infinite pill-shaped universe?

Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

Here's the proof. I'll do a simple experiment.

Someone at a job site asked me for an apple. I threw an apple in their
direction. They watched me throw is and grabbed it from the air.

They did this naturally and easily because of the hardwiring in their
brain.

Want to do your own experiment? Learn to juggle three balls easily.
Try it. Its fun, and entertaining! And a practical demonstration of
your innate ability to solve complex problems in Newtonian motion in
real-time.

The ability to predict the precise location of an object flying
ballistically through a gravity field short distances at low speed,-
directly without calculation, as in placing your hand in a position to
catch the object - is a practical demonstration of our hard-wired
understanding of Newtonian/Galilean physics.

Appealing to this innate ability gives knowledge derived from it a
solid grounding in real world experience.


You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. ) or are
tangential to the point and obscure clear discussion.

wrote:
Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

I completely agree, but nature is not so limited and
our mathematical description of it should not be so
constrained.

You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. )

That was me, I assumed you knew the answer since
you seemed familiar with SR. The correct equation is:

p = m [ v c / sqrt(c^2 - v^2) ]

or mass multiplied by a slightly more complex function
of speed.

Of course you can group it like this

p = [ m c / sqrt(c^2 - v^2) ] v

and call the term in square brackets "relativistic mass"
but it is just a cludge to allow the old Newtonian equation
to be used in a relativistic situation.

George

George Dishman wrote:
wrote:
Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

I completely agree, but nature is not so limited

I agree with this.

and
our mathematical description of it should not be so
constrained.

Our mathematical description is NOT constrained, and I never said
anything about our mathematical description, so your point is moot.


You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. )

That was me, I assumed you knew the answer since
you seemed familiar with SR.

I am intimately familiar with special relativity among other things, so
your presumption that I am wrong is itself wrong! And your statement
was wrong in the context of my discussion anway.

The correct equation is:

What is correct and what is not correct depends on the context of our
discussion. You presume our disagreement stems from my lack of
knowledge, when in reality it stems from your lack of appreciation of
certain important details in your thought process about knowledge we
both share..

p = m [ v c / sqrt(c^2 - v^2) ]

In the context of special relativity this equation has certain
important meaning. It might be said to be correct in certain contexts.


In the low speed context with v c the statement mass times velocity
is close enough to be said to be true.

For example, if you set c=1 and v=1/1000000 then p = mv is true to one
part in 5 x 10^-15 If you had a gram of copper and wished to calculate
the momentum of a gram of the stuff moving at 300 m/sec the difference
between p=mv and the 'correct' SR formula the error would amount to 5 x
10^-15 grams of material. Since the atomic weight of copper is 63.546
amu, this amounts to 47,367,261 atoms difference, which is
substantially correct in any realistic since. So, the Newtonian
equation is obviously an important equation since this is what our
brains are hardwired to know intuitively - and by referencing this
equation in our discussion of relativity, our intuitive knowledge is
tapped to deepen and enrich our understanding of relativity.


or mass multiplied by a slightly more complex function
of speed.

Yes, but its a moot point in the context of my earlier discussion as
I've already pointed out.

Of course you can group it like this

p = [ m c / sqrt(c^2 - v^2) ] v

and call the term in square brackets "relativistic mass"

Yes, which allows you to make important connections to your intuitive
understanding of reality. This explains why it was done this way at the
outset in our history of learning about the universe.

but it is just a cludge to allow the old Newtonian equation
to be used in a relativistic situation.

If your goal is isolate your intellect from your intuition this is a
way to proceed. I prefer a more integrative approach since it provides
the basis of a richer understanding by tapping the into the depths of
what humans are. As I've already explained about 10x


George

wrote:
George Dishman wrote:
wrote:
Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

I completely agree, but nature is not so limited

I agree with this.

and
our mathematical description of it should not be so
constrained.

Our mathematical description is NOT constrained, and I never said
anything about our mathematical description, so your point is moot.

I didn't suggest you did, the point remains valid.

You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. )

That was me, I assumed you knew the answer since
you seemed familiar with SR.

I am intimately familiar with special relativity among other things, so
your presumption that I am wrong is itself wrong! And your statement
was wrong in the context of my discussion anway.

The context of the discussion is the use of invariant
mass versus "relativistic mass" in SR.

The correct equation is:

What is correct and what is not correct depends on the context of our
discussion. You presume our disagreement stems from my lack of
knowledge,

I presume no such thing, I believe our disagreement
reflects a change in teaching practice over the last
few decades to get away from the old pseudo-
Newtonian approach to a more fully relativistic
treatment.

when in reality it stems from your lack of appreciation of
certain important details in your thought process about knowledge we
both share..

p = m [ v c / sqrt(c^2 - v^2) ]

In the context of special relativity this equation has certain
important meaning. It might be said to be correct in certain contexts.

Indeed, it is obviously only valid for massive objects
and inappropriate for photons, but in the context of
discussing "relativistic mass" it is correct.

In the low speed context with v c the statement mass times velocity
is close enough to be said to be true.

It is close enough to be a useable approximation of
course, but our context was the use of "relativistic
mass" which is specifically used where the
approximation p ~ m v is not adequate.

For example, if you set c=1 and v=1/1000000 then p = mv is true to one
part in 5 x 10^-15 If you had a gram of copper and wished to calculate
the momentum of a gram of the stuff moving at 300 m/sec the difference
between p=mv and the 'correct' SR formula the error would amount to 5 x
10^-15 grams of material. Since the atomic weight of copper is 63.546
amu, this amounts to 47,367,261 atoms difference, which is
substantially correct in any realistic since. So, the Newtonian
equation is obviously an important equation since this is what our
brains are hardwired to know intuitively -

Our brains are hardwired to know intuitively that
momentum is a linear function of speed as v
approaches c? I don't think so.

and by referencing this
equation in our discussion of relativity, our intuitive knowledge is
tapped to deepen and enrich our understanding of relativity.


or mass multiplied by a slightly more complex function
of speed.

Yes, but its a moot point in the context of my earlier discussion as
I've already pointed out.

Of course you can group it like this

p = [ m c / sqrt(c^2 - v^2) ] v

and call the term in square brackets "relativistic mass"

Yes, which allows you to make important connections to your intuitive
understanding of reality. This explains why it was done this way at the
outset in our history of learning about the universe.

but it is just a cludge to allow the old Newtonian equation
to be used in a relativistic situation.

If your goal is isolate your intellect from your intuition this is a
way to proceed. I prefer a more integrative approach since it provides
the basis of a richer understanding by tapping the into the depths of
what humans are. As I've already explained about 10x

My goal was to ensure that the lurkers who may
follow these conversations and aren't as familiar
with SR as you are not misled into thinking that
mass varies with speed and are instead aware
that the anachronistic "relativistic mass" is a
composite term which includes the actual invariant
mass and a speed-dependent term which is
frequently associated with the mass in the real
equations. You are welcome to use whatever
approach you like of course.

George

Wow, George, you are an argumentative old cuss... hmm...

George Dishman wrote:
wrote:
George Dishman wrote:
wrote:
Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

I completely agree, but nature is not so limited

I agree with this.

and
our mathematical description of it should not be so
constrained.

Our mathematical description is NOT constrained, and I never said
anything about our mathematical description, so your point is moot.

I didn't suggest you did, the point remains valid.

You are confused here. I never suggested we should constrain our
mathematical descriptions. I merely suggested that appealing to
intuitive notions of space and time add real depth to our understanding
of the mathematics.

You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. )

That was me, I assumed you knew the answer since
you seemed familiar with SR.

I am intimately familiar with special relativity among other things, so
your presumption that I am wrong is itself wrong! And your statement
was wrong in the context of my discussion anway.

The context of the discussion is the use of invariant
mass versus "relativistic mass" in SR.

As a means to tap into our intuitive understanding of things, yes. I
didn't suggest we stop there.

The correct equation is:

What is correct and what is not correct depends on the context of our
discussion. You presume our disagreement stems from my lack of
knowledge,

I presume no such thing,

Whenever you say something like 'the correct equation is...' presumes
all other modes of understanding are somehow incorrect. You should
really avoid brow-beating students in this way. It silences their own
rich understanding by assuming they have nothing to contribute merely
because it doesn't follow the lesson plan.

I believe our disagreement
reflects a change in teaching practice over the last
few decades

A agree. Some things have changed for the worse! lol.

to get away from the old pseudo-
Newtonian approach to a more fully relativistic
treatment.

Hogwash. The new approaches merely seek to avoid the same tired old
questions because they're boring for teachers to handle year in and
year out. They're quite efficient to this end. But they have a cost,
and that cost is making relativity seem like a different field of
experience than the one they know intuitively - which isolates
understanding from experience - and which I judge to be a bad thing.


when in reality it stems from your lack of appreciation of
certain important details in your thought process about knowledge we
both share..

p = m [ v c / sqrt(c^2 - v^2) ]

In the context of special relativity this equation has certain
important meaning. It might be said to be correct in certain contexts.

Indeed, it is obviously only valid for massive objects
and inappropriate for photons, but in the context of
discussing "relativistic mass" it is correct.

Except that it avoids any connection with our intuitive understanding
of these things evidenced by for example, juggling.

In the low speed context with v c the statement mass times velocity
is close enough to be said to be true.

It is close enough to be a useable approximation of
course,

Which is a starting point of richer understanding, not the end point.

but our context was the use of "relativistic
mass" which is specifically used where the
approximation p ~ m v is not adequate.

Except as a starting point of making connections to the intuitive
knowledge that exists in all learners.

For example, if you set c=1 and v=1/1000000 then p = mv is true to one
part in 5 x 10^-15 If you had a gram of copper and wished to calculate
the momentum of a gram of the stuff moving at 300 m/sec the difference
between p=mv and the 'correct' SR formula the error would amount to 5 x
10^-15 grams of material. Since the atomic weight of copper is 63.546
amu, this amounts to 47,367,261 atoms difference, which is
substantially correct in any realistic since. So, the Newtonian
equation is obviously an important equation since this is what our
brains are hardwired to know intuitively -

Our brains are hardwired to know intuitively that
momentum is a linear function of speed as v
approaches c? I don't think so.

You are being obtuse.

Our hardwiring doesn't understand massive objects approaching c. Our
hardwiring does understand our experience of moving masses in a deep
way - as catching a softball or juggling attest to. It is connecting
to that experience that I am speaking of. Tapping into deeply known
things is the source of much knowledge - encoded in our beings by
evolution. I believe we lose something by changing curricula to avoid
such connections merely to make the jobs of teachers easier.

and by referencing this
equation in our discussion of relativity, our intuitive knowledge is
tapped to deepen and enrich our understanding of relativity.


or mass multiplied by a slightly more complex function
of speed.

Yes, but its a moot point in the context of my earlier discussion as
I've already pointed out.

Of course you can group it like this

p = [ m c / sqrt(c^2 - v^2) ] v

and call the term in square brackets "relativistic mass"

Yes, which allows you to make important connections to your intuitive
understanding of reality. This explains why it was done this way at the
outset in our history of learning about the universe.

but it is just a cludge to allow the old Newtonian equation
to be used in a relativistic situation.

If your goal is isolate your intellect from your intuition this is a
way to proceed. I prefer a more integrative approach since it provides
the basis of a richer understanding by tapping the into the depths of
what humans are. As I've already explained about 10x

My goal was to ensure that the lurkers who may
follow these conversations and aren't as familiar
with SR as you are not misled into thinking that
mass varies with speed

But that idea that mass varies with speed (or that time varies with
speed) can be a useful way of understanding what is going on at a deep
level by appealing to what things seem like (if not pushed too far) - I
see value in maintaining that connection you do not. You see only the
benefit in avoiding tired old questions that lead to deeper
understanding among learners when those questions are answered. They
may be tired for us, but not for them and that's the point.

and are instead aware
that the anachronistic "relativistic mass" is a
composite term which includes the actual invariant
mass and a speed-dependent term which is
frequently associated with the mass in the real
equations.

YES!

You are welcome to use whatever
approach you like of course.

Haha... good solid statement followed by pointless brow-beating! lol.
I knew it was too good to last! haha..

George

Wow, George, you are an argumentative old cuss... hmm...

George Dishman wrote:
wrote:
George Dishman wrote:
wrote:
Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

I completely agree, but nature is not so limited

I agree with this.

and
our mathematical description of it should not be so
constrained.

Our mathematical description is NOT constrained, and I never said
anything about our mathematical description, so your point is moot.

I didn't suggest you did, the point remains valid.

You are confused here. I never suggested we should constrain our
mathematical descriptions. I merely suggested that appealing to
intuitive notions of space and time add real depth to our understanding
of the mathematics.

You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. )

That was me, I assumed you knew the answer since
you seemed familiar with SR.

I am intimately familiar with special relativity among other things, so
your presumption that I am wrong is itself wrong! And your statement
was wrong in the context of my discussion anway.

The context of the discussion is the use of invariant
mass versus "relativistic mass" in SR.

As a means to tap into our intuitive understanding of things, yes. I
didn't suggest we stop there.

The correct equation is:

What is correct and what is not correct depends on the context of our
discussion. You presume our disagreement stems from my lack of
knowledge,

I presume no such thing,

Whenever you say something like 'the correct equation is...' presumes
all other modes of understanding are somehow incorrect. You should
really avoid brow-beating students in this way. It silences their own
rich understanding by assuming they have nothing to contribute merely
because it doesn't follow the lesson plan.

I believe our disagreement
reflects a change in teaching practice over the last
few decades

A agree. Some things have changed for the worse! lol.

to get away from the old pseudo-
Newtonian approach to a more fully relativistic
treatment.

Hogwash. The new approaches merely seek to avoid the same tired old
questions because they're boring for teachers to handle year in and
year out. They're quite efficient to this end. But they have a cost,
and that cost is making relativity seem like a different field of
experience than the one they know intuitively - which isolates
understanding from experience - and which I judge to be a bad thing.


when in reality it stems from your lack of appreciation of
certain important details in your thought process about knowledge we
both share..

p = m [ v c / sqrt(c^2 - v^2) ]

In the context of special relativity this equation has certain
important meaning. It might be said to be correct in certain contexts.

Indeed, it is obviously only valid for massive objects
and inappropriate for photons, but in the context of
discussing "relativistic mass" it is correct.

Except that it avoids any connection with our intuitive understanding
of these things evidenced by for example, juggling.

In the low speed context with v c the statement mass times velocity
is close enough to be said to be true.

It is close enough to be a useable approximation of
course,

Which is a starting point of richer understanding, not the end point.

but our context was the use of "relativistic
mass" which is specifically used where the
approximation p ~ m v is not adequate.

Except as a starting point of making connections to the intuitive
knowledge that exists in all learners.

For example, if you set c=1 and v=1/1000000 then p = mv is true to one
part in 5 x 10^-15 If you had a gram of copper and wished to calculate
the momentum of a gram of the stuff moving at 300 m/sec the difference
between p=mv and the 'correct' SR formula the error would amount to 5 x
10^-15 grams of material. Since the atomic weight of copper is 63.546
amu, this amounts to 47,367,261 atoms difference, which is
substantially correct in any realistic since. So, the Newtonian
equation is obviously an important equation since this is what our
brains are hardwired to know intuitively -

Our brains are hardwired to know intuitively that
momentum is a linear function of speed as v
approaches c? I don't think so.

You are being obtuse.

Our hardwiring doesn't understand massive objects approaching c. Our
hardwiring does understand our experience of moving masses in a deep
way - as catching a softball or juggling attest to. It is connecting
to that experience that I am speaking of. Tapping into deeply known
things is the source of much knowledge - encoded in our beings by
evolution. I believe we lose something by changing curricula to avoid
such connections merely to make the jobs of teachers easier.

and by referencing this
equation in our discussion of relativity, our intuitive knowledge is
tapped to deepen and enrich our understanding of relativity.


or mass multiplied by a slightly more complex function
of speed.

Yes, but its a moot point in the context of my earlier discussion as
I've already pointed out.

Of course you can group it like this

p = [ m c / sqrt(c^2 - v^2) ] v

and call the term in square brackets "relativistic mass"

Yes, which allows you to make important connections to your intuitive
understanding of reality. This explains why it was done this way at the
outset in our history of learning about the universe.

but it is just a cludge to allow the old Newtonian equation
to be used in a relativistic situation.

If your goal is isolate your intellect from your intuition this is a
way to proceed. I prefer a more integrative approach since it provides
the basis of a richer understanding by tapping the into the depths of
what humans are. As I've already explained about 10x

My goal was to ensure that the lurkers who may
follow these conversations and aren't as familiar
with SR as you are not misled into thinking that
mass varies with speed

But that idea that mass varies with speed (or that time varies with
speed) can be a useful way of understanding what is going on at a deep
level by appealing to what things seem like (if not pushed too far) - I
see value in maintaining that connection you do not. You see only the
benefit in avoiding tired old questions that lead to deeper
understanding among learners when those questions are answered. They
may be tired for us, but not for them and that's the point.

and are instead aware
that the anachronistic "relativistic mass" is a
composite term which includes the actual invariant
mass and a speed-dependent term which is
frequently associated with the mass in the real
equations.

YES!

You are welcome to use whatever
approach you like of course.

Haha... good solid statement followed by pointless brow-beating! lol.
I knew it was too good to last! haha..

George

wrote:
Wow, George, you are an argumentative old cuss... hmm...

'Fraid so ;-)

However, let me remind you of your comment that
started all this. You wrote in message:
http://groups.google.co.uk/group/sci...b9a4a05fdf1593

Mass is not an invariant quantity, it changes with relative speed.
That's what the special and general theory of relativity is all about.

The mass of a particle at rest can be invariant. But the mass of a
particle in motion changes with its speed. You can see this with
electrons in a vacuum tube ...

Mass varying with speed is most definitely not "what
the special and general theory of relativity is all about."
nor IMO is it a good way to start learning what SR or
GR are really about.

George Dishman wrote:
wrote:
George Dishman wrote:
wrote:
Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

I completely agree, but nature is not so limited

I agree with this.

and
our mathematical description of it should not be so
constrained.

Our mathematical description is NOT constrained, and I never said
anything about our mathematical description, so your point is moot.

I didn't suggest you did, the point remains valid.

You are confused here. I never suggested we should constrain our
mathematical descriptions.

I know, and I didn't say you did, so now who's being
argumentative? If you want to push the point, what I
was saying is that, for example, we shouldn't cast
our equation for momentum is this form:

p = m_r * v

from which we must have

m_r = m c / sqrt(c^2 - v^2)

only to be compliant with everday experience. Much of
modern science (and all of QM!) is counter-intuitive and
students will at some point need to break that connection.
It is my feeling that writing the equation in this form:

p = m [ v c / sqrt(c^2 - v^2) ]

makes it much clearer that mass is an invariant scalar.

I merely suggested that appealing to
intuitive notions of space and time add real depth to our understanding
of the mathematics.

I, on the other hand, think it unnecessarily creates a
misunderstanding, the idea that mass varies with speed.

You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. )

That was me, I assumed you knew the answer since
you seemed familiar with SR.

I am intimately familiar with special relativity among other things, so
your presumption that I am wrong is itself wrong! And your statement
was wrong in the context of my discussion anway.

The context of the discussion is the use of invariant
mass versus "relativistic mass" in SR.

As a means to tap into our intuitive understanding of things, yes. I
didn't suggest we stop there.

No, you simply said that I was wrong when I said
the following in message
http://groups.google.co.uk/group/sci...07e0dedb0e2f49

The FAQ:

http://math.ucr.edu/home/baez/physic...y/SR/mass.html

Scientifically speaking, mass is invariant.

Again, consider what you said of that:

Mass is not an invariant quantity, it changes with relative speed.
That's what the special and general theory of relativity is all about.

The mass of a particle at rest can be invariant. But the mass of a
particle in motion changes with its speed. ...


The correct equation is:

What is correct and what is not correct depends on the context of our
discussion. You presume our disagreement stems from my lack of
knowledge,

I presume no such thing,

Whenever you say something like 'the correct equation is...' presumes
all other modes of understanding are somehow incorrect.

No, it meant that one equation:

p = m [ v c / sqrt(c^2 - v^2) ]

is accurate to the best of current scientific knowledge while the

p = m v

is only an approximation. It may be a very useful approximation
but we shouldn't give lurkers the idea that it can be used on all
occasions.

You should
really avoid brow-beating students in this way. It silences their own
rich understanding by assuming they have nothing to contribute merely
because it doesn't follow the lesson plan.

I am against giving students incorrect information. Starting
by showing

p = m [ v c / sqrt(c^2 - v^2) ]

and then go on to discuss the situations where p = mv
is a valid approximation is IMO much more informative
and aids the understaing of when use of approximations
in general is appropriate.

I believe our disagreement
reflects a change in teaching practice over the last
few decades

A agree. Some things have changed for the worse! lol.

YMMV ;-)

to get away from the old pseudo-
Newtonian approach to a more fully relativistic
treatment.

Hogwash. The new approaches merely seek to avoid the same tired old
questions because they're boring for teachers to handle year in and
year out. They're quite efficient to this end. But they have a cost,
and that cost is making relativity seem like a different field of
experience than the one they know intuitively - which isolates
understanding from experience - and which I judge to be a bad thing.

I on the other hand think it gets them into thinking in
a 4D way which is essential as they move into GR.

when in reality it stems from your lack of appreciation of
certain important details in your thought process about knowledge we
both share..

p = m [ v c / sqrt(c^2 - v^2) ]

In the context of special relativity this equation has certain
important meaning. It might be said to be correct in certain contexts.

Indeed, it is obviously only valid for massive objects
and inappropriate for photons, but in the context of
discussing "relativistic mass" it is correct.

Except that it avoids any connection with our intuitive understanding
of these things evidenced by for example, juggling.

If you want to be a juggler use Newton. If you want to
work in high-energy physics or cosmology or any other
field where SR and GR matter then you need to start
think in 4D.

In the low speed context with v c the statement mass times velocity
is close enough to be said to be true.

It is close enough to be a useable approximation of
course,

Which is a starting point of richer understanding, not the end point.

I disagree, IMO, it avoids understanding the true behaviour
of nature by coating it in a veneer of Newtonian thinking.

but our context was the use of "relativistic
mass" which is specifically used where the
approximation p ~ m v is not adequate.

Except as a starting point of making connections to the intuitive
knowledge that exists in all learners.

No, you simply said my statement

Scientifically speaking, mass is invariant.

was wrong. In fact at the ed of your post you
implied it was "bs".

For example, if you set c=1 and v=1/1000000 then p = mv is true to one
part in 5 x 10^-15 If you had a gram of copper and wished to calculate
the momentum of a gram of the stuff moving at 300 m/sec the difference
between p=mv and the 'correct' SR formula the error would amount to 5 x
10^-15 grams of material. Since the atomic weight of copper is 63.546
amu, this amounts to 47,367,261 atoms difference, which is
substantially correct in any realistic since. So, the Newtonian
equation is obviously an important equation since this is what our
brains are hardwired to know intuitively -

Our brains are hardwired to know intuitively that
momentum is a linear function of speed as v
approaches c? I don't think so.

You are being obtuse.

It's what you seemed to be saying.

Our hardwiring doesn't understand massive objects approaching c. Our
hardwiring does understand our experience of moving masses in a deep
way - as catching a softball or juggling attest to. It is connecting
to that experience that I am speaking of. Tapping into deeply known
things is the source of much knowledge - encoded in our beings by
evolution. I believe we lose something by changing curricula to avoid
such connections merely to make the jobs of teachers easier.

Whereas I believe we gain a deeper understanding by using
our ability to visualise 3D to see how the 4D universe works
by visualise worldlines and spacetime using an x,y,t view.
The aim isn't to make the teacher's job easier but to give
the students the tools they will need in their careers.

If your goal is isolate your intellect from your intuition this is a
way to proceed. I prefer a more integrative approach since it provides
the basis of a richer understanding by tapping the into the depths of
what humans are. As I've already explained about 10x

My goal was to ensure that the lurkers who may
follow these conversations and aren't as familiar
with SR as you are not misled into thinking that
mass varies with speed

But that idea that mass varies with speed (or that time varies with
speed) can be a useful way of understanding what is going on at a deep
level ..

At the deeper level, mass does _not_ change with
speed, it is invariant. It only _appears_ to change when
you assume for example that p = m v and then calculate
m as p/v. That is the whole point, you are advocating
teaching a concept that subsequently students will have
to discard.

by appealing to what things seem like (if not pushed too far) - I
see value in maintaining that connection you do not. You see only the
benefit in avoiding tired old questions that lead to deeper
understanding among learners when those questions are answered. They
may be tired for us, but not for them and that's the point.

No, I have no problem with the questions, it is teaching
erroneous concepts to make life easier for the teacher
that I am objecting to.

and are instead aware
that the anachronistic "relativistic mass" is a
composite term which includes the actual invariant
mass and a speed-dependent term which is
frequently associated with the mass in the real
equations.

YES!

You are welcome to use whatever
approach you like of course.

Haha... good solid statement followed by pointless brow-beating! lol.
I knew it was too good to last! haha..

Not "brow-beating" at all, I was merely acknowledging that
once while one may understand the deeper aspects, it is
perfectly reasonable and pragmatically very appropriate
to use the old "relativistic mass" approach in getting
numbers out of the theory.

George

George Dishman wrote:
wrote:
Wow, George, you are an argumentative old cuss... hmm...

'Fraid so ;-)

Welcome to the club!


However, let me remind you of your comment that
started all this. You wrote in message:
http://groups.google.co.uk/group/sci...b9a4a05fdf1593

Mass is not an invariant quantity, it changes with relative speed.
That's what the special and general theory of relativity is all about.

The mass of a particle at rest can be invariant. But the mass of a
particle in motion changes with its speed. You can see this with
electrons in a vacuum tube ...

Mass varying with speed is most definitely not "what
the special and general theory of relativity is all about."

Yes it is. We think of mass as a constant unvarying with speed. The
apparent change of mass at high speeds demands an explanation! Which
gives us the 4-form of unvarying mass rotating in 4-space, projected
onto 3-space as a 3-form with apparently varying mass.

nor IMO is it a good way to start learning what SR or
GR are really about.

We disagree here.


George Dishman wrote:
wrote:
George Dishman wrote:
wrote:
Momentum, mass, the galilean notion of relativity, the newtonian notion
of absolute time, - all those aspects of every-day science and
engineering, are hard-wired into our brains.

I completely agree, but nature is not so limited

I agree with this.

and
our mathematical description of it should not be so
constrained.

Our mathematical description is NOT constrained, and I never said
anything about our mathematical description, so your point is moot.

I didn't suggest you did, the point remains valid.

You are confused here. I never suggested we should constrain our
mathematical descriptions.

I know, and I didn't say you did, so now who's being
argumentative?

I don't know since your reply is very confusing since all context is
lost.

If you want to push the point, what I
was saying is that, for example, we shouldn't cast
our equation for momentum is this form:

p = m_r * v

from which we must have

m_r = m c / sqrt(c^2 - v^2)

only to be compliant with everday experience.

You don't value the depth of everyday experience because you don't see
the deeper connections to non-intellectual experience and the value
they have.

Much of
modern science (and all of QM!) is counter-intuitive

Yes.

and
students will at some point need to break that connection.

I would say students need to MAKE the connection! lol.

It is my feeling that writing the equation in this form:

p = m [ v c / sqrt(c^2 - v^2) ]

makes it much clearer that mass is an invariant scalar.


Yes.

I merely suggested that appealing to
intuitive notions of space and time add real depth to our understanding
of the mathematics.

I, on the other hand, think it unnecessarily creates a
misunderstanding, the idea that mass varies with speed.


Mass apparently changes with speed in the 3-form projection, this is an
important observation in making a connection to deeper experience.

You folks make absolute statements that are highly suspect, or plain
wrong, (as when I was told to try again by one poster at one point when
I merely said momentum was mass times velocity! haha.. )

That was me, I assumed you knew the answer since
you seemed familiar with SR.

I am intimately familiar with special relativity among other things, so
your presumption that I am wrong is itself wrong! And your statement
was wrong in the context of my discussion anway.

The context of the discussion is the use of invariant
mass versus "relativistic mass" in SR.

As a means to tap into our intuitive understanding of things, yes. I
didn't suggest we stop there.

No, you simply said that I was wrong when I said
the following in message
http://groups.google.co.uk/group/sci...07e0dedb0e2f49

The FAQ:

http://math.ucr.edu/home/baez/physic...y/SR/mass.html

Scientifically speaking, mass is invariant.

Again, consider what you said of that:


I have considered what I said. You have not! lol.


Mass is not an invariant quantity, it changes with relative speed.
That's what the special and general theory of relativity is all about.

The mass of a particle at rest can be invariant. But the mass of a
particle in motion changes with its speed. ...


The correct equation is:

What is correct and what is not correct depends on the context of our
discussion. You presume our disagreement stems from my lack of
knowledge,

I presume no such thing,

Whenever you say something like 'the correct equation is...' presumes
all other modes of understanding are somehow incorrect.

No, it meant that one equation:

p = m [ v c / sqrt(c^2 - v^2) ]

is accurate to the best of current scientific knowledge while the

p = m v

is only an approximation. It may be a very useful approximation
but we shouldn't give lurkers the idea that it can be used on all
occasions.

You should
really avoid brow-beating students in this way. It silences their own
rich understanding by assuming they have nothing to contribute merely
because it doesn't follow the lesson plan.

I am against giving students incorrect information. Starting
by showing

p = m [ v c / sqrt(c^2 - v^2) ]

and then go on to discuss the situations where p = mv
is a valid approximation is IMO much more informative
and aids the understaing of when use of approximations
in general is appropriate.

I believe our disagreement
reflects a change in teaching practice over the last
few decades

A agree. Some things have changed for the worse! lol.

YMMV ;-)

to get away from the old pseudo-
Newtonian approach to a more fully relativistic
treatment.

Hogwash. The new approaches merely seek to avoid the same tired old
questions because they're boring for teachers to handle year in and
year out. They're quite efficient to this end. But they have a cost,
and that cost is making relativity seem like a different field of
experience than the one they know intuitively - which isolates
understanding from experience - and which I judge to be a bad thing.

I on the other hand think it gets them into thinking in
a 4D way which is essential as they move into GR.

when in reality it stems from your lack of appreciation of
certain important details in your thought process about knowledge we
both share..

p = m [ v c / sqrt(c^2 - v^2) ]

In the context of special relativity this equation has certain
important meaning. It might be said to be correct in certain contexts.

Indeed, it is obviously only valid for massive objects
and inappropriate for photons, but in the context of
discussing "relativistic mass" it is correct.

Except that it avoids any connection with our intuitive understanding
of these things evidenced by for example, juggling.

If you want to be a juggler use Newton. If you want to
work in high-energy physics or cosmology or any other
field where SR and GR matter then you need to start
think in 4D.

In the low speed context with v c the statement mass times velocity
is close enough to be said to be true.

It is close enough to be a useable approximation of
course,

Which is a starting point of richer understanding, not the end point.

I disagree, IMO, it avoids understanding the true behaviour
of nature by coating it in a veneer of Newtonian thinking.

but our context was the use of "relativistic
mass" which is specifically used where the
approximation p ~ m v is not adequate.

Except as a starting point of making connections to the intuitive
knowledge that exists in all learners.

No, you simply said my statement

Scientifically speaking, mass is invariant.

was wrong. In fact at the ed of your post you
implied it was "bs".

For example, if you set c=1 and v=1/1000000 then p = mv is true to one
part in 5 x 10^-15 If you had a gram of copper and wished to calculate
the momentum of a gram of the stuff moving at 300 m/sec the difference
between p=mv and the 'correct' SR formula the error would amount to 5 x
10^-15 grams of material. Since the atomic weight of copper is 63.546
amu, this amounts to 47,367,261 atoms difference, which is
substantially correct in any realistic since. So, the Newtonian
equation is obviously an important equation since this is what our
brains are hardwired to know intuitively -

Our brains are hardwired to know intuitively that
momentum is a linear function of speed as v
approaches c? I don't think so.

You are being obtuse.

It's what you seemed to be saying.

Our hardwiring doesn't understand massive objects approaching c. Our
hardwiring does understand our experience of moving masses in a deep
way - as catching a softball or juggling attest to. It is connecting
to that experience that I am speaking of. Tapping into deeply known
things is the source of much knowledge - encoded in our beings by
evolution. I believe we lose something by changing curricula to avoid
such connections merely to make the jobs of teachers easier.

Whereas I believe we gain a deeper understanding by using
our ability to visualise 3D to see how the 4D universe works
by visualise worldlines and spacetime using an x,y,t view.
The aim isn't to make the teacher's job easier but to give
the students the tools they will need in their careers.

If your goal is isolate your intellect from your intuition this is a
way to proceed. I prefer a more integrative approach since it provides
the basis of a richer understanding by tapping the into the depths of
what humans are. As I've already explained about 10x

My goal was to ensure that the lurkers who may
follow these conversations and aren't as familiar
with SR as you are not misled into thinking that
mass varies with speed

But that idea that mass varies with speed (or that time varies with
speed) can be a useful way of understanding what is going on at a deep
level ..

At the deeper level, mass does _not_ change with
speed, it is invariant. It only _appears_ to change when
you assume for example that p = m v and then calculate
m as p/v. That is the whole point, you are advocating
teaching a concept that subsequently students will have
to discard.

by appealing to what things seem like (if not pushed too far) - I
see value in maintaining that connection you do not. You see only the
benefit in avoiding tired old questions that lead to deeper
understanding among learners when those questions are answered. They
may be tired for us, but not for them and that's the point.

No, I have no problem with the questions, it is teaching
erroneous concepts to make life easier for the teacher
that I am objecting to.

and are instead aware
that the anachronistic "relativistic mass" is a
composite term which includes the actual invariant
mass and a speed-dependent term which is
frequently associated with the mass in the real
equations.

YES!

You are welcome to use whatever
approach you like of course.

Haha... good solid statement followed by pointless brow-beating! lol.
I knew it was too good to last! haha..

Not "brow-beating" at all, I was merely acknowledging that
once while one may understand the deeper aspects, it is
perfectly reasonable and pragmatically very appropriate
to use the old "relativistic mass" approach in getting
numbers out of the theory.

George

wrote in message
oups.com...

George Dishman wrote:
wrote:
Wow, George, you are an argumentative old cuss... hmm...

'Fraid so ;-)

Welcome to the club!


However, let me remind you of your comment that
started all this. You wrote in message:
http://groups.google.co.uk/group/sci...b9a4a05fdf1593

Mass is not an invariant quantity, it changes with relative speed.
That's what the special and general theory of relativity is all about.

The mass of a particle at rest can be invariant. But the mass of a
particle in motion changes with its speed. You can see this with
electrons in a vacuum tube ...

Mass varying with speed is most definitely not "what
the special and general theory of relativity is all about."

Yes it is.

No. SR was about producing a new model of time and
space to replace those of Newton which resolved many
of the problems in late 19th century physics. GR was
about extending that to cope with gravity to replace
Newton's "action at a distance" model.

We think of mass as a constant unvarying with speed.

It is.

The
apparent change of mass at high speeds demands an explanation! Which
gives us the 4-form of unvarying mass rotating in 4-space, projected
onto 3-space as a 3-form with apparently varying mass.

Right, it is merely an effect of projection. That
understanding is lost when you use the relativistic
mass approach.

nor IMO is it a good way to start learning what SR or
GR are really about.

We disagree here.

Indeed.

snip

I don't know since your reply is very confusing since all context is
lost.

OK, I've snipped that.

If you want to push the point, what I
was saying is that, for example, we shouldn't cast
our equation for momentum is this form:

p = m_r * v

from which we must have

m_r = m c / sqrt(c^2 - v^2)

only to be compliant with everday experience.

You don't value the depth of everyday experience because you don't see
the deeper connections to non-intellectual experience and the value
they have.

I do value them, but they conflict with the deeper
understanding of the effect of projection within
a 4D viewpoint.

Much of
modern science (and all of QM!) is counter-intuitive

Yes.

and
students will at some point need to break that connection.

I would say students need to MAKE the connection! lol.

It is my feeling that writing the equation in this form:

p = m [ v c / sqrt(c^2 - v^2) ]

makes it much clearer that mass is an invariant scalar.


Yes.

I merely suggested that appealing to
intuitive notions of space and time add real depth to our understanding
of the mathematics.

I, on the other hand, think it unnecessarily creates a
misunderstanding, the idea that mass varies with speed.


Mass apparently changes with speed in the 3-form projection, this is an
important observation in making a connection to deeper experience.

Right, it "apparently changes", as a projection only,
it is actually invariant as I said

I'll snip the rest as you didn't respond. I doubt
there's much more to say on the matter, our views
on teaching simply differ though I don't think we
disagree about the physics.

George