Here is a web page adding speeds v and w.

https://demonstrations.wolfram.com/EinsteinsFormulaForAddingVelocities/

Suppose a baseball team is traveling on a train moving at v = 60 mph. The star fastball pitcher needs to tune up his arm for the next day’s game. Fortunately, one of the railroad cars is free, and its full length is available. If his w = 90 mph pitches are in the same direction the train is moving, the ball will actually be moving at V = 150 mph relative to the ground. The law of addition of velocities in the same direction is relatively straightforward, V = w + v. But according to Einstein’s special theory of relativity, this is only approximately true...

Unquote.

Lets say the speed limit on the track is c = 120 miles per hour. Nothing on track goes faster than speed-c, not even the baseball.

Use ( 5 /4 ) for dimensionless reduction factor greater than 1.

V = ( 60 mph + 90 mph ) / ( 5 /4 ) = 120 mph

60 mph-train + 60 mph-bball = 120 mph

30 mph-train + 90 mph-bball = 120 mph

48 mph-train + 72 mph-bball = 120 mph

The last option is what you might call “symmetric.”

V = 60 / ( 5 / 4 ) + 90 / ( 5 / 4 ) = 120

Einstein-EDoMB-1905-Section §5, quote:

“It is worthy of remark that v and w enter into the expression for resultant velocity in a symmetrical manner.”

The train is going down the track at 60 mph. Somebody decides to toss a baseball. The train must slow down to 48 mph.

Gimme a break !

On 1/13/2024 6:19 AM, xip14 wrote:
> Here is a web page adding speeds v and w.
>
> https://demonstrations.wolfram.com/EinsteinsFormulaForAddingVelocities/
>
> Suppose a baseball team is traveling on a train moving at v = 60 mph. The star fastball pitcher needs to tune up his arm for the next day’s game. Fortunately, one of the railroad cars is free, and its full length is available. If his w = 90 mph pitches are in the same direction the train is moving, the ball will actually be moving at V = 150 mph relative to the ground. The law of addition of velocities in the same direction is relatively straightforward, V = w + v. But according to Einstein’s special theory of relativity, this is only approximately true...
>
> Unquote.
>
> Lets say the speed limit on the track is c = 120 miles per hour. Nothing on track goes faster than speed-c, not even the baseball.
>
> Use ( 5 /4 ) for dimensionless reduction factor greater than 1.
>
> V = ( 60 mph + 90 mph ) / ( 5 /4 ) = 120 mph
>
> 60 mph-train + 60 mph-bball = 120 mph
>
> 30 mph-train + 90 mph-bball = 120 mph
>
> 48 mph-train + 72 mph-bball = 120 mph
>
> The last option is what you might call “symmetric.”
>
> V = 60 / ( 5 / 4 ) + 90 / ( 5 / 4 ) = 120
>
> Einstein-EDoMB-1905-Section §5, quote:
>
> “It is worthy of remark that v and w enter into the expression for resultant velocity in a symmetrical manner.”
>
> The train is going down the track at 60 mph. Somebody decides to toss a baseball. The train must slow down to 48 mph.
>
> Gimme a break !

You would need to use the equivalent of the relativistic speed
combination formula, which is w=(u+v)/(1+uv/c²). For your 60 mph train
and 90 mph fastball, it would be w=(60+90)/(1+(60*90/(120*120))) or
150/(1+5400/14400) or 150/(1+0.375) or 109.0909... mph seen from the ground.

On Saturday 13 January 2024 at 22:18:32 UTC+1, Volney wrote:
> On 1/13/2024 6:19 AM, xip14 wrote:
> > Here is a web page adding speeds v and w.
> >
> > https://demonstrations.wolfram.com/EinsteinsFormulaForAddingVelocities/
> >
> > Suppose a baseball team is traveling on a train moving at v = 60 mph. The star fastball pitcher needs to tune up his arm for the next day’s game. Fortunately, one of the railroad cars is free, and its full length is available. If his w = 90 mph pitches are in the same direction the train is moving, the ball will actually be moving at V = 150 mph relative to the ground. The law of addition of velocities in the same direction is relatively straightforward, V = w + v. But according to Einstein’s special theory of relativity, this is only approximately true...
> >
> > Unquote.
> >
> > Lets say the speed limit on the track is c = 120 miles per hour. Nothing on track goes faster than speed-c, not even the baseball.
> >
> > Use ( 5 /4 ) for dimensionless reduction factor greater than 1.
> >
> > V = ( 60 mph + 90 mph ) / ( 5 /4 ) = 120 mph
> >
> > 60 mph-train + 60 mph-bball = 120 mph
> >
> > 30 mph-train + 90 mph-bball = 120 mph
> >
> > 48 mph-train + 72 mph-bball = 120 mph
> >
> > The last option is what you might call “symmetric.”
> >
> > V = 60 / ( 5 / 4 ) + 90 / ( 5 / 4 ) = 120
> >
> > Einstein-EDoMB-1905-Section §5, quote:
> >
> > “It is worthy of remark that v and w enter into the expression for resultant velocity in a symmetrical manner.”
> >
> > The train is going down the track at 60 mph. Somebody decides to toss a baseball. The train must slow down to 48 mph.
> >
> > Gimme a break !
>
> You would need to use the equivalent of the relativistic speed

And do you still believe that adjudting clocks
to tour 9 192 631 770 ISO idiocy means some "Newton
mode"? You're such an agnorant idiot, stupid Mike, even
considering the average in your insane relativistic church.

> You would need to use the equivalent of the relativistic speed
> combination formula, which is w=(u+v)/(1+uv/c²). For your 60 mph train
> and 90 mph fastball, it would be w=(60+90)/(1+(60*90/(120*120))) or
> 150/(1+5400/14400) or 150/(1+0.375) or 109.0909... mph seen from the ground.

Sci/phys no longer works for me as a web page so I am throwing in the towel..

Google’s blogspot works, at least for now.

https://dibdeck.blogspot.com/

The symmetry problem is not 150 → 109 versus 150 → 120. Who cares?

Problem: Do you cut back one or both speeds v and w?

Cutting train speed-v when baseball mass is negligible makes no sense.

On 1/14/2024 1:47 PM, xip14 wrote:
>
>> You would need to use the equivalent of the relativistic speed
>> combination formula, which is w=(u+v)/(1+uv/c²). For your 60 mph train
>> and 90 mph fastball, it would be w=(60+90)/(1+(60*90/(120*120))) or
>> 150/(1+5400/14400) or 150/(1+0.375) or 109.0909... mph seen from the ground.
>
> Sci/phys no longer works for me as a web page so I am throwing in the towel.
>
> Google’s blogspot works, at least for now.
>
> https://dibdeck.blogspot.com/
>
> The symmetry problem is not 150 → 109 versus 150 → 120. Who cares?

Anyone who wants the correct answer cares.
>
> Problem: Do you cut back one or both speeds v and w?

Neither. Your mistake is assuming the speeds are strictly a sum. It's
not. A simple sum is an *approximation* that works for low speeds
compared to c. Like a real baseball thrown from a real train.
>
> Cutting train speed-v when baseball mass is negligible makes no sense.

That's because "cutting" the speed of either the train or the ball is
completely wrong.

On Monday 15 January 2024 at 06:28:13 UTC+1, Volney wrote:
> On 1/14/2024 1:47 PM, xip14 wrote:
> >
> >> You would need to use the equivalent of the relativistic speed
> >> combination formula, which is w=(u+v)/(1+uv/c²). For your 60 mph train
> >> and 90 mph fastball, it would be w=(60+90)/(1+(60*90/(120*120))) or
> >> 150/(1+5400/14400) or 150/(1+0.375) or 109.0909... mph seen from the ground.
> >
> > Sci/phys no longer works for me as a web page so I am throwing in the towel.
> >
> > Google’s blogspot works, at least for now.
> >
> > https://dibdeck.blogspot.com/
> >
> > The symmetry problem is not 150 → 109 versus 150 → 120. Who cares?
> Anyone who wants the correct answer cares.
> >
> > Problem: Do you cut back one or both speeds v and w?
> Neither. Your mistake is assuming the speeds are strictly a sum. It's
> not.

Assertions are not any arguments, stupid Mike.

Your suggestion is in fact possible. Normally when the train goes down the track at 60 mph, Lorentz Contraction and time dilation kick in – on the train. That is, miles and hours on the train differ from miles and hours on the ground.

Reverse that conception. Miles and hours on the train are exactly like miles and hours on the ground. Thus baseball speed of 90 mph on the train is exactly like 90 mph on the ground.

Combined train and baseball speed is measured on the ground, most simply as 150 mph. But the moving train transforms miles and hours on the ground – at least those miles and hours which look at the baseball. According to the new milepost and new clock on the ground, the baseball is going 120 mph. But this newness does not look at old train ground speed of 60 mph.

This model says in effect that the stationmaster who observes baseball speed of 120 mph cannot observe train speed of 60 mph. Very strange.

Einstein’s 1920 derivation might suggest something along these lines. On my blog, I paraphrase the 1920 derivation without suggesting the reversed interpretation.

I did an eyewitness account, no equations, no ISO 8-bit, just text, as the last the last few paragraphs of the blog. Einstein’s 1920 accounting is hard to figure.

I did an eyewitness account, no equations, no ISO 8-bit, just text, as the last few paragraphs of the blog. Einstein’s 1920 accounting is hard to figure.

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