- #1

BiGyElLoWhAt

Gold Member

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## Main Question or Discussion Point

Let us have an observer moving at some velocity v.

And let our observer have 2 mirrors, one on either side of their vehicle, that they will use to measure time.

In this situation, our observer is using a single photon (or ray, it really doesn't matter) to measure time. A ray of light bounces from one mirror and hits the other. Our observer uses the formula ##\frac{distance}{time}## to calculate the speed of light. If the light indefinitely bounces back and forth between the same 2 spots in the (parallel) mirrors, then at rest, our observer will calculate a speed equal to c.

If our observer moves at a velocity v, they will calculate a value less than c.

This is because our observer's (with respect to an outside observer's) coordinate system is in motion, and thus he/she see's only one component of the lights velocity, lets assume the x component (our observer is traveling along the y axis)

To our rider (our subjective observer), light is moving back and forth along some line (for simplicity y=0) indefinitely. To an outside observer, light is traveling with the same x component, but also a y-component that accounts for the difference in measured values of c.

Now, let us assume that our riders mirrors also have a way of emitting a photon (SPDC or whatever). So we have the same photon bouncing back and forth between the mirrors, and giving a measured value of less than c, which he/she compensates for via time dilation.

Since our (subjective) observer, has a way of emitting light, they take advantage of this fact, and emit a photon with a velocity perpendicular to the surface of the mirror (because in their rest frame, this should cause it to bounce back and forth between the same 2 spots on the mirrors, just like the first photon). To our observers dismay, it doesn't. If our observer is traveling at .5c, then the angle (with respect to the perspective of our subjective observer) is 45 degrees. If our observer then measures the distance traveled based on the angle and distance between the 2 mirrors, and then uses that to calculate c, it will appear that this particular photon is moving faster than c, whereas to an outside observer it is merely a photon oscillating along a line (say y=1) as long as there are mirrors there to reflect it.

If our observer uses photon 1 to calculate the time dilation, it will appear as though time is moving slower (greater delta t) and if he/she uses photon 2 to calculate time, it will appear as though time is moving faster (greater delta x).

This is entirely different to an outside observer who would see the y-component of photon 1 and be able to calculate the accepted value of c, and would see that photon 2 is just oscillating along a line (y=1) and would be able to calculate the accepted value of c using photon 2 as well!

Am I misunderstanding the concept of time dilation or what's the explanation for this?

And let our observer have 2 mirrors, one on either side of their vehicle, that they will use to measure time.

In this situation, our observer is using a single photon (or ray, it really doesn't matter) to measure time. A ray of light bounces from one mirror and hits the other. Our observer uses the formula ##\frac{distance}{time}## to calculate the speed of light. If the light indefinitely bounces back and forth between the same 2 spots in the (parallel) mirrors, then at rest, our observer will calculate a speed equal to c.

If our observer moves at a velocity v, they will calculate a value less than c.

This is because our observer's (with respect to an outside observer's) coordinate system is in motion, and thus he/she see's only one component of the lights velocity, lets assume the x component (our observer is traveling along the y axis)

To our rider (our subjective observer), light is moving back and forth along some line (for simplicity y=0) indefinitely. To an outside observer, light is traveling with the same x component, but also a y-component that accounts for the difference in measured values of c.

Now, let us assume that our riders mirrors also have a way of emitting a photon (SPDC or whatever). So we have the same photon bouncing back and forth between the mirrors, and giving a measured value of less than c, which he/she compensates for via time dilation.

Since our (subjective) observer, has a way of emitting light, they take advantage of this fact, and emit a photon with a velocity perpendicular to the surface of the mirror (because in their rest frame, this should cause it to bounce back and forth between the same 2 spots on the mirrors, just like the first photon). To our observers dismay, it doesn't. If our observer is traveling at .5c, then the angle (with respect to the perspective of our subjective observer) is 45 degrees. If our observer then measures the distance traveled based on the angle and distance between the 2 mirrors, and then uses that to calculate c, it will appear that this particular photon is moving faster than c, whereas to an outside observer it is merely a photon oscillating along a line (say y=1) as long as there are mirrors there to reflect it.

If our observer uses photon 1 to calculate the time dilation, it will appear as though time is moving slower (greater delta t) and if he/she uses photon 2 to calculate time, it will appear as though time is moving faster (greater delta x).

This is entirely different to an outside observer who would see the y-component of photon 1 and be able to calculate the accepted value of c, and would see that photon 2 is just oscillating along a line (y=1) and would be able to calculate the accepted value of c using photon 2 as well!

Am I misunderstanding the concept of time dilation or what's the explanation for this?