Contradictory time dilation equations.

That distance isn't 0.8 light seconds for John.

Again, you are confusing the two frames of reference.

Sally is moving to the right at 0.6c the leftward movement of the light is 0.6c so that means that John doesn't see the light move right or left but from the floor to ceiling a distance of 0.8 light-seconds.
Do I have to keep repeating myself because you are mentally deficient?

You have to keep repeating yourself because you are wrong.Your math is leading to contradictions. You admit this yourself. This should be enough for you to admit that you are doing something wrong. Instead you have decided that your mistake means other people (including people who actually undery what they are talking about are mentally deficient.

1. Length in one frame of reference is not the same as it is for another frame. This fact is pretty basic.

2. You are the one arriving at basic contradiction is your mathemarics. I don't have this problem.

For anyone still reading who is interested in the science. These "time dialation equations" that are giving Fruity such difficulties aren't a proof of anything. They were a thought experiment used to develop a hypothesis. Fruity is wrong in his math, but he is also wrong in what the time dialation function means.

The function is

T1 = T0 √(1 - v^2/c^2)

Where T0 is time elapsed in the stationary frame, T1 is the time elapsed in the moving frame. And v is the velocity of the moving frame relative to the stationary frame.

The reason we know this correct is that we use this equation to make predictons that we can the confirm by experiment. Physicists accept time dialation because they confirmed it experimentally in multiple ways.

Fruity's problems with his contradictory logic don't change that.

The function is

T1 = T0 √(1 - v^2/c^2)

That equation is derived in the textbooks by Sally in a moving spaceship having a flashlight pointed straight up. Why are we required to use only that situation? If Sally is moving to the right why can't Sally have her flashlight pointed upward and to the left at an angle of 53.13 degrees from the horizontal? If that happens the function is now...

T0 = T1 √(1 - v^2/c^2)

Both equations are equally valid depending on how we set up the situation unless there is some fundamental reason why Sally can't have her flashlight pointed upward and to the left.

Earlier I stated that using the first equation we get...

So 0.8 seconds for Sally = 1 second for John.

Using the second equation we get...

So 1 second for Sally = 0.8 seconds for John.

The response was that there is no contradiction because each observer sees the other observer's clock as running more slowly than their own clock. That is a misunderstanding.

It is not...

0.8 seconds for Sally = 1 second for John according to John. (1st equation)
1 second for Sally = 0.8 seconds for John according to Sally. (1st equation)

That is using the first equation only. It is actually...

0.8 seconds for Sally = 1 second for John according to John. (1st equation)
1 second for Sally = 0.8 seconds for John according to John. (2nd equation)

It should be clear now that there is a contradiction.

Obviously if you are getting a contradiction you are making a mistake somewhere. I keep explaining to you what you are doing wrong. You keep persistently making the same mistake.

What you are doing is confusing the to reference frames. For each calculation you need to be clear about whose reference frame you are measuring in. Once you jump from one frame to the other, your logical reasoning no longer applies.

You are also confusing the derivation with a "proof".

The reason we know special relativity is "correct" (I am using quotes because the word "correct" is problematic) is that it has been tested by experiment. Over the past 100 years, Physicists have run experiments and made predictions... and yes, Special Relativity holds up.

Even if you could find a contradicton in the derivation, it would mean that the derivation is wrong. It wouldn't disprove the theory.

To disprove the theory you would need to show an experimental result that disagreed with the predicted result.

"What you are doing is confusing the to reference frames. For each calculation you need to be clear about whose reference frame you are measuring in. Once you jump from one frame to the other, your logical reasoning no longer applies."

When Sally points her flashlight straight up the distance from floor to ceiling is 0.8 light-seconds in Sally's frame of reference. The distance from floor to ceiling is 1 light-second along the diagonal of a hypotenuse in John's frame of reference.

When Sally points her flashlight up and to the left at an angle of 53.13 degrees from the horizontal the distance is 1 light-second along the diagonal of a hypotenuse in Sally's frame of reference. The distance is 0.8 light-seconds straight up from floor to ceiling in John's frame of reference.

I don't know what you mean by I'm "confusing the reference frames" or I'm "jumping from one frame to the other".

You are going around in circles.

Obviously if you are reaching a contradiction, then your mathematical reasoning is incorrect. If you reach a point where there is a contradiction then you have made a mistake somewhere.

Do you accept this?

There is no mistake as far as I can tell. The situation is exactly reversed so I don't see how there can be a mistake.

Flashlight straight up:
Sally sees light going straight up.
John sees light going at an angle of 53.13 degrees.

Flashlight at an angle of 53.13 degrees:
Sally sees light going at an angle of 53.13 degrees.
John sees light going straight up.

If there is a mistake I don't see what it could be.

You are making a couple I can see.

1. You second paragraph makes no sense. The distance from ceiling to floor is clearly a vertical line.

2. Your calculation in the third sentence is mathematically incorrect. I think you are trying to reverse the math from the original correct calculation and claim it is not the same.

Your problem is that time dilation only happens in the horizontal diection (yhe direction of motion). So your belief that these are equivalent is simply mathematically incorrect.

You say the situation is reversed. You are wrong. You shouls know you are wrong because that is where you are finding the contradictoon on your math.

Sorry I was reading you previous post...

Your assertion that "John sees the light go staight up" is incorrect. Special Relativity comes into play in this case... Because 53 Degrees in one frame of reference is not 53 degrees in another.

In the first case... For the horizontal component of motion is zero. Do you see why? That us why in the forst case v is zero for our transformation and we can simply the calculation.

In the aecond casw, the light is moving in the direction of the motion of travel. In this case, V is not zero and you are going to have to do the full calculation.

They are not equivalent. I think that is the simplest way to explain your mistake in this example.