If airplanes' highest speed depends directly on the air it is moving through and ..

by cdux
Tags: airplanes, depends, directly, moving, speed
 P: 190 If airplanes' highest speed depends directly on the air it is moving through and not the ground, does it mean we can build a time machine if only the air moves near the speed of light?
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,904 Sorry but I can't make heads or tails of this! First there is no clear evidence that "moving near the speed of light" will help you build a time machine! There are some ways of interepreting relativity that lead to the idea that going faster than the speed of light has an effect on time but it is not clear whether that interpretation is true and, in any case, there is no way of going faster than the speed of light. And, finally, why talk about "air moving near the speed of light" when there is no better way of getting air to move "near the speed of light" (relative to what, by the way?) than the airplane itself.
Emeritus
PF Gold
P: 2,352
 Quote by cdux If airplanes' highest speed depends directly on the air it is moving through and not the ground, does it mean we can build a time machine if only the air moves near the speed of light?
I'm going to assume that you mean this: If the air were moving at near the speed of light and the plane was moving at a speed with respect to the air such that it's speed plus the speed of the air was greater than the speed of light, does it mean that we can get the plane moving faster than light?

The answer is no. This is because the speed of the air and the plane do not add up that way (no velocities do).

The formula you would have to use is

$$\frac{u+v}{1+\frac{uv}{c^2}}$$

Here u is the speed of the air and u the speed of the plane with respect to it. c is the speed of light (in a vacuum).

If you play around with this, you will quickly see that no matter how large u an v are (as long as they are less than c) the answer comes out to being less than c.

However, if u and v are very small compared to c, like they are in everyday experience, the answer comes out to being very nearly the same as u+v.

This is why we would say that the speed of the plane with respect to the ground is equal to the velocity of the air plus the airspeed of the plane. At normal speeds, using the simpler equation gives you an answer so close to the real answer that the difference is much much smaller than the uncertainty of the speeds that we start with. In addition, the simple equation is more intuitive to work with.

P: 190

If airplanes' highest speed depends directly on the air it is moving through and ..

 Quote by HallsofIvy Sorry but I can't make heads or tails of this! First there is no clear evidence that "moving near the speed of light" will help you build a time machine!
I had the impression time dilation is consensus accepted.
Mentor
P: 22,010
 Quote by cdux I had the impression time dilation is consensus accepted.
Time dilation is well established, but it only goes in one direction.
Thanks
P: 2,973
 Quote by cdux I had the impression time dilation is consensus accepted.
Both consensus-accepted and well and thoroughly experimentally verified. But that has absolutely nothing to do with building a time machine - at least what most people are thinking of when they say "time machine".

You might want to google the Hafele-Keating experiment to see what can be done by moving clocks around in airplanes.
P: 190
 Quote by Nugatory Both consensus-accepted and well and thoroughly experimentally verified. But that has absolutely nothing to do with building a time machine - at least what most people are thinking of when they say "time machine".
I thought it was accepted that any object moving faster than another is effectively in a time machine going into the future in relation to the slower object. It's also seen experimentally and on GPS satellites.
 P: 768 cdux, yes you're right it would indeed be a "time machine". In fact, every time there is relative motion you have a "time machine". Even if I wave my arms around they end up travelling in time relative to my body. As you mentioned, this only works going into the future. Everybody else seems to have assumed you were talking about a classical time machine which allows for going into the past...and your post did seem to lead towards that direction. So yes, it would be a time machine. HOWEVER, contrary to the implication of your post, adding the stipulation "if only the air moves near the speed of light?" doesn't make it any simpler or easier to accomplish any appreciable time travel.
PF Gold
P: 11,398
 Quote by cdux I thought it was accepted that any object moving faster than another is effectively in a time machine going into the future in relation to the slower object. It's also seen experimentally and on GPS satellites.
By your argument, everything is a time machine because SR always applies to moving objects. Problem is that the time shift is very small, usually and it's just a one way trip. Not a lot of practical use, I think.
P: 190
 Quote by sophiecentaur By your argument, everything is a time machine because SR always applies to moving objects.
Yes.
PF Gold
P: 11,398
 Quote by cdux Yes.
Thanks
P: 2,973
 Quote by cdux I thought it was accepted that any object moving faster than another is effectively in a time machine going into the future in relation to the slower object. It's also seen experimentally and on GPS satellites.
That's why I put in that disclaimer about what people usually mean when they talk abut a "time machine" - and you'll notice that the H-K experiment I pointed you at is literally using an airplane to study this effect.

You may have the sense of the dilation backwards as well?
P: 190
 Quote by Nugatory You may have the sense of the dilation backwards as well?
Why do you say that?