Verified answer

(a) any frame that does measurement, yields proper duration and distance measurements, so 1.39*10^-3 m

(b) gamma = 1/sqrt( 1 - (v/c)^2) = 4.592

contracted distance = 1.39*10^-3 / 4.592 (report to 3 sig figs)

(c) proper lifetime = distance traveled / speed = 1.39*10^-3 m / 299792458 (seconds, report to 3 sig figs)

(d) dilated lifetime = measured (proper) lifetime / gamma (report to 3 sig figs)

[EDIT:

Since you now have an alternate definition for "proper" in another response, know that it is an outdated term, mostly because no one gets it right.

http://en.wikipedia.org/wiki/Proper_time

http://en.wikipedia.org/wiki/Proper_length

... note that both definitions refer to measurements. The particle does not measure, the lab does.

]

[EDIT: "I get a bad answer on part d."

If you got part c right, then you just divide that answer by 4.592 (reporting only 3 sig figs).

And if they altered and used the other responders definition in error, try multiplying by 4.592.

]

Relativity is the idea that the laws of physics do not change from one inertial reference frame and another. Any experiment that you can do in your laboratory at home should work equally well in a train coach or the stateroom of a ship (provided the train/ship is just cruising along and not accelerating, bumping, rolling, or turning). This was known since before the time of Galileo. Newtonian mechanics incorporates relativity. Specifically, Newtonian mechanics work under the following transformation (called the Galilean transformation) from one reference frame (x,t) to another (x',t') moving at a speed v. x -> x' - vt' t -> t' That's pretty straightforward. Everybody measures the same time and their positions are off by a reasonable, intuitive amount based on the relative motion. Everyone agrees on the time and distance between two events. Now the trouble is that the laws of electricity and magnetism (discovered by various folks and compiled by Maxwell) are NOT invariant under this transformation. Some folks thought that the old concept of relativity does not apply to electricity and magnetism--that the laws of E&M only work with respect to an ether. Einstein, however, assumed that relativity SHOULD apply to E&M and that Newtonian mechanics must be flawed. He thereby developed special relativity and derived new transformation laws (which had already been figured out by Lorentz, so they have his name). x -> gamma (x' - vt') t -> gamma (t' - vx' / c^2) Under these new laws, not everybody measures the same times and distances between events. That factor of gamma goes from one at slow speeds up towards infinity as you approach the speed of light. Moving clocks run slow and moving rulers are short!

¹ ² ³ ½ ¼ ¾ ⅓ ⅔ ∑ ∫

δ ε ω μ σ α ß Ω

¢ £ ≡ ≤ ≥ ≠ ∞ ÷ ∩ ~ ≈

± √ π r ²

λ θ • °

Αα Ββ Γγ Δδ Εε Ζζ Ηη Θθ Ιι Κκ Λλ Μμ Νν

Ξξ Οο Ππ Ρρ Σσς Ττ Υυ Φφ Χχ Ψψ Ωω

≡ ≈ ≅ ≠ ≤ ≥ · ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ∩ ⊥ ô

∫ Σ → ∞ Π Δ Φ Ψ Ω Γ ∮ ∇∂ √ ∅ °

α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω

⁰ ¹ ² ⁻³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

⅓ ⅔ ⅕ ⅖ ⅗ ⅘ ⅙ ⅚ ⅛ ⅜ ⅝ ⅞

(a) What is the proper distance traveled? (in meters): 1.39*10⁻³ m

(b)What is the distance measured by a hypothetical person traveling with the particle?(in m):0 m

(c)Determine the particle's the proper lifetime (in s)[(1.39*10⁻³)/(3*10⁸)]/[1-0.976²] =1.0*10⁻¹² s

s

(d) Determine the particle's dilated lifetime (in seconds)

= (1.39*10⁻³)/(3*10⁸) = 0.463*10⁻¹¹1 = 4.63*10⁻¹² s

S= s'(t) . b) is uncorrect qwestion. c) is better not to count too. d) v/s. In a) i mean s= S0+vt +at^2/2=S0+s'+s''=s'=vt.