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Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connectionsPath: ...!news.misty.com!weretis.net!feeder6.news.weretis.net!i2pn.org!i2pn2.org!.POSTED!not-for-mail From: "Paul B. Andersen" Newsgroups: sci.physics.relativity Subject: Re: [SR] Usefulness of real velocities in accelerated relativistic frames of reference. Date: Fri, 15 Mar 2024 15:13:54 +0100 Organization: i2pn2 (i2pn.org) Message-ID: References: <1bIiiMt-l_wW2d7hcr84gCA75z0@jntp> MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Fri, 15 Mar 2024 14:12:30 -0000 (UTC) Injection-Info: i2pn2.org; logging-data="2076623"; mail-complaints-to="usenet@i2pn2.org"; posting-account="8Yhz2eYcUsjFGSoMAG25uV/n1O3WYK/Xqk0svbo8Ftc"; User-Agent: Mozilla Thunderbird In-Reply-To: Content-Language: en-US X-Spam-Checker-Version: SpamAssassin 4.0.0 Bytes: 4103 Lines: 100 Den 14.03.2024 17:18, skrev Richard Hachel: > Le 14/03/2024 à 15:02, "Paul B. Andersen" a écrit : >> A rocket is accelerating at the constant proper acceleration a. >> An inertial frame of reference K(x,t) is at the time t = 0 >> instantly co-moving with the rocket. >> >> You claim: >> According to SR the speed of the rocket in K is Vr(t) = a⋅t >> =========================================================== >> >> Note that this means that Vr > c when t > c/a >> which according to SR is impossible. >> >> A rocket is accelerating at the constant proper acceleration a. >> An inertial frame of reference K(x,t) is at the time t = 0 >> instantly co-moving with the rocket. >> >> You claim: >> According to SR the speed of the rocket in K is Vr(t) = a⋅t >> =========================================================== >> >> Note that this means that Vr > c when t > c/a >> which according to SR is impossible. >> >> >> Contradicting fact: >> ------------------- >> So this is wrong. >> You can see the correct derivation here: >> https://paulba.no/pdf/TwinsByMetric.pdf >> See chapter 2.3, equation (15) >> >> Vr(t) = a⋅t/√(1+(a⋅t/c)²) >> >> Note that: >>   Vr → a⋅t when t → 0 >>   Vr → c   when t → ∞ >> >> >> Your problem is that you do not understand the difference >> between proper acceleration of the rocket, and the rocket's >> coordinate acceleration in the inertial frame. >> >> If A is the coordinate acceleration in K, we have: >> >> A = dVr/dt = a/(√(1+(a⋅t/c)²))³ >> >> Note that: >>   A → a when t → 0 >>   A → 0 when t → ∞ >> >> So  Vr(t) = ∫(from 0 to t)A⋅dt = a⋅t/√(1+(a⋅t/c)²) >> >> You claim: >> According to SR is the average speed of the rocket Vm(t) = Vr(t)/2 >> ===================================================================== >> >> Contradicting fact: >> ------------------- >> This is wrong. >> >> Vr(t) = a⋅t/√(1+(a⋅t/c)²) >> >> The average speed Vm at the time t is: >> Vm = (integral from t=0 to t=t of Vr(t)dt)/t >> Vm = c²⋅(√(1+(a⋅t/c)²)-1)/a⋅t >> >> Note that: >>   Vm → a⋅t/2 when t → 0 >>   Vm → c     when t → ∞ >> >> So: >>   Vm/Vr  → 1/2  when t → 0 >>   rm/Vr  → 1    when t → ∞ >> >> So for any t > 0   Vm > Vr/2 >> >> It is not possible to make SR predict anything else! >> ==================================================== > > You don't understand anything I'm telling you... I do indeed understand that you telling me: Vr(t) = a⋅t and: Vm(t) = Vr(t)/2 And I do indeed understand that what you are telling me is wrong. And it is a very naive and elementary blunder! > > In these conditions, it is very difficult to discuss. I do understand that you find it difficult to defend your own words. So that's why you don't even try, right? -- Paul https://paulba.no/