Just little note explaining the wrongness of the statement. Lorentz and other ether supporter (etherians?) had no problem with particles going faster than the speed of light. In fact the equations governing Cherenkov radiation (radiation that occurs when a particle exceeds c in a medium) were initially developed assuming a vacuum in 1904 by Sommerfeld. A year later Sommerfeld's work was made irrelevent until Frank & Tamm were able to explain Cherenkov's observations with it.

I'll need to go back to the original papers, but I believe you're wrong in saying Lorentz did not predict time dilation. Time dilation is a direct consequence of the Lorentz transformations. The big problem with Lorentz's theory is that the Lorentz-Fitzgerald contraction is caused by a physical force. Where is this force? What causes it? As you point out, Einstein showed this was completely unnecessary.

While it's a direct consequence of the transformations, it is not derived from first principles (nor can it be) in Lorentz's papers. He introduces gamma to show how much contraction there is, but does not explain why it works (see his 1904 paper).

This is one of the problems Sam5 has with Einstein. He claims that there must be some force to account for the contraction, relative motion will not cause contraction. He also claims that Einstein recognized this and "corrected" SR with GR so that gravity (Sam5 uses the phrase "motion through fields") accounts for the contraction.

Several tims he has mistakenly claimed the the Lorentz Force is what causes the contraction. In this he either cannot understand or refuses to accept that the Lorentz Force (the force on a charged particle moving through a magnetic field) is different from Lorentz's ideas and papers dealing with contraction due to motion.

He truly believes that Einstein was wrong with SR and Lorentz is correct (at least until Einstein developed GR). He has shown he doesn't understand the idea of an absolute reference frame by claiming that an object at absolute rest in aether (in Lorentzian theory) is equivalent to choosing which frame in SR is at rest. There's a lot more, but I think you get the idea.

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Hi, Tensor,

Nope, sorry, here is the invention of Lorentz Time Dilation as published in his 1895 book:

LINK TO 1895 LORENTZ TIME DILATION

Einstein finally credited him with the invention of time dilation in his own 1907 update of his SR paper.

Lorentz invented time dilation, length contraction, the speed limit of c, objects “shriveling up” to plane figures at “c”, mass increase due to motion, the relativistic Doppler Effect, atomic clocks slowing down when moving. In fact, the 1905 SR theory IS the 1895 Lorentz theory, with some things changed in the 1905 theory.

Lorentz’s original “absolute frame” was the universe-stationary “ether” frame. Einstein’s “absolute frame” was originally a “stationary inertial system”. But with the GR theory Einstein discovered that the center of an astronomical body serves as a type of “absolute frame” in many respects, because the body’s local gravity field is centered there. There are some interesting consequences of this point of view, including an a possible explanation of the null results of the Michelson Morley experiment.

If the original Lorentz ether concept is modified slightly, and the Einstein no-ether concept is modified slightly too, then a local gravity field of an astronomical body becomes an absolute local “frame of reference”, especially regarding local light speed.

Yes. If the ship's crew measures the acceleration as constant, then the outside people will measure it as decaying (we probably need a caveat here. If the outside people think the ship is increasing in velocity they think the acceleration vector is decreasing. The situation is symmetrical, of course, so if they think the ship is slowing down then they will think the amount of acceleration is increasing).

SInce the center of mass of the earth-moon system is not at the center of the earth, this would seem to be saying that the velocity laboratories measure for the speed of light depend on the time of day and the phase of the moon.

It is very difficult to get detailed information out of the labs about this. I think it was Essen who wrote some stuff about it back in the ‘40s. He found different speeds of light near the surface of the earth, in different directions, while working on a government project, but in his book he said that such a thing wasn’t allowed to be discussed in physics at that time. I’ve seen the title of a recent Navy study that is supposed to discuss East-West variations in the speed of light, but I haven’t been able to obtain a copy of the paper yet.

Also, the variations are so slight, they are difficult to measure. Plus, there is the problem with the atomic clocks changing rates at different altitudes and during different states of motion through the gravity field. I’ve been trying to find information about whether or not the earth’s gravity field “rotates” with the earth, but that info is difficult to find. If gravity is “radiated” out into space, from the earth, at the approximate speed of “c”, then that might give some cause to say that the gravity field doesn’t actually rotate with the earth.

First let's define the word "theory", so we are all starting from the same point. The American Heritage dictionary defines a theory as
Are the Lorentz transformations, presented in 1895, a theory? No. The paper basically says "We know Maxwell's equations are not invariant under Gallilean transformation, but look, Maxwell's equations are invariant using these nifty transformations." (Yes, I'm paraphrasing. ) Lorentz does not attempt any physical explanation; hence, this is not a theory.

We have to wait until 1904 before Lorentz presents a coherent theory (hereafter referred to as LT). He makes the following postulates: 1.) a force causes the Lorentz-Fitzgerald contraction, 2.) the stationary ether frame is the preferred reference frame, and 3.) the correctness of Maxwell's equations. In a LT, length contraction, time dilation, and other effects are physical consequences of high velocity.

Einstein's 1905 theory postulates 1.) the "principle of relativity", there is no preferred reference frame, 2.) the correctness of Maxwell's equations. In SR, length contraction, time dilation, and other effects are geometrical artificats of the source and observers relative velocities.

The physical interpretation of these theories is vastly different. Their derivations are vastly different. To say these theories are the same trivializes both Lorentz's and Einstein's work.

This is an odd statement. LT, SR, and GR predict a null result for Michelson-Morley. I fail to see any relevance.

All three theories, LT, SR, and GR, predict that a local observer will all measure the speed of light as c. Again, I fail to see any relevance. It seems like you're trying to fix something that ain't broke.

Both Lorentz and Einstein’s relativity theories were very advanced and they tended to “predict” more things than they “explained”. They “predicted” things that had not been discovered yet by means of experiment or observation. In fact, Lorentz’s idea about a long tether generating a lot of electricity was not even tried until NASA did it in space a few years ago. It generated so much electricity it melted the tether and it snapped.

They were presented in detail in his 1895 book:

PAGE FROM LORENTZ’S 1895 BOOK

You are most likely talking about his brief short 1895 paper, as published in “The Principle of Relativity”. I’m talking about his 138 page 1895 book. You have been misled just as I was, by so many of the modern pop-sci books. Lorentz started his relativity and electrodynamics theories of moving bodies as early as 1892. Then he wrote his important book in 1895. It was that book, and some of his papers, that gave Einstein his idea for his 1905 SR theory.

No, not exactly. You need to read Einstein’s 1907 paper in which he says that relative motion can NOT change the “geometric” shape of a body, just as I’ve been saying all along. He caught so much flack about that “relative motion” changing the geometrical shape of bodies, after the publication of his 1905 paper, he felt compelled to remove the geometrical shape change in his 1907 theory.

Then later, he added it back to his 1916 book, then after that, in 1918, he decided that some of his ideas did not always make sense in terms of “reality”, so he added this comment to a paper to handle that problem:

“First I have to point out that the distinction of real verses non-real is not very productive.”

..and he included with it a long essay about “real” vs. “non-real”, and he basically tried to blur the line between what is “real” and “not-real” in his relativity theories, so he could dodge the increasing world-wide criticism of his SR theory.

One of the most difficult things to understand about Einstein relativity is trying to decide what is “real” and what is “not-real” in his theories. It didn’t seem to matter to him. For example, the “geometrical” shape of the bodies changes in 1905, but not in 1907. But again, in 1916 they change, but in 1918 he said it didn’t really matter and one should not inquire too much about what is “real” or “not-real” in his relativity theories. I see that as purely an escape route, so if he turned out to be wrong about anything, he could claim that idea was “not-real”, but if it turned out to be right, then he could say it was “real”. If no one ever knew, including himself, then this general postulate of his would apply: “First I have to point out that the distinction of real verses non-real is not very productive.” That way, the guy had all his bases covered, whether he was right, wrong, or if no one really knew. That allowed the myth to get started that he was perfect, never made mistakes, was the world's smartest man.

That is why I’ve had guys here on this board argue in favor of the SR theory, but they still can not tell me if the clock slowdown and the length contraction is “real” or “not-real”, because they just don’t know.

You’ve got to do more than just read “The Principle of Relativity” and “Relativity: the Special and General theory”. Those two books will mislead you, because they don’t contain enough information or enough historical background about this subject.

Why is that? Where were all the 19th Century electrodynamical experiments conducted? What local “stationary system” was the M-M apparatus resting on the surface of? What travels through space with that system, centered on the system’s center? What was the M-M apparatus resting in? Not on, but in. What made it "rest"? What held it to the floor?

Wiley, do you see what I mean about his confusion between the Lorentz Force (which is what the experiment he describes above is about) and Lorentzian ideas on explanation of contraction? BTW, Sam5 has stated that he does not understand any of the math.

Ok Sam5, please explain why, in Lorentzian theory, magnetic field lines can appear to have ends (more ends the faster the object creating the field is traveling) depending on the observer, something which has not been observed. But in SR, where it is valid and in GR, magnetic field lines thread back through the object, no matter who is observing, something which has been observed.

Lorentzian theory simply does not match our observations, which is why is has been rejected. And SR and GR do match our observations, within their realm of validity, whch is why they have been accepted.

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Part One

Sorry, I should have jumped in this earlier. I am going to give a rough, back-of-the-envelope style calculation of the ratio of the clock-rate on Mars to that of Earth. The calculation will start out very difficult because our starting point will be General Relativity, but at each step I will throw small effects away in order to arrive at an easily calculated answer. As with Kenny Rogers' Gambler, the trick is knowing what to throw away and what to keep.

We can ignore anything outside the Solar System. The most significant source of gravity in our problem is the Sun. The velocity of the Earth is 30 km/s, which is 10^-4c. The naive estimate from Special Relativity is (1/2)*(v/c)^2 = 5*10^-9, but that's just considering the Earth's velocity, it says nothing about Mars. Still the velocity squared of the Earth is the right order of magnitude for the problem. We will consider 10^-8 to be a term of the small order and throw away second-order terms in what follows.

The only significant mass is that of the Sun, and the only significant velocities are those of the planets, so we may use spherical coordinates t, r, theta, and phi with the Sun at the origin, and write the Schwarzschild line-element of a planet orbiting the Sun as follows:

(c*dT)^2 = (1-2*G*M/c^2/r)*(c*dt)^2 - (1-2*G*M/c^2/r)^-1*dr^2 - r^2*dtheta^2 - r^2*sin^2(theta)*dphi^2.

G is the Newtonian gravitation constant, c is the speed of light in vacuo, M is the mass of the Sun, r is the distance between the Sun and the Planet. Relax, it gets easier from here.

The orbital velocity squared is a small quantity of the first order, as is the potential term 2*G*M/c^2/r, so we may drop the potential multiplying dr^2:

(c*dT)^2 = (1-2*G*M/c^2/r)*(c*dt)^2 - dr^2 - r^2*dtheta^2 - r^2*sin^2(theta)*dphi^2.

We may then divide both sides through by (c*dt)^2,

(dT/dt)^2 = (1-2*G*M/c^2/r) - (dr/dt)^2 - r^2*(dtheta/dt)^2 - r^2*sin^2(theta)*(dphi/dt)^2,

and recognize that the spatial part is just (v/c)^2, thus arriving at:

(dT/dt)^2 = (1-2*G*M/c^2/r) - (v/c)^2.

To the first order, this becomes

dT/dt = 1 - G*M/c^2/r - (1/2)*(v/c)^2. (Equation 1)

If M were zero, that is, if we could neglect gravity, we would have the usual Special Relativity formula. General Relativity does not "correct" Special Relativity, it extends Special Relativity to a larger domain of validity.

To be continued...

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Part Two

Planetary perturbations are negligible here, so we can consider the orbit to be the standard two-body solution from elementary celestial mechanics. We can use the integral of vis-viva,

(1/2)*v^2 - G*(M+m)/r = -G*(M+m)/2/a.

Here m is the mass of the planet, and a is the semimajor axis of the orbit. Substituting this in Equation 1 above we find:

dT/dt = 1 - G*M/c^2/r - G*(M+m)/c^2/r + G*(M+m)/2/a.

The mass of the Earth is 3*10^-6 that of the Sun and that of Mars is 3*10^-7, so we will ignore m. We will also ignore the periodic variation of r and replace it with a, the semi-major axis. This neglected variation of of the order of 1/60 for the Earth, but for Mars it is about 0.1. We are not interested in the periodic variation, but if we were, we could use the standard expansions of elliptic motion. Performing this substitution leads to:

dT/dt = 1 - (3/2)*G*M/c^2/a.

The ratio of the clock rates is then, with the subscript 3 for Earth and 4 for Mars,

dT_4/dT_3 = 1 + (3/2)*G*M/c^2*(1/a_3 - 1/a_4).

The clock runs faster on Mars because it is higher in the gravitational well of the Sun. Now we are ready to plug in some numbers! In SI units G=6.67*10^-11 m^3/kg/s^2, M=2*10^30 kg, c=3*10^8 m/s, and a_3 = 1.5*10^11 m. We will round a_4 to be 1.5*a_3. Then

dT_4/dT_3 = 1 + (3/2) * 6.67*10^-11 * 2*10^30 / 9*10^16 / 1.5*10^11 * (1/1 - 1/1.5).

1-1/1.5 is 1/3, which cancels the 3/2*2, and 9*1.5 is 13.5, so we have 6.67/13.5 * 10^-8 = 5*10^-9 approximately. Oddly enough, the naive calculation gave the same thing, but we know it must be wrong because it neglected the velocity of Mars. We have full confidence in this calculation because it does include Mars.

Finally, since there are about 3*10^7 seconds in a year, the difference will be 3*10^7 s/yr * 5*10^-9 = 0.15 s/yr.

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Can you tell me if I've got this represented right with the fancier Tex stuff here? If not, can you tell me what I need to move around where?


Added: In particular, are the "dT" etc. really 'd's, or that funny looking partial derivative 'd'-like thing? I can do that too.

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Celestial Mechanic,
That is beautiful. =D>
Too bad Sam5 probably quit reading at the first equation!
To express it graphically, you are (at least in his case) ](*,)

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Nothing on that page refers to time dilation at all. Nothing at all. All of the calculations refer to vector changes in length depending on relative motion.

Why do you assume that everyone can't read German?

Another direct lie.

No he didn't, and you have not demonstrated any of the above claims.

These statements are completely inaccurate and scientifically absurd.

He did no such thing. This statement is a complete travesty of Einstein's General Theory of Relativity. There is no absolute frame in Einstein's Theory, only metrics which are chosen arbitrarily to explain the behavior of matter and clocks in the presence of a gravitational field which Einstein explained was actually a change in the geometry of spacetime.

There is none required except by anti-Einstein cranks.

Absolute rubbish. Any anstronomical body is also in the gravitational field of everything else in the Universe, from which by Mach's Principle, everything derives inertia. Light does not slow down in a gravitational field, time slows down and distances contract, while light follows a geodesic and not a Euclidean straight line. At no point does the speed of light change.

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No they really are "dT" not partial derivatives. You have just produced the Schwarzchild Metric for a spherically symmetric non-rotating mass (complete with Schwarzchild radius for a spherical non-rotating black hole).

According to Sam5, this is supposed to be an absolute frame of reference (!), when its simply a metric, a convenient mathematical construct.

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"If lightspeed has something to do with speed.
how come things can move fast in the dark?"
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No-one has ever made such a claim. Its a straw man invented entirely by you to knock down. You've made this claim repeatedly, because your only intention is to minimize Einstein's work and congratulate him only for his mistakes.

Yes we have. And the answer is: what is real is what is measured. Lengths contract, time dilates, light follows geodesics, mass alters the geometry of spacetime, Sam5 talks rubbish.

We do read more than these books. Curiously they do contain enough information to know when you're talking rubbish and refute you at every possible occasion. Curiously you claim to read Lorentz's work in German without being able to speak German. Is it a psychic gift? Should Randi know?

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"If lightspeed has something to do with speed.
how come things can move fast in the dark?"
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Celestial Mechanic:

So if I were on Mars, I'd age by 0.15*70= 10.5 seconds over a lifetime. Not exactly the greatest reason to go, is it? :wink:

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Hold up!

That agrees with what I was saying!

I thought you, Eroica, said that that would violate the principle of equivalence?

No I didn't. You were the one who said that the people on board the ship would be experiencing about 1.5 g by the time they reached half c. :-?

I suspect the confusion is due to a breakdown in communication. I misunderstood what point you were making, and you mistook my point.

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You got it! It's beautiful! Too bad HTML doesn't have something like TeX built in, ironic considering where the first web browser originated. The d's are just ordinary d's, not partial derivative symbols.

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Yep! But I'd still want to go because it's there!

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Hey JohnOwens, how did you make that equation?

What did you think was a violation of the Principle of Equivalence?

I got to admit, when I look back at daver's post, I see that there are plenty of places where the "they"s could be interpreted to mean different things.

I took your post to mean that the crew of the spaceship would feel one-and-a-half times heavier when they reached 0.5 c. I guess that's not what you meant.

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No, that's what I meant, in the context of the problem. I may have miscalculated (I included those calculations, for review), but that's right in essence.

What do you mean it violates the Principle of Equivalence? The weight that they feel depends upon their acceleration--and I calculated that they would perceive their acceleration to be 1.5 times 9.8 m/s/s. That's assuming that their ship, from an outside observer's point of view, was accelerating at a constant 9.8 m/s/s.

Let's see if I have this right. I'm going to paraphrase rather severely.

milli360 stated that if the space ship maintains what an outside observer sees as a constant acceleration then the crew of the spaceship will experience a monotonically increasing acceleration. milli360 didn't explicitly say, but almost certainly thinks, that the acceleration felt by the crew will tend towards infinity as the ship approaches light speed.

Contrariwise (and this is the situation i described) if the ship's crew thinks they are experiencing a constant acceleration, the outside observer will see the ship's acceleration assymptotically approach zero as the ship approaches light speed.

I agree with both of the above scenarios.

I'll take a pass on the principle of equivalence--it's been too long since I played with GR. I vaguely recall that if you drop your space ship into a black hole, an outside viewer would never actually see the ship cross the schwartzchild radius (the outside observer sees the ship approach the radius asymptotically), whereas the crew of the ship would measure a finite time until they crossed the radius. There's a good chance that my memory has garbled things.

I put it in over at Wikipedia, where you can do the fancy Tex stuff, then saved the PNG and put it on my own web server. You can see it on this page down at the bottom (along with way too much information on Sedna's orbit in between).
It's based on a program I've got on my machine anyway, but I've never yet gotten around to using it directly, only through the Wikipedia.

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Ah, this is where our wires got crossed. I thought you meant a constant force was accelerating them, in which case their acceleration to an outside observer would not be constant. 8)

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