# Measuring the speed of light on moving systems

• B
• CHAIM123
In summary, according to the second postulate of relativity, if an object moves at half the speed of light then time is slower for that object.
CHAIM123
A spaceship moves at half the speed of light, what will be the results of measuring the speed of light for it: in relation to the light source it is approaching and in relation to the light source from which it is moving away?

What do you mean by "in relation to"? And what does the second postulate of relativity say?

If I'm not understood it's because I have to translate into English. I'm sorry.
I learned that the speed of light is always constant, and if I move at half the speed of light then time is slower, so I can't measure the speed of light as higher. The question is in relation to the light coming from a light source from which I move away, is the speed measured constant even then?
I apologize for my ignorance... I'm barely a beginner...

PeroK
CHAIM123 said:
is the speed measured constant even then?
The answer to your question is the second postulate if relativity. Can you quote it?

CHAIM123 said:
if I move at half the speed of light then time is slower, so I can't measure the speed of light as higher.
This is half of the story, which may be confusing you. You also need to take into account the relativity of simultaneity.

CHAIM123
Ibix said:
This is half of the story, which may be confusing you. You also need to take into account the relativity of simultaneity.
Thank you !!!
I started reading about the subject. It will take me a long time to figure it out...

CHAIM123 said:
If I'm not understood it's because I have to translate into English. I'm sorry.
I learned that the speed of light is always constant, and if I move at half the speed of light then time is slower, so I can't measure the speed of light as higher. The question is in relation to the light coming from a light source from which I move away, is the speed measured constant even then?
I apologize for my ignorance... I'm barely a beginner...
There is no such thing as "moving at half the speed of light". All motion is relative. You must be moving at half the speed of light relative to something. There is also no such thing as "time running slower".

Consider these two scenarios, which are physically equivalent:

You are on Earth and a spacecraft is moving towards the Earth at half the speed of light. Note that this means the Earth is moving towards the spacecraft at half the speed of light.

You emit a light signal towards the spacecraft. Both you and the spacecraft measure the speed of that light signal as ##c##.

The spacecraft emits a light signal towards Earth. Both you and the spacecraft measure the speed of that light signal as ##c##.

In relativity, there is no physical difference between the Earth and spacecraft in this scenario. There is no sense in which the spacecraft is "really" moving or the Earth is "really" moving. The motion is relative.

PeroK said:
There is no such thing as "moving at half the speed of light". All motion is relative. You must be moving at half the speed of light relative to something. There is also no such thing as "time running slower".

Consider these two scenarios, which are physically equivalent:

You are on Earth and a spacecraft is moving towards the Earth at half the speed of light. Note that this means the Earth is moving towards the spacecraft at half the speed of light.

You emit a light signal towards the spacecraft. Both you and the spacecraft measure the speed of that light signal as ##c##.

The spacecraft emits a light signal towards Earth. Both you and the spacecraft measure the speed of that light signal as ##c##.

In relativity, there is no physical difference between the Earth and spacecraft in this scenario. There is no sense in which the spacecraft is "really" moving or the Earth is "really" moving. The motion is relative.
Isn't time slower in a body that is in fast motion or when the density of matter in its environment is high?

CHAIM123 said:
Isn't time slower in a body that is in fast motion
No. If you are in inertial motion moving fast relative to me then in my rest frame I will measure your clocks to be ticking slowly. But you will measure my clocks to be ticking slowly. So "time runs slowly" is an inadequate description.
CHAIM123 said:
or when the density of matter in its environment is high?
"Time runs slowly" is always a terrible description. But with some very large caveats, it's less terrible in this context. Clocks at lower gravitational potential will tick slower than those at high potential.

PeroK and CHAIM123
CHAIM123 said:
Isn't time slower in a body that is in fast motion
There is no such thing as "a body in fast motion".
CHAIM123 said:
or when the density of matter in its environment is high?
It's best to leave gravitation (general relativity) until you understand special relativity (no gravity).

CHAIM123 said:
The question is in relation to the light coming from a light source from which I move away, is the speed measured constant even then?
Yes. In your rest-frame, the source is moving away from you.
As others mentioned, see the two postulates of SR:

Wikipedia said:
1. First postulate (principle of relativity)

The laws of physics take the same form in all inertial frames of reference.​

2. Second postulate (invariance of c)

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same value c in all inertial frames of reference.​
Source:
https://en.wikipedia.org/wiki/Postulates_of_special_relativity

From the definition of an inertial standard coordinate system, the assumption, that the transformation must be linear and those two postulates follows the Lorentz transformation:
https://en.wikipedia.org/wiki/Lorentz_transformation

Sorry, what if we take the constancy of the speed of the sound as second postulate of special relativity ? As far I know the speed of the sound is independent from the motion of the source as well.

Motore
cianfa72 said:
Sorry, what if we take the constancy of the speed of the sound as second postulate of special relativity ? As far I know the speed of the sound is independent from the motion of the source as well.
It's dependant on the speed of the medium, though, so it isn't frame invariant and doesn't lead to relativity.

PeroK
Ibix said:
It's dependant on the speed of the medium, though, so it isn't frame invariant and doesn't lead to relativity.
So consider the following scenario: let's take an inertial frame in which the medium is at rest and source in moving with a given velocity. The measured speed of sound in this inertial frame will be let me say ##s## regardless of the motion of the source.

Now switch to another inertial frame (where the source and the medium are moving): in this inertial frame the measured speed of sound will be independent from the motion of the source as well, however it will be different from ##s##, hence it is not frame invariant.

Ibix

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