The Movement of Electricity in a Space Ship

In summary, the conversation discusses the Classic Spaceship Mental Experiment, in which an observer on a spaceship traveling near the speed of light turns on a light bulb and whether or not it can be seen by an observer on Earth. Factors such as the speed of light and the relativity of velocities are mentioned, and it is clarified that the light will turn on for both observers due to the relativistic velocity addition formula. The concept of length contraction is also brought up as a potential explanation.
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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?
 
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  • #2
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
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
DonB said:
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
DonB said:
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
DonB said:
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
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
Ben123 said:
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
Thanks everyone for the input!
 
  • #10
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).
 

1. How does electricity move in a space ship?

The movement of electricity in a space ship is similar to its movement on Earth. It travels through conductors, such as wires and circuits, to power different systems and equipment. However, in space, there is no gravity to pull the electricity down, so it moves in all directions until it reaches its destination.

2. What powers the electricity in a space ship?

The electricity in a space ship is powered by various sources, such as batteries, solar panels, and fuel cells. These sources generate electricity through chemical reactions or the conversion of light into energy. The type of power source used depends on the specific needs and capabilities of the space ship.

3. How is electricity distributed throughout a space ship?

Electricity is distributed throughout a space ship through a series of interconnected circuits. These circuits are designed to deliver the right amount of electricity to different systems and equipment, and to prevent overloading or short circuits. In larger space ships, there may be multiple circuits and backup systems to ensure a steady supply of electricity.

4. How is electricity used in different systems on a space ship?

Electricity is used in various systems on a space ship, such as navigation, life support, communication, and propulsion. In navigation systems, electricity powers instruments and sensors to help the space ship navigate through space. In life support, it is used to regulate temperature, provide oxygen, and recycle air. Communication systems use electricity to transmit and receive signals, and propulsion systems use it to power engines and control movement.

5. What are the risks of electricity in a space ship?

The main risk of electricity in a space ship is the potential for malfunctions or failures in the electrical systems. This can be caused by various factors, such as damage from space debris, radiation exposure, or human error. In the event of an electrical failure, it could impact the functioning of critical systems, putting the crew and mission at risk. Proper maintenance and backup systems are crucial to minimize these risks.

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