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.

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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.

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