The Underlying Problem With Some Science Is Interpretation.

[A-wal]

No, what I’m talking about is a simple application of SR and an unusual but simply and well-defined alternate definition of “speed” – which, to avoid confusion, I called “pseudospeed”.

'Proper Velocity' ;)

[OceanBreeze]

No, what I’m talking about is a simple application of SR and an unusual but simply and well-defined alternate definition of “speed” – which, to avoid confusion, I called “pseudospeed”.

I’m trying to threadjack this thread from its original and IMHO silly “I don’t understand math or modern physics so I deny that SR makes sense” theme to a lighthearted look at how the real science of SR impeaches the common notion that SR places disheartening limits on interstellar travel. It doesn’t. The daunting challenges are of engineering, and were as or more daunting under classical physics as under modern.

 

There is no such thing as "pseudospeed" in SR.  But I suppose as long as you refer to it that way, and admit it is not a part of SR, then do your own thing.

 

If you were really interested in looking at the science of SR you might correct A-Wal on his velocity addition, that is what a responsible moderator would do, isn't it?

 

He has:  The velocity addition formula is applied if you want to work out what the velocity of the two objects moving away from is relative to each other in their frames! In your frame they're both moving away from you at 0.75c so of course they're moving away from each other at 1.5c.

 

Or maybe you think that is right? The two moving objects are moving away from each other at 1.5 c from my frame? Do you realize he is saying that my frame is special in that I can see a relative velocity that they do not see?

 

I have already corrected him two or three times, and showed him the correct math, but you have said nothing. Is that what "science for everyone" means? Everyone can do their own crackpot science?

[OceanBreeze]

 

 

Wow, you're really up confused creek without a clue. I don't know where to start with that mess. None of that remotely makes anything approaching something that in some way resembles sense.

 

And you know better? lol!

 

Yea okay. :) Prepare to feel very stupid!

 

As I said...

The velocity addition formula is applied if you want to work out what the velocity of the two objects moving away from is relative to each other in their frames! In your frame they're both moving away from you at 0.75c so of course they're moving away from each other at 1.5c.

 

This kind of fundamental error is exactly what happens when you try to memorise stuff without having any actual understanding of it. If you have trouble with something this basic you stand no chance of understanding the rest of it.

 

 

You are hopeless and I won't waste any more time with you. I will appeal to the mods to correct your crackpot ideas, that is, if they want correct science on this forum. If they prefer your crackpot nonsense then this forum is a joke and not worth my bother.

[A-wal]

There is no such thing as "pseudospeed" in SR.  But I suppose as long as you refer to it that way, and admit it is not a part of SR, then do your own thing.

 

If you were really interested in looking at the science of SR you might correct A-Wal on his velocity addition, that is what a responsible moderator would do, isn't it?

 

He has:  The velocity addition formula is applied if you want to work out what the velocity of the two objects moving away from is relative to each other in their frames! In your frame they're both moving away from you at 0.75c so of course they're moving away from each other at 1.5c.

 

Or maybe you think that is right? The two moving objects are moving away from each other at 1.5 c from my frame? Do you realize he is saying that my frame is special in that I can see a relative velocity that they do not see?

 

I have already corrected him two or three times, and showed him the correct math, but you have said nothing. Is that what "science for everyone" means? Everyone can do their own crackpot science?

You're just digging yourself even deeper. What makes you think that it implies a 'preferred frame' (that's the correct terminology)?

 

You still haven't answered my question xyz2...

Do you think that if an object is moving away from you at say 0.75c and another object accelerates away from you in the opposite direction, the first object's velocity relative to you will be slowed down by the relative velocity of the second object and/or the the velocity of the second object relative to you will be in some way restricted by the relative velocity of the first object?

 

You are hopeless and I won't waste any more time with you. I will appeal to the mods to correct your crackpot ideas, that is, if they want correct science on this forum. If they prefer your crackpot nonsense then this forum is a joke and not worth my bother.

 

Waaa!

Yes you're not the joke, the forum is. Careful where you spit that dummy, you'll have someones eye out!

 

Edit:

Oh and how the hell is using the elapsed proper time for the journey "not a part of SR"?

Edited December 7, 2016 by A-wal

[xyz]

@awal 

 

I just noticed this in one of the posts. 

 

''Taking your example: “If an object is moving away from you at 0.75c and anther object is moving away from you at 0.75c in the opposite direction then those two objects are moving away from each other at 1.5c in your reference frame”.''

 

 

Yes that's almost correct, I was saying this to you  but in another way. You have said it wrong. 

 

 

If you are moving away from an object at .75c and the object is moving away from you at .75c, relative to you ,, you do not know who is moving, relative to you the object is moving away from you at 1.5c and you are not moving.

 

 

[xyz]

BUT, a central ''stationary'' observer  and reference frame will observe both moving objects moving away at 0.75c.

Edited December 7, 2016 by xyz

[A-wal]

@awal 

 

I just noticed this in one of the posts. 

 

''Taking your example: “If an object is moving away from you at 0.75c and anther object is moving away from you at 0.75c in the opposite direction then those two objects are moving away from each other at 1.5c in your reference frame”.''

 

 

Yes that's almost correct, I was saying this to you  but in another way. You have said it wrong.

Why is it wrong?

 

If you are moving away from an object at .75c and the object is moving away from you at .75c, relative to you ,, you do not know who is moving, relative to you the object is moving away from you at 1.5c and you are not moving.

If you are moving away from an object at 0.75c and the the other object is moving away from you at 0.75c then you're moving away from each other at 0.75c. It's the same thing.

 

BUT, a central ''stationary'' observer  and reference frame will observe both moving objects moving away at 0.75c.

Yes, and moving away from each other at 1.5c. Congratulations, you're a step ahead of OceanBreeze.

 

Here's the problem you're having though. Like it or not, from the perspective of either of those objects, they're are not moving away from each other at 1.5c, nothing can reach the speed of light relative to the reference frame. Time dilation and length contraction mean that velocities don't add together in a liniar way like that. This is why...

 

"1. Two planets, Planet X and Planet Y.

2. Observer A is travelling from Planet X to Planet Y.

3. Observer B is making the same journey but faster than observer A.

4. Light passes observer A at c from A's frame and they work out how long it takes the light to make the journey.

5. The same light passes observer B at c from B's frame and they work out how long it takes the light to make the journey.

6. Observer B is moving between the two planets faster than observer A so the light will take less time to make the same journey from B's perspective.

 

How could that be possible without length contraction and/or time dilation?"

 

In the central object's reference frame they're both moving <c relative to that frame (they're moving at <c relative to the central object that's at rest in that frame) despite moving at >c relative to each other in that frame. If you want to see from their frames you have to apply the Lorenz transformations/the relative velocity addition formula/time dilation and length contraction, it's all different ways of saying the same thing, that objects in motion relative to each other can't measure the same lengths in time and space because the speed of light is the same for all of them.

[xyz]

Why is it wrong?

 

If you are moving away from an object at 0.75c and the the other object is moving away from you at 0.75c then you're moving away from each other at 0.75c. It's the same thing.

 

Yes, and moving away from each other at 1.5c. Congratulations, you're a step ahead of OceanBreeze.

 

Here's the problem you're having though. Like it or not, from the perspective of either of those objects, they're are not moving away from each other at 1.5c, nothing can reach the speed of light relative to the reference frame. Time dilation and length contraction mean that velocities don't add together in a liniar way like that. This is why...

 

"1. Two planets, Planet X and Planet Y.

2. Observer A is travelling from Planet X to Planet Y.

3. Observer B is making the same journey but faster than observer A.

4. Light passes observer A at c from A's frame and they work out how long it takes the light to make the journey.

5. The same light passes observer B at c from B's frame and they work out how long it takes the light to make the journey.

6. Observer B is moving between the two planets faster than observer A so the light will take less time to make the same journey from B's perspective.

 

How could that be possible without length contraction and/or time dilation?"

 

In the central object's reference frame they're both moving <c relative to that frame (they're moving at <c relative to the central object that's at rest in that frame) despite moving at >c relative to each other in that frame. If you want to see from their frames you have to apply the Lorenz transformations/the relative velocity addition formula/time dilation and length contraction, it's all different ways of saying the same thing, that objects in motion relative to each other can't measure the same lengths in time and space because the speed of light is the same for all of them.

I really don't understand what you are asking, however let me explain something to you that may just help you if you have the ability to understand. 

 

When we look at a distance and discuss something like the above, most people seem to miss one really important point and make an error in thought.  Let me discuss this error which hopefully you may understand.     

 

When considering something such has time dilation or even a Photon travelling a distance, the reference frame is generally a starting point and an end point.  So let us consider a distance, we say approx 200,000km, we will observe a vehicle travelling the distance, onboard the vehicle is a dilated clock , however the dilating clock does not affect the reference frame. 

The reference frame remains a constant 200,000km. 

So when you say to me light overtakes ( :cool: or what ever it is, you are not considering your reference points that remain constant . 

 

1, Two planets x and y , your reference points. 

 

2. 2. Observer A is travelling from Planet X to Planet Y. ok straight forward. 

 

3. Observer B is making the same journey but faster than observer A.The hare and the tortoise

 

4,4. Light passes observer A at c from A's frame and they work out how long it takes the light to make the journey. NO, X and Y is involved

 

5.5. The same light passes observer B at c from B's frame and they work out how long it takes the light to make the journey.no x and y are involved

 

 

6.6. Observer B is moving between the two planets faster than observer A so the light will take less time to make the same journey from B's perspective.no X and Y is involved

 

''How could that be possible without length contraction and/or time dilation?"

 

How could what possibly be?

 

 

 

x to y = 299 792 458 m 

 

 

time for light to travel 299 792 458 m  = 1 second

 

Both observer A  and B already know this . The speed of light is constant between two points at rest. 

 

The time between x and y is constant

 

the distance is constant

 

the distance on a caesium graph is constant

 

the frequency is a variant over the constant distance

 

fr/d=1

 

fr/d=0.5

 

 

d=constant

 

 

d1=1 inch 

 

t1=1.s

 

d2=1 inch

 

t2 = 0.5s

Edited December 7, 2016 by xyz

[OceanBreeze]

 

 

As I said...

The velocity addition formula is applied if you want to work out what the velocity of the two objects moving away from is relative to each other in their frames! In your frame they're both moving away from you at 0.75c so of course they're moving away from each other at 1.5c.

 

 

 

 

 

Just to put a fine point on this, reverse the positions of the two objects and now they are moving towards one another, as in a particle collider.

Now you are sitting at the console near the particle detector, (very unlikely, but you can imagine it) in your lab frame. In your lab frame, according to you, the two particles are approaching each other at 1.5c. Don’t try to deny it now, because that is exactly what you have been saying. In fact, in another example you came up with two relative velocities for the speed of light!

 

So, you will set up your experiment to detect energies and particles according to a collision at 1.5c as seen from your lab frame, and your experiment will be a huge blunder!

 

The only velocity that matters is the relative velocity between the two objects, and that is exactly 0.96c as I have calculated. The energy released in the collision will correspond to that relative velocity.

 

Your doodle of 1.5c relative velocity is meaningless, just as meaningless as Craig’s made up word “pseudovelocity”. I still challenge him to find any reference to pseudovelocity that deals with special relativity and provide the LINK.

 

As for the relative velocity of 0.96c between the two objects, it is relative to each other, and their relative velocity of 0.96c is also relative to you! But I doubt you are capable of understanding that; it is just too deep for your limited intelligence.

 

So, you and Craig can invent your own “special’ speedometers, make up your own “special” words and even come up with your own “special” relative velocities all you want, to try and make your arguments come out right, but NONE of that belongs in any serious discussion of SR.

 

Of course, by now I realize this is anything but a serious discussion of SR, so please carry on, at least it has some entertainment value.

[sluggo]

Using the example from xyz:

A moves at 2/3c to B's frame 2/3 ls distant.(left fig.)

She calculates transit time as 1 sec. She arrives at .75 sec. due to motion induced phenomenon of time dilation. Since her perception is altered to the same degree as her clock, she is not aware of the clocks changed frequency, and thinks her arrival E has occurred at E', and all space in the x direction has contracted.

Assuming a pseudo rest frame (right fig.) A perceives B moving from a distance of .50 at 2/3c, and arriving at .75 sec.

 

With two anauts moving in opposite directions at .75 (c=1), each will measure (using light) the speed of the other using the form (b-a)/(1-ab), which equals .96.

If we ask, what is the rate of changing separation or gap speed, it is 1.5.

Separation is a relation of positions, and has no restrictions relative to light speed.

There is no mass moving faster than light!

[CraigD]

There is no such thing as "pseudospeed" in SR.

Thanks to this from A-wall

'Proper Velocity' ;)

I see that what I thought was an informal idea has actually been in the physics literature since at least 1968, under the term proper velocity, or the catchier and IMHO less problematically confusing celerity. The definition given in the linked Wikipedia article

proper velocity is the ratio between distance traveled relative to a reference map frame (used to define simultaneity) and proper time τ elapsed on the clocks of the traveling object

is the same as my made-up-on-the-fly

Rather than the usual [math]v = \frac{\Delta d}{\Delta t}[/math], where [math]\Delta d[/math] is change in position as measured by the moving observer and [math]\Delta t[/math] is change in time as measured by his accurate clock, for pseudospeed [math]v[/math], [math]\Delta d[/math] is change in position as measured by the observer at rest relative to the destination (“Bob’s house” in the original post).

If you were really interested in looking at the science of SR you might correct A-Wal on his velocity addition, that is what a responsible moderator would do, isn't it?

I must admit I wasn’t following your exchange with A-Wal closely, but in an effort to be a responsible moderator, I’ll everyone to read and follow our site rules. The most important and most transgressed is “back up your claims by using links or references”, but “respect the opinions of others” is important, too, and IMHO harder, because it’s hard to be respectful when you see someone being obviously wrong.

 

My take on A-wal, from some months of back and forth in these fora, is that he’s doing his best to understand and promote SR as it’s generally understood by physicists, but approaches it informally, more in words and mental pictures than mathematically. As someone who more than I would like has to resort to this myself, I know it’s a perilous approach, because our informal intuition often misguides us.

 

SR is a mathematical physics theory, so best approached mathematically. Fortunately for folk like me with a limited science and math background, it has a huge and well-refereed literature, so most of the hard math work is done and just waiting for hacks of my ilk to enjoy vicariously and apply. Having enough background to do even this is IMHO an accomplishment.

 

That said, Velocity addition in SR is simple and uncontroversial, ( in units of c, it’s a pleasantly simple

[math]v_1’ = \frac{v_1 + v_2}{1+ v_1 v_2}[/math]

) so there shouldn’t be much disagreement about it here. Be clear, write as much math, and as little natural language as you can, have a link on hand showing you’re correct (which in my experience often saves one from erring before one posts), and don’t be hurried. Good things should follow.

 

The worst and most pernicious problem with this and other “science for everyone” forums is, I think, people who reject this approach in favor of the “I find this too difficult, so it must be wrong” justification, most often with the “I don’t want to pollute my original thinking by understanding anything written by anyone else” addendum.

 

You are hopeless and I won't waste any more time with you. I will appeal to the mods to correct your crackpot ideas, that is, if they want correct science on this forum. If they prefer your crackpot nonsense then this forum is a joke and not worth my bother.

I’m happy if these fora lead people to more correct science. Absolutely correct science, or even science correct in the sense of giving the correct answer in a class or GRE, is I think beyond us. We’re a forum, not a school.

[A-wal]

I really don't understand what you are asking, however let me explain something to you that may just help you if you have the ability to understand. 

 

When we look at a distance and discuss something like the above, most people seem to miss one really important point and make an error in thought.  Let me discuss this error which hopefully you may understand.     

 

When considering something such has time dilation or even a Photon travelling a distance, the reference frame is generally a starting point and an end point.  So let us consider a distance, we say approx 200,000km, we will observe a vehicle travelling the distance, onboard the vehicle is a dilated clock , however the dilating clock does not affect the reference frame. 

The reference frame remains a constant 200,000km. 

So when you say to me light overtakes ( :cool: or what ever it is, you are not considering your reference points that remain constant . 

 

1, Two planets x and y , your reference points. 

 

2. 2. Observer A is travelling from Planet X to Planet Y. ok straight forward. 

 

3. Observer B is making the same journey but faster than observer A.The hare and the tortoise

 

4,4. Light passes observer A at c from A's frame and they work out how long it takes the light to make the journey. NO, X and Y is involved

 

5.5. The same light passes observer B at c from B's frame and they work out how long it takes the light to make the journey.no x and y are involved

 

 

6.6. Observer B is moving between the two planets faster than observer A so the light will take less time to make the same journey from B's perspective.no X and Y is involved

 

''How could that be possible without length contraction and/or time dilation?"

 

How could what possibly be?

1. Two planets, Planet X and Planet Y.

 

2. Observer A is travelling from Planet X to Planet Y.

 

3. Observer B is making the same journey but faster than observer A.

 

4. Light passes observer A at c from A's frame and they work out how long it takes the light to make the journey.

 

Light moves at a constant velocity relative to all inertial observers. From A's perspective the light takes less time to make the journey between X and Y than it does from X and Y's perspective because the light is moving at A's velocity between those two points PLUS c because the light is overtaking A at c from A's perspective. So the light is taking less time to make the same journey from A's frame than it is from X and Y's frame (X and Y are at rest relative to each to keep it simple).

 

5. The same light passes observer B at c from B's frame and they work out how long it takes the light to make the journey.

 

Light moves at a constant velocity relative to all inertial observers. From B's perspective the light takes less time to make the journey between X and Y than it does from A's perspective because the light is moving at B's velocity between those two points PLUS c because the light is overtaking B at c from B's perspective. So the light is taking less time to make the same journey from B's frame than it is from not only X and Y's frame but also taking less time to make the same journey from B's frame than it is from A's frame because B's velocity between X and Y is greater than A's velocity between X and Y.

 

How could that be possible without length contraction and/or time dilation?

 

Just to put a fine point on this, reverse the positions of the two objects and now they are moving towards one another, as in a particle collider.

Now you are sitting at the console near the particle detector, (very unlikely, but you can imagine it) in your lab frame. In your lab frame, according to you, the two particles are approaching each other at 1.5c. Don’t try to deny it now, because that is exactly what you have been saying. In fact, in another example you came up with two relative velocities for the speed of light!

 

So, you will set up your experiment to detect energies and particles according to a collision at 1.5c as seen from your lab frame, and your experiment will be a huge blunder!

 

The only velocity that matters is the relative velocity between the two objects, and that is exactly 0.96c as I have calculated. The energy released in the collision will correspond to that relative velocity.

 

Your doodle of 1.5c relative velocity is meaningless, just as meaningless as Craig’s made up word “pseudovelocity”. I still challenge him to find any reference to pseudovelocity that deals with special relativity and provide the LINK.

 

As for the relative velocity of 0.96c between the two objects, it is relative to each other, and their relative velocity of 0.96c is also relative to you! But I doubt you are capable of understanding that; it is just too deep for your limited intelligence.

 

So, you and Craig can invent your own “special’ speedometers, make up your own “special” words and even come up with your own “special” relative velocities all you want, to try and make your arguments come out right, but NONE of that belongs in any serious discussion of SR.

 

Of course, by now I realize this is anything but a serious discussion of SR, so please carry on, at least it has some entertainment value.

And your hole just keeps getting deeper. Moving towards each other at 0.96c in their own frame is THE SAME as moving towards each other at 1.5c in the lab's frame so how could it possibly change the result of the experiment? You're really grasping at straws now.

 

Or maybe you think that is right? The two moving objects are moving away from each other at 1.5 c from my frame? Do you realize he is saying that my frame is special in that I can see a relative velocity that they do not see?

Why do you think that objects moving relative to each faster than c from the perspective of a third object implies a preferred frame of reference?

 

Of course two objects are moving away from each other at 1.5c from your frame if they're moving away from you at 0.75c in opposite directions. Do you think that if an object is moving away from you at say 0.75c and another object accelerates away from you in the opposite direction, the first object's velocity relative to you will be slowed down by the relative velocity of the second object and/or the the velocity of the second object relative to you will be in some way restricted by the relative velocity of the first object?

 

With two anauts moving in opposite directions at .75 (c=1), each will measure (using light) the speed of the other using the form (b-a)/(1-ab), which equals .96.

If we ask, what is the rate of changing separation or gap speed, it is 1.5.

Separation is a relation of positions, and has no restrictions relative to light speed.

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.

 

Thanks to this from A-wall

I see that what I thought was an informal idea has actually been in the physics literature since at least 1968, under the term proper velocity, or the catchier and IMHO less problematically confusing celerity. The definition given in the linked Wikipedia article

proper velocity is the ratio between distance traveled relative to a reference map frame (used to define simultaneity) and proper time τ elapsed on the clocks of the traveling object

is the same as my made-up-on-the-fly

You're kidding! :) I just thought that's what it should be called because it uses proper time. The validity of a statement is dependent on its validity and should be judged on its own merits, not whether or not you can dig up a link for it, that's insane!

 

That said, Velocity addition in SR is simple and uncontroversial, ( in units of c, it’s a pleasantly simple

[math]v_1’ = \frac{v_1 + v_2}{1+ v_1 v_2}[/math]

) so there shouldn’t be much disagreement about it here.

This issue isn't the velocity addition formula itself, it's when to apply it. OceanBreeze is under the impression that it applies to objects that are moving relative to each other from the perspective of a third observer. In other words he thinks that you need to apply the Lorenz transformations without changing the reference frame. He also thinks that not doing this would lead to a preferred reference frame. The transformations only applying when you change reference frames is the most basic and fundamental aspect of SR. Someone who doesn't even understand that has no business pretending to understand any of and will only embarrass themselves if they try, as he keeps demonstrating.

 

SR is a mathematical physics theory, so best approached mathematically. Fortunately for folk like me with a limited science and math background, it has a huge and well-refereed literature, so most of the hard math work is done and just waiting for hacks of my ilk to enjoy vicariously and apply. Having enough background to do even this is IMHO an accomplishment.

I completely disagree.

 

If you understand how SR applies to real situations but don't use the mathematics of the theory to generate the exact answers for specific examples then you still understand how SR applies to real situations.

 

If on the other hand you can only use the maths but don't understand why those equations apply to real situations then you have no actual understanding of the theory. Anyone can look up the equation.

[OceanBreeze]

 

 

And your hole just keeps getting deeper. Moving towards each other at 0.96c in their own frame is THE SAME as moving towards each other at 1.5c in the lab's frame so how could it possibly change the result of the experiment? You're really grasping at straws now.

 

Why do you think that objects moving relative to each faster than c from the perspective of a third object implies a preferred frame of reference?

 

Of course two objects are moving away from each other at 1.5c from your frame if they're moving away from you at 0.75c in opposite directions. Do you think that if an object is moving away from you at say 0.75c and another object accelerates away from you in the opposite direction, the first object's velocity relative to you will be slowed down by the relative velocity of the second object and/or the the velocity of the second object relative to you will be in some way restricted by the relative velocity of the first object?

 

 

 

 

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?

 

Now, you in your frame make a doodle that they are really approaching each other at 1.5 c (that is what you are claiming) To test that “theory” you open the inspection hatch on the beam accelerator and stick your head in right at the point of collision. Your head is attached to the rest of your body so it is at rest in the lab frame.

 

Questions:

 

1). Does your head being present in the accelerator change the velocity at which the particles collide?

 

2). Does the presence of your head, at rest in the lab frame, change the relative velocities between the two particles at all?

 

Maybe now you can see that what you doodle in your lab frame has no significance at all to the two particles that are moving at relativistic speeds to one another, it is a meaningless “pseudovelocity” and is of no use to you or to science. It is rubbish!

 

Now, that is established, I would like to call you out on your other claim that you can derive E=mc^2 with just algebra and common sense.

 

As per the forum rules, which Craig just reminded us about, either put up or shut up, or at least post a link where somebody has done this.

 

If you do that, I will post my derivation, completely from scratch and no memorized formulas, but I must warn you it involves calculus so beyond your understanding.

[OceanBreeze]

 

 

 

With two anauts moving in opposite directions at .75 (c=1), each will measure (using light) the speed of the other using the form (b-a)/(1-ab), which equals .96.

If we ask, what is the rate of changing separation or gap speed, it is 1.5.

Separation is a relation of positions, and has no restrictions relative to light speed.

There is no mass moving faster than light!

hypo-1.gif

 

 

 

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.

 

Now, you are free to add the velocities any way you like and get whatever number you like, such as 1.5c, but is has no meaning at all in science. The velocities that have meaning are 0.75c between you and each of the objects, and 0.96c between the two objects. That is all.

[OceanBreeze]

Thanks to this from A-wall

I see that what I thought was an informal idea has actually been in the physics literature since at least 1968, under the term proper velocity, or the catchier and IMHO less problematically confusing celerity. The definition given in the linked Wikipedia article

proper velocity is the ratio between distance traveled relative to a reference map frame (used to define simultaneity) and proper time τ elapsed on the clocks of the traveling object

is the same as my made-up-on-the-fly

 

I must admit I wasn’t following your exchange with A-Wal closely, but in an effort to be a responsible moderator, I’ll everyone to read and follow our site rules. The most important and most transgressed is “back up your claims by using links or references”, but “respect the opinions of others” is important, too, and IMHO harder, because it’s hard to be respectful when you see someone being obviously wrong.

 

My take on A-wal, from some months of back and forth in these fora, is that he’s doing his best to understand and promote SR as it’s generally understood by physicists, but approaches it informally, more in words and mental pictures than mathematically. As someone who more than I would like has to resort to this myself, I know it’s a perilous approach, because our informal intuition often misguides us.

 

SR is a mathematical physics theory, so best approached mathematically. Fortunately for folk like me with a limited science and math background, it has a huge and well-refereed literature, so most of the hard math work is done and just waiting for hacks of my ilk to enjoy vicariously and apply. Having enough background to do even this is IMHO an accomplishment.

 

That said, Velocity addition in SR is simple and uncontroversial, ( in units of c, it’s a pleasantly simple

[math]v_1’ = \frac{v_1 + v_2}{1+ v_1 v_2}[/math]

) so there shouldn’t be much disagreement about it here. Be clear, write as much math, and as little natural language as you can, have a link on hand showing you’re correct (which in my experience often saves one from erring before one posts), and don’t be hurried. Good things should follow.

 

The worst and most pernicious problem with this and other “science for everyone” forums is, I think, people who reject this approach in favor of the “I find this too difficult, so it must be wrong” justification, most often with the “I don’t want to pollute my original thinking by understanding anything written by anyone else” addendum.

 

I’m happy if these fora lead people to more correct science. Absolutely correct science, or even science correct in the sense of giving the correct answer in a class or GRE, is I think beyond us. We’re a forum, not a school.

 

 

Fair enough, but you did several things that fall into the category of "special pleading": making up your own word, your own special speedometer to justify a velocity of 260,000 km/s in violation of SR, for example. So, I feel justified in pointing that out.

 

As for the velocity addition formula, yes, that is what I posted, but not what others here have been doing.

 

And A-Wal says he CAN do the math! He claims he can derive E=mc^2 with just algebra and common sense, and says that any higher math is "nonsense".

 

OK, as per site rules, let him do this! If he does, I will post my derivation of E=mc^2 from first principles using differential calculus.

[exchemist]

Fair enough, but you did several things that fall into the category of "special pleading": making up your own word, your own special speedometer to justify a velocity of 260,000 km/s in violation of SR, for example. So, I feel justified in pointing that out.

 

As for the velocity addition formula, yes, that is what I posted, but not what others here have been doing.

 

And A-Wal says he CAN do the math! He claims he can derive E=mc^2 with just algebra and common sense, and says that any higher math is "nonsense".

 

OK, as per site rules, let him do this! If he does, I will post my derivation of E=mc^2 from first principles using differential calculus.

I think it would be very interesting and valuable for us non-specialist spectators to see you and A-Wal provide your rival derivations of this. 

 

I am intrigued by A-Wal's claim that is easy, as I had thought one needed GR (tensors and that) to derive it. But my training is in chemistry, so I easily get out of my depth with relativity. (I am a bit sounder on QM). 

[OceanBreeze]

I think it would be very interesting and valuable for us non-specialist spectators to see you and A-Wal provide your rival derivations of this. 

 

I am intrigued by A-Wal's claim that is easy, as I had thought one needed GR (tensors and that) to derive it. But my training is in chemistry, so I easily get out of my depth with relativity. (I am a bit sounder on QM). 

 

I made my derivation as simple as I could, no tensor or vector calculus, just using the Lorentz transform and basic differential calculus. A purist would not approve, but it is mathematically correct, but perhaps not rigorous. I am a marine engineer, not a physicist or a mathematician, but SR and GR interest me.

 

As for A-Wal's claim of deriving E=mc^2 with only algebra and common sense, I predict he will default on it.