The Movement of Electricity in a Space Ship

  • B
  • Thread starter DonB
  • Start date
  • #1
71
0
Hello. I am an occasional poster here with little background but a big interest in the mental experiments (ME) of Einstein and others. Of particular interest to me are factors related to what I call the Classic Spaceship Mental Experiment. [mentor's note: a link to an unacceptable reference under the Physics Forums rules has been removed]

From previous discussions (some here) I understand that it is generally accepted (and correct me if I'm wrong) that:

1) Nothing can exceed the speed of light relative to any given "rigid point" (Einstein's term);

2) In a vacuum electricity travels through a wire at the speed of light.

That being the case, for a spaceship traveling at/near the speed of light relative to the earth, if an observer (O1) inside the spaceship turns on an electrical switch allowing electricity to flow from a battery located in the rear of the spaceship to a light bulb in his compartment, he will see the light come on since the electricity is traveling within the ship at c relative to him. However, an observer (O2) on the earth arguably will not be able to see the light come on since it would require electricity to travel at 2c relative to him.

Now let's take this ME to a more down to earth scenario. For a jet traveling at mach one, the electricity that runs the length of the fuselage is c relative to the pilot (O1). But according to our two givens above, since electricity can't travel at >c relative to O2, it must travel at <c relative to the fuselage as observed by O2 (i.e., no faster than c - mach-one)? So O2 would here see variations in lights and/or instrument readouts due to the abnormal speed of electricity relative to the jet? And would only the speed of electricity flow in the direction of flight be 'warped,' but the flow from the light back to the battery be normal?

The ramifications of the two givens seem to demand unworkable scenarios. So where is my thinking wrong on the ME above?
 
Last edited by a moderator:

Answers and Replies

  • #2
Dale
Mentor
Insights Author
2020 Award
30,844
7,445
The main mistake is assuming that velocities add the same way as they do in the Galilean transform. The correct formula is called the relativistic velocity addition formula. That always returns a value less than or equal to c.

A minor mistake is the idea that electricity travels through a wire at c. Light travels through a vacuum at c, but EM waves will travel slightly slower in a wire depending on the material properties. This is a minor point because you could replace all of your thought experiment wires with thought experiment lasers in vacuum for a very minimal cost.
 
  • #3
71
0
I appreciate the insights and corrections, Dale. But it still doesn't tell me if the light will be on for O1 yet off for O2 -- and if so, how that is possible. (I'm such a novice. Sorry.)
 
  • #4
russ_watters
Mentor
20,240
6,813
I appreciate the insights and corrections, Dale. But it still doesn't tell me if the light will be on for O1 yet off for O2 -- and if so, how that is possible. (I'm such a novice. Sorry.)
Subject to the signal propagation delays, each will see the light come on in due time.
 
  • #5
Nugatory
Mentor
13,230
6,093
But it still doesn't tell me if the light will be on for O1 yet off for O2 -- and if so, how that is possible.
Either the light turns on or it doesn't, and that has nothing to do with any observers moving at any speed anywhere - if the light is going to turn on, it's going to turn on no matter who is watching it. If one observer calculates that the light turns on and the other one calculates that it does not... Then one of them has miscalculated. As others have already mentioned, in this particular case the miscalculation is the result of not using the correct formula for addition of velocities - if you search this forum for references to "relativistic velocity addition" you will find many good explanations.
 
  • #6
Dale
Mentor
Insights Author
2020 Award
30,844
7,445
But it still doesn't tell me if the light will be on for O1 yet off for O2 -- and if so, how that is possible. (I'm such a novice. Sorry.)
In the scenario you described it will turn on in both O1 and O2 frames. The relativistic velocity addition formula explains how that can be compatible with the "speed limit" of c.
 
  • #7
18
3
Is this not the same question as if a person in the back of the ship shines a flashlight forward? Or if the ship turns its headlights on?
 
  • #8
Nugatory
Mentor
13,230
6,093
Is this not the same question as if a person in the back of the ship shines a flashlight forward? Or if the ship turns its headlights on?
It is indeed the same question.
 
  • #9
71
0
Thanks everyone for the input!
 
  • #10
821
192
I believe the length of the spaceship contracts, so the electricity doesn't have as far to go to reach the bulb (from the point of view of a stationary observer on Earth).
 

Related Threads on The Movement of Electricity in a Space Ship

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
469
Replies
16
Views
4K
  • Last Post
Replies
9
Views
4K
  • Last Post
Replies
2
Views
3K
Replies
8
Views
4K
Top