Would computers accelerated to high speeds compute "faster" from our point of view?

There are some cosmic ray muons hitting the ground that would disagree with your perverse and confused interpretation of special relativity.

It is precisely *because* they are moving so quickly that they *DO* last much longer in our almost stationary observers rest frame on the Earth.

Their clock time is subject to a gamma factor of about 40x.

It is possible to derive the classic SR Lorentz transformations by very careful consideration of the mutual events of two metre rules as measured in their respective rest frames passing each other at a speed v enough for relativistic corrections to apply by invoking reciprocity.

I think it is more appropriate to ask you that question.

I think the problem here is the conflict between two oft-heard statements:

1. Velocity is relative - there is no such thing as a single fixed coordinate system for the universe, so there cannot be such a thing a as absolute velocity.
2. So local time in a moving platform (like a spaceship) passes slower and slower the faster the platform is moving.

So in the twin paradox, given that velocity is relative, one ought to be able to arbitrarily say that ship 2 is stationary, and ship 1 is traveling at 0.9 C, or vice versa. So, how is it that one ages but the other doesn't? By symmetry, they cannot differ.

What then breaks the symmetry? The obvious answer is the differences in the acceleration histories of the two ships? How?

A clear answer might settle this debate thread.

Joe Gwinn

just depend on agreeing whether you get paid for the hours worked, or you get paid for the hours you couldn't do something else

Actually there is - the microwave background defines a a zero velocity coordinate from which it looks essentially uniform in every direction.

It's a proxy for the "fixed stars" which is now the retreating galaxies.

Integrating the acceleration gives you velocities.

Probably not. If you are silly enough to ask the question, you are probably too silly to understand the answer.

You can't even state the problem correctly. Our frame of reference is no more stationary than the muon. This is why it is impossible to define simultaneity under some conditions. In one frame of reference A precedes B, in another frame of reference B precedes A. There is no right answer just as there is no stationary frame of reference.

Please analyze the muon reaching the ground with the observer moving with the muon rather than on the ground.

I was discussing a topic. Was there something I said that you found unclear?

I'm pretty sure that's a fallacy. Every point in the universe sees the entire rest of the universe expanding away from that point, including the microwave background. It should appear the same everywhere in the universe if you are referring to the extent of the red-shift. What do you mean exactly by "it looks essentially uniform"? Uniform in what aspect?

That's hard to do. When we consider the moving train analogy, that typically ignored the method of viewing what is happening on the other train. I expect this can complicate the matter as well.

It isn't.

As soon as you start moving with respect to the rest of the universe the segment of the microwave background you are moving towards is Doppler shifted to a shorter wavelength, and the segment you are moving away from is Doppler-shifted to a longer wavelength.

If you are in the business of getting and staying confused, you can find a lot of stuff to get confused about.

Our rest frame is stationary with respect the visible universe (give or take our orbital velocity around out galactic centre, and the fact that our galaxy is moving towards the Andromeda galaxy, both at rather small fractions of the speed of light).

Except that the "fixed stars", now called the cosmic microwave background, is just such a stationary frame of reference. Hubble recession means that it isn't exactly stationary, but it does serve the purpose.

The observer moving with the muon got converted to an extremely warm plasma as soon as it reached the outskirts of the atmosphere.

They won't be interested in hearing about your analysis.

Oh, but it is.

So I can measure my speed through the ether? Wow! Too bad Michelson and Morley didn't know about this. Who has measured out speed through the microwave background? What is our speed relative to the universe?

Wow! What if the Universe is itself moving? Maybe the Universe is moving at some huge factor of the speed of light? That would be trippy!

Yeah, let us know how it works out for you.

Why? That definition is a bit circular. The part of the universe is defined by our rest frame. The muon doesn't care about any of that, does it?

The purpose of what? What we can observe, will be defined by our rest frame. Saying our rest frame is defined by what we see is meaningless.

What if we were accelerated to 0.99 c relative to our previous rest frame by passing by a star or black hole? Would that make our rest frame different? Would it change the view of the universe? Would it change the microwave background?

Yeah, that's what I figured. This stuff is beyond you these days. Sorry about that.

Clearly it does, otherwise it would decay a lot faster.

If we couldn't see it, how could we call it a rest frame?

Quite obviously it would. Our view of the universe would be distorted by Lorenz contraction, for a start, and the cosmic ray background would look at lot hotter in the direction we were heading and a lot cooler in the direction we were leaving behind.

We'd probably get mashed by tidal forces in the process

It looks more as if it is beyond you.

"a dipole anisotropy from the Doppler shift of the background radiation. The latter is caused by the peculiar velocity of the Sun relative to the co-moving cosmic rest frame as it moves at some 369.82 ± 0.11 km/s towards the constellation Leo (galactic longitude 264.021 ± 0.011, galactic latitude 48.253 ± 0.005).[11] The CMB dipole and aberration at higher multipoles have been measured, consistent with galactic motion.[12]

It wasn't looking at the ether (which doesn't seem to exist) but the microwave backgrounds photons flying around, which do.

The Sun is moving at about 0.123%of the speed of light in the direction of the constellation Leo. Most of that is probably its orbital velocity around the centre of our galaxy - I haven't checked that recently but 0.123% of c seems to be in the right ballpark.

I just did.

It comes back to two fairly simple axioms.

1. The laws of physics are identical for any observer in an inertial frame of reference (ie in constant linear motion - not accelerating).

1. The speed of light in vacuum is a constant of nature.

Everything else in special relativity follows from that.

And that is clearly verified experimentally!

The thing that matters is that you can only compare times between mutual events that are defined at fixed coordinates in spacetime. Events where the twins are colocated however briefly (though preferably in the same frame of reference) have a well defined spacetime distance between them.

Once they are spatially separated you can choose other reference frames to alter their spacetime coordinates within certain limits determined by the light cone of causality. The consequences of an event cannot ever stray outside the causally connected zone defined by the speed of light.

The only way the twin who travels can ever get back to where he started is to accelerate in some fashion. Either to go around in a big circle like the particles in a CERN particle accelerator or for a spaceship by firing a huge booster rocket when they get a suitable distance away from the Earth. It will be a long while before we see anything macroscopic travelling at an appreciable fraction of c.

The experiment has been done a few times with clocks on airplanes and a stay at home one. Interpretation is complicated by the fact that the moving clock spends time higher in the Earth's gravitational potential as well as travelling at ~500kph. The two clocks behaviour exactly accord with the predictions of special and general relativity.

Moving clocks appear to tick more slowly the faster that they are

It has been measured as the cosmic microwave background anisotropy pretty much ever since the first relatively low resolution COBE probe. There is a roughly 7% difference in intensity at the survey wavelength in opposing directions caused by our relative motion with respect to the original frame of reference of the Big Bang.

It shows up as a ~2.5 sigma detection in the latest data. This isn't a bad introduction to current state of the art see Figure 2 COBE data.

The Earth is moving with a very modest velocity relative to the original Big Bang spacetime coordinate (0,0,0,0). It is mostly dominated by the motion of our galactic cluster towards the great attractor with minor corrections for attraction to Andromeda galaxy (collision due in 4.5B years), suns orbit around our galaxy and Earth's orbit around the sun.

Go far enough in any direction and there is a good chance that some of it is already moving away from us faster than the speed of light.

The so called particle horizon that is forever inaccessible to us even if we set off now at the speed of light. Infinity is *BIG*.

He is basically right although it is more of a philosophical point and it makes no difference whatsoever to the twin paradox. Which isn't a paradox at all - it just confuses people who don't understand SR.

Trouble is, he's worked for say a few months and comes back to find his mortgage is a few years in arrears. Mind you with enough dilation, he could inherit plenty from his children.

What happens to a clock in orbit, ie in freefall?

Look up the relativistic corrections for the Global Positioning System satellites. The corrections involved are quite big enough that the system wouldn't without them.

There's 56 pages of stuff there, and it's not written to be easy to read.

This may be easier to read, but I can't access the full text.

Physics Today 55, 5, 41 (2002);

Yes.

Yes. Always a good thing.

True, but all this is hard for non-physicists in the audience to follow or really understand.

Yes.

The problem is that the above assumes too much background.

Now, Einstein did not start with all that math, he started with a collection of gedanken experiments. I suspect that Einstein has a few relevant examples, which would be very useful if stated (or linked) here.

Joe Gwinn

The pendulum stops swinging :)