

 

Here is the scenario you are talking about:

 

The speed of light is the speed limit of the universe, so it follows that no observer will see any other observer approaching or receding at a speed greater than c. But what if observers A and B are both moving toward each other with speeds approaching c as seen by an external observer? How will A and B measure their relative speeds? This is an example of Einstein velocity addition. In the calculation below, velocities to the right are taken as positive.

 

 

A common resistance to the speed limit is to suggest that you just accelerate two different objects to more than half of the speed of light and point them toward each other, giving a relative speed greater than c. But that doesn't work! Time and space are interwoven in such a way that no one observer ever sees another object moving toward them at greater than c. The Einstein velocity addition deals with the transformation of velocities, always yielding a relative velocity less than c. It doesn't agree with your common sense, but it appears to be the way the universe works.

No, no, NO! :) That's only if you want to view it from the frame of reference of one of those observers. That's not the scenario I'm taking about.

 

Please read all of the above, including the link. I repeat the key phrase below:

The speed of light is the speed limit of the universe, so it follows that no observer will see any other observer approaching or receding at a speed greater than c.

That's talking about relative to the observer in question, not about the relative velocity between two other objects. It should say this: The speed of light is the speed limit of the universe, so it follows that no observer will see any other observer approaching or receding themselves at a speed greater than c.

 

No observer, no exceptions, will ever see any other observer approaching or receding greater than c. In the case of two other observers, Einstein's velocity addition formula must be used within Special Relativity.

Definitely not! That's not how it works at all.

 

 

Nothing to do with the discussion.

 

If you are adding velocities and getting a result greater than c, you are not working with special relativity.

 

You are making up your own rules to convince yourself you are right, when you are clearly and definitively wrong.

 

You are no longer arguing with me, but with every source that deals with SR. How does that make you feel? I think you are smarter than that.

No I'm not. Not that it would bother me if I was. The true validity of any idea/theory/model/description can only be determined on its own merits.

 

The fallacy here would seem to be the idea that an "observer" is somehow necessary for the speed limit of c to apply. This is wrong of course, but I find it interesting that this is not the first time I have seen this error on this forum. 

 

I wonder if this is a byproduct of quantum woo, which seems to be terribly fashionable. The notion seems to be that there is something subjective about physics, in that an act of observation by a conscious entity somehow changes what happens. This is a false idea.  

You've misunderstood the discussion. The presence of an observer has no effect on the situation in the frames of reference of the objects that are in motion relative to that observer. All I'm doing is adding a third object an equal distance between two other objects that are in motion relative to each other and viewing it from the frame of reference of the middle object. It doesn't change anything, they're still moving away from each other at 0.8c in their own frames.

 

0.8c

A<-------------------------------------------------------------------->B

 

 

  1.2c

<------------------------------------------------------------------------>

A<------------------------------------X----------------------------------->B

  0.6c                                    0.6c

 

To be fair to A-wal, he seems to be saying something similar but not quite as far-fetched as the observer effect in quantum woo. He is saying that the presence of a third observer in his own IRF allows for measurement of velocities greater than c. He understands that both moving observers will measure their velocity with respect to each other as less than c. He also understands that the third observer will measure the velocity of each of the moving observers with respect to him, as less than c.

I'm relieved to read that paragraph. What you wrote there is all that TSTOR really says about it. You can't apply that to the velocity of other objects relative to each other.

 

Where he goes wrong is in thinking that the third observer can measure the closing velocities of the two moving observers as greater than c. He can’t!

 

This is something that SR does not allow! The third observer can only measure the velocities between him and the moving observers one at a time, he has no means of measuring the relative velocities between them, with reference to himself. So he measures the velocity of A, with respect to himself, as 0.8c. Now he measures the velocity of B with respect to himself, as 0.7 c.

In order to compute the relative velocity between A and B, he must use Einstein’s velocity addition formula giving the result as 0.9615c:

 

A-wal infers that he can  add the velocities intuitively, getting 1.5 c, which is fine for some applications, as I told him before. I have no objection to him doing this at all. What I object to is his claim that this is a valid way to add velocities under SR. It is not permitted under SR where the maximum possible velocity is c.

 

When working with SR it is necessary to forget about intuition and Galilean velocity addition, no matter how difficult it may be to let go of.

Nope. I know exactly where you're going wrong. Look at it like this. As soon as you apply the velocity addition formula you are applying time dilation and length contraction since that is what's responsible for the non-linear addition. As soon as you apply time dilation and length contraction you are by definition, changing the frame of reference. You never apply that formula without changing frames! In this scenario we are staying in the same frame of reference. An object is moving away from the observer at 0.6c and a second object is moving away from the observer at 0.6c in the opposite direction. They are moving away from each other at 1.2c in this frame. Now if we apply the velocity addition formula to get 0.8c we have now moved into the reference frame of either one of the other objects.

 

In the particle accelerator example you have two particles colliding at relative velocity 1.2c in the reference frame of the lab and at a velocity of 0.8c in their own frames of reference. The collision velocity is greater in the lab frame but all frames are equally valid. This works because the combined mass of the two particles is greater in their own frames of reference than in the lab's frame. You could work out the masses and collision velocity of 0.8c of the particles in their own frames and say 'look, the velocity addition formula does apply' but you can also simply use masses and collision velocity of 1.2c of the particles in the lab's frame without applying the velocity addition formula.

 

I think the essence of confusion around statement like

Comes from considering quantities like “the rate of change of distance between 2 bodies moving relative to a third as measured by the third” as speeds, when speed is properly the scalar of the rate of change of position of a single body in a specific inertial frame ([math]v = \left | \frac{\Delta D}{\Delta t} \right |[/math]).

 

Though “the distance between 2 bodies” is a well-defined quantity, it isn’t a position ([math]D[/math]), so its rate of change isn’t a speed ([math]v[/math]).

 

There are many well-defined quantities with dimension length (L) that have rate of changes (which, like speed, have dimension L T^-1) greater than the speed of light. The sum of the speed of all the cars and truck on the road right now, for example, is about 100 c. Few people would find this confusing, because it’s so obviously due to there being so many cars and trucks in the world, but it’s essentially the same confusion as with A-wal’s scenario.

Yep kind of. You can have any arbitrarally large velocity when you're combining more than two though. The objects can only move at velocities less than 2c relative to each other.

Edited December 29, 2016 by A-wal

[OceanBreeze]

Okay I'll make this perfectly clear because their seems to be some confusion:

SR = Special relativity, as in the effects of relative motion in nature.

TSTOR = The Special Theory Of Relativity, a specific scientific paper that deals with the same subject.

 

What I'm talking about is SR, not TSTOR which only deals with the velocity of objects relative to the observer. I'm talking about the velocity of other objects relative to each other from the perspective of the observer, something that TSTOR doesn't go into.

 

This isn't about wanting to be right. I'd openly admit to being wrong if that was the case. I like knowing I was wrong, it means I've learned something.

 

There's no need to back up my claims because everything I've said is in accordance with standard theory. It's a very silly rule anyway: No opinions my be expressed on this forum unless you can show that those opinions have been previously expressed by others before you and accepted by the scientific community.

 

 

 

 

 

WTF are you on about?

 

Now you are saying there is a SR and a TSTOR? And everything you have said is in accord with this SR (some voodoo version of TSTOR that you just made up) but not in accord with The Special Theory of Relativity (formulated by Einstein and accepted by main stream science)

 

Do I have that right?

 

How about a citation about the Difference between SR and TSTOR, or is that asking too much?

 

Oh wait, I see that "There's no need to back up my claims because everything I've said is in accordance with standard theory".

And as for the site rule:  "It's a very silly rule anyway"

 

 

You claimed you could derive E=mc^2 with just simple algebra and common sense. When I called you on that, you ran away to your Momma.

 

When I posted my derivation, using calculus, you didn't know what the d meant, you don't know what calculus is. I even offered to help you with that, but instead you doubled down on stupid.

 

Now you are making up your own version of *SR* that is not the same as Einstein's SR.

 

I suppose it is up to Craig whether or not he wants to let you to continue to post your crackpot nonsense here, but I will not be replying to your crap from this point on.

[OceanBreeze]

Thanks for the clarification: not as bad as I feared, then.  

 

Keep reading. It is actually much worse than either of us feared.

[A-wal]

WTF are you on about?

 

Now you are saying there is a SR and a TSTOR? And everything you have said is in accord with this SR (some voodoo version of TSTOR that you just made up) but not in accord with The Special Theory of Relativity (formulated by Einstein and accepted by main stream science)

 

Do I have that right?

 

How about a citation about the Difference between SR and TSTOR, or is that asking too much?

 

Oh wait, I see that "There's no need to back up my claims because everything I've said is in accordance with standard theory".

And as for the site rule:  "It's a very silly rule anyway"

 

 

You claimed you could derive E=mc^2 with just simple algebra and common sense. When I called you on that, you ran away to your Momma.

 

When I posted my derivation, using calculus, you didn't know what the d meant, you don't know what calculus is. I even offered to help you with that, but instead you doubled down on stupid.

 

Now you are making up your own version of *SR* that is not the same as Einstein's SR.

 

I suppose it is up to Craig whether or not he wants to let you to continue to post your crackpot nonsense here, but I will not be replying to your crap from this point on.

:) Well I can see someone hates to be proven wrong. Watch out, flying dummy alert!

 

TSTOR is a specific paper that describes some of the effects of relative motion. SR is the effects of relative motion. TSTOR is one specific piece of work relating to how nature works. SR is how nature works. What you're saying is equivalent to trying to refute the great mass extinctions of life on the basis that they don;t fall withing the framework of evolution. It makes no sense!

 

This paragraph explained exactly where you confusion is:

 

Nope. I know exactly where you're going wrong. Look at it like this. As soon as you apply the velocity addition formula you are applying time dilation and length contraction since that is what's responsible for the non-linear addition. As soon as you apply time dilation and length contraction you are by definition, changing the frame of reference. You never apply that formula without changing frames! In this scenario we are staying in the same frame of reference. An object is moving away from the observer at 0.6c and a second object is moving away from the observer at 0.6c in the opposite direction. They are moving away from each other at 1.2c in this frame. Now if we apply the velocity addition formula to get 0.8c we have now moved into the reference frame of either one of the other objects.

Edited December 29, 2016 by A-wal

[HydrogenBond]

Here is an example of misinterpretation of time. 

 

One conceptual problem with our current understanding of time and measuring time, is our understanding of time does not correspond to the way we measure time. Time moves to the future in a unidirectional way. Time does not move in cycles. We can depend on tomorrow spontaneously appearing, but we can't expect the past to repeat, in time. Clocks are all based on repeat cycles, while time is unidirectional. Clocks are better designed for measuring energy, instead of time, since energy cycles and repeats, but time does not cycle and repeat. 

 

A better device for measuring time would be something like the frozen fish clock. We take a standard sized frozen dead fish, and leave it out on the countertop. When it begins to smell a certain stink, we call that a unit of time. This type of clock does not cycle and is not repeatable, but behaves like time; unidirectional and unique each day. Just as time does not go backwards, we can't un-stink the fish clock. The fish clock is based on entropy instead of cyclic energy. Entropy increases to the future; 2nd law, and can be different each day,  like time. 

 

Relative to relativity, slowing cyclic clocks, is not about time, since time is a unidirectional phenomena. Relativity impacts the measurement of a cyclic event, that is based on frequency and wavelength; time and distance. 

 

With the dead fish clock, we can slow or speed up this clock with refrigeration and heating, to get results similar to relativity and velocity. Special relativity is based on Velocity, which is time/distance, like the cyclic clock. Heat is unidirectional; will spontaneously cool. 

 

 

The question becomes how did we get this wrong? By wrong, I means modeling 1-D time with 2-D clocks? The clock is a helpful device used by humans for the needs of civilization. You don't find clocks in nature. Humans define things for clocks. The original clock may have began with noticing the cyclic natures of the sun and moon, with these being used to plan repetitive events; sleep and wake. Repetition is not how time flows in the natural sense of being unidirectional. But humans became unnatural, when civilization began to form. 

 

The sun rising, moving and setting, is based on position as well as time. We call this time, ignoring the positional nature of cyclic clocks at some unconscious level. 

Edited December 29, 2016 by HydrogenBond