# Time dilation

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#### AndrewS

I will begin with a standard opening.

When two observers, A and B, move inertially in relation to each other, SR predicts they will each see each other’s clock has slowed down. Suppose the speed of A’s clock is x and the speed of B’s is y. A will know that x>y and B will know that x<y. If a mathematical proposition gave rise to this result it would obviously be considered to be false. So it is with SR. A quantity cannot simultaneously be both larger and smaller than something else. SR leads to logically inconsistent predictions and so it must be false.

#### Woody

It is a matter of perspective

The seeming paradox can be looked at in almost the same way as 3D perspective.

The maths is made more complicated because it is a 4D problem,
but the basic situation is similar.

Because the observers are looking at the situation from a different "angle"
they "see" things differently

#### studiot

Since you are taking a more reasonable questioning line for soemthing you don't know here is the simple explanation.

In maths we can say that a < b and b < a are only true iff and only if a = b

In maths if a = b then they are the same thing.

In Physics saying this implies that there is an absolute time and that each observer observes this. That is they are observing the same thing.

They are not observing the same thing.

Each is observing the measurement relative to his own frame.

Because there is no absolute time (this is a consequence of special relativity) each can make a seemingly paradoxical measurement.

It is said that the fact there is no absolute time or absolute space is the most difficult thing to grasp in special relativity.

#### AndrewS

The seeming paradox can be looked at in almost the same way as 3D perspective.

The maths is made more complicated because it is a 4D problem,
but the basic situation is similar.

Because the observers are looking at the situation from a different "angle"
they "see" things differently
A very interesting answer, but this seems to have wider implications. When mathematicians dismiss a proposition on the basis that it leads to x>y and x<y, how can they be sure the proposition does not make sense in higher dimensions. How can logic ever be used with certainty in our everyday "3D" world?

It seems to me that relativists must say that each observer, and each particle, lives in their own universe (unless they happen to have absolutely identical velocities). This way the universe belonging to each particle, and each atom in our brains, might have its own time, size, mass and clock rate. And of course each particle keeps changing its universe when its velocity changes.

This denial of a single objective world is, of course, something that most non-relativists do not share. As far as I know, experiments do not support this denial, but I'd like to learn of anything to the contrary.

The denial of a single objective universe seems bad enough, but to risk undermining the certainty of "3D" logic would be a dangerous and seemingly needless step. Science depends on logic. Can't you just say that observers have their own universes giving x>y' and x'<y ?

#### HallsofIvy

I will begin with a standard opening.

When two observers, A and B, move inertially in relation to each other, SR predicts they will each see each other’s clock has slowed down. Suppose the speed of A’s clock is x and the speed of B’s is y. A will know that x>y and B will know that x<y. If a mathematical proposition gave rise to this result it would obviously be considered to be false. So it is with SR. A quantity cannot simultaneously be both larger and smaller than something else. SR leads to logically inconsistent predictions and so it must be false.

This does not say a quantity has two different values. It says that the times observed by the two different observers are two different quantities.

#### AndrewS

This does not say a quantity has two different values.
I don't see why you say this. Putting it another way, A sees that B's clock runs at 0.99 of the speed of A's clock and so deduces that A's clock is 1.01 faster. But B sees that A's clock is 0.99 as fast. This speed ratio has two different values. At least in our 3D world of logic, SR leads to the prediction that 0.99 = 1.01.

#### studiot

I don't see why you say this. Putting it another way, A sees that B's clock runs at 0.99 of the speed of A's clock and so deduces that A's clock is 1.01 faster. But B sees that A's clock is 0.99 as fast. This speed ratio has two different values. At least in our 3D world of logic, SR leads to the prediction that 0.99 = 1.01.
You have already been told that this is because they are measuring different quantities.

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#### AndrewS

They are both measuring the same ratio. Possibly they are different ratios in Minkowski space, but in the real world it is one ratio. In the example given it is the rate of A's clock divided by the rate of B's clock. Which other ratio are you talking about?

To make this more concrete, imagine the rockets send out regular radio time signals (at different frequencies so they can be distinguished). Each rocket makes a recording of when both signals are received. Back on Earth the recordings are compared. The rate of the approaching signals can be reduced by v/c to account for the reducing distance. In which case, if there is no time dilation the signal rates could be made identical. For each rocket, the signals could then be aligned at the start of the recording and no time lag would develop.

SR predicts that A's signals will be faster than B's and B's will be faster than A's. In other words the signals would be found to progressively lag each other. If the two sets of lags were plotted on a graph, A's set of lines would be to the right of B's and B's would be to the right of A's.

Can someone please tell me how this is possible in the real world.

#### studiot

They are both measuring the same ratio. Possibly they are different ratios in Minkowski space, but in the real world it is one ratio. In the example given it is the rate of A's clock divided by the rate of B's clock. Which other ratio are you talking about?

To make this more concrete, imagine the rockets send out regular radio time signals (at different frequencies so they can be distinguished). Each rocket makes a recording of when both signals are received. Back on Earth the recordings are compared. The rate of the approaching signals can be reduced by v/c to account for the reducing distance. In which case, if there is no time dilation the signal rates could be made identical. For each rocket, the signals could then be aligned at the start of the recording and no time lag would develop.

SR predicts that A's signals will be faster than B's and B's will be faster than A's. In other words the signals would be found to progressively lag each other. If the two sets of lags were plotted on a graph, A's set of lines would be to the right of B's and B's would be to the right of A's.

Can someone please tell me how this is possible in the real world.
Please define the 'rate of a clock', I do believe Einstein and the rest of the Physics world omitted this small detail.

The rate of anything has to be measured against something.

The whole point of special relativity is that there is no such something to measure against.

You are incorrectly attributing statements to SR that it does not make.

If you were to properly learn and understand the statements it does make I'm sure you would find things a great deal easier.

You should beware the popsci fraternity who are resposnsible for much misinformation on the subject often for the sake of sensationalism.

I repeat (after Berkson) The most difficult part of SR to get your head round is the assertion that there is no absolute space or absolute time to compare against.

#### AndrewS

Which other ratio are you talking about?
You still haven't answered my question.

If the ratio of clock rates is causing a problem then think of it as the ratio of clock speeds.

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