Is special relativity consistent with thermodynamics?

  • #26
marcus
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calculating the temperature effect on weight

How small is the temp effect on weight?
Sammywu, why not calculate this for yourself, from fundamental constants.

Here is the National Institute of Standards and Technology (NIST) website for the constants.

http://physics.nist.gov/cuu/Constants/

choose "physicochemical" from the menu to find (among other things) the recommended value of Boltzmann's k.

or else choose "frequently used constants" from the menu and you
will find Boltzmann k very near the top of the list.

In a chunk of metal the heat capacity per atom is about 3k
(one k for each dimension of space in which the atom can jiggle)

So to find how many joules of energy (per atom) the metal soaks up when you heat it by 100 degrees kelvin you just multiply
3k by 100 kelvin

To find the increase in mass (per atom) you just divide the joules by c2.

Then compare that with the rest mass of an atom. The increase in mass will be a very very small fraction of the total. This is the problem.
-----------------

is it inconvenient for you to calculate on a "per atom" basis? if you like chemistry you may prefer to calculate the quantities of mass and energy "per mole". A mole is just some large number of atoms. Is this all familiar to you?

If you are comfortable calculating on a per atom basis, then you just look at NIST and it says
k= 1.38E-23 joule per kelvin (very basic! everybody should know Boltzmann k constant!!!) so multiply by 3 for 3 dimensions.

3k= about 4E-23 joule per kelvin

so to heat metal up by 100 degrees must put in 4E-21 joules!

But speed of light is 3E8 m/s and so square is 9E16 sqmeter/sqsecond.

One must divide 4E-21 by 9E16 and this gives about 0.5E-37 kg.

Compare that mass (added by raising temp) to the mass of the
atom. An atomic mass unit, NIST website says, is 1.66E-27 kg.
Suppose it is aluminum, weight 27, multiply by 27 and get
45E-27 kg.

(you are used to SI metric units? all constants at NIST are in standard metric units, joules, kilograms etc)

So the aluminum atom is 45E-27 kilo, and heating the block of metal
by 100 degrees puts in extra mass of 5E-38 kilo, per atom. The extra mass is only a trillionth!!!

How can weighing scales be sensitive to changes of one part in a trillion?
But I have decided that I will not be discouraged by this and that
I will firmly believe Eee-equals-em-cee-square anyway. You too I hope.
 
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  • #27
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Marcus, Thank you for your reply. I completely understood what you discussed in the mass and temporature. I am fine with the system of kg and m, etc... . I understood the difficulty in measuring it.

The GR and SR effects were not proposed by me. They were proposed in another thread by somebody else. I have posted a few questions there to try to grasp the idea of GR and how correctly apply it and still wait for answers.I saw your name appeared in there supplying info. about the flat universe prevailing over the past 5 years, which is new to me. Most of publicized common books still mention about the big bang from a single point. I thought the flatness only means that we will be difficult to find a timespace warp. Your saying that the universe starting as infinte space is new to me. So, does that mean big bang is out of fasion now?

My another question is about the mass of a spinning object. Do you think I got it right, or there are issues there?

I assume you are also familiar with the nuclear binding energy that was used to explain how nuclear fussion and fssion producing energy in pure form of lights.

Now applying that concept to the chemical bond energy, coule we say that we actually lose mass when we produce heat when burning some carborns, however small that is?

Any experiments have been done on the spinning objects or chemical bond mass loss?

Welcome any comments from whoever might be familiar with these issues.

As to temporature measure from a far distance or in a two diffrent reference frames, I thought it's very incomprehensible. To me, at this point, it does seem to only purported to explain redshift.
 
  • #28
marcus
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Originally posted by Sammywu
Marcus, Thank you for your reply. I completely understood what you discussed in the mass and temporature. I am fine with the system of kg and m, etc... . I understood the difficulty in measuring it.

...Now applying that concept to the chemical bond energy, coule we say that we actually lose mass when we produce heat when burning some carborns, however small that is?
Good, there's probably not much I need to say.

About chemical energy, indeed the mass of one O2 and two H2 molecules adds up to more mass than what you get by letting them combine and radiate away the heat of combustion and come back to room temp.

the two water molecules you get are going to have less mass
than the combined total for the O2 and 2H2, but its so slight a difference in mass that I cannot imagine anyone measuring it.

I guess a similar statement could be made about human metabolism----you put a subject in a sealed tank with some sugar and enough air and let the metabolic heat be conducted away so the whole tank stays at room temperature. sounds horrible doesnt it?

Originally posted by Sammywu
...I saw your name appeared in there supplying info. about the flat universe prevailing over the past 5 years, which is new to me. Most of publicized common books still mention about the big bang from a single point. I thought the flatness only means that we will be difficult to find a timespace warp. Your saying that the universe starting as infinte space is new to me. So, does that mean big bang is out of fashion now?
Best thing would be if you would look at page 32, Table 1, of
Lineweaver
http://arxiv.org/astro-ph/0305179 [Broken]

It quantifies the uncertainty about Omega-naught.
This is the cosmology number which if it is exactly 1, then the
universe is spatially flat and the BB started with an infinitely extensive space
But if Omega-naught is even the slightest bit bigger than 1, then the universe expansion began from a point and there is a (possibly very very slight) positive curvature to space. So the sum of the angles of a triangle is very very slightly more than 180 degrees.

You can see by looking at Table 1 that the best estimate by
the pros, for Omega-naught, is, as of May 2003,
1.02 +/- 0.02.

that is extremely frustrating. It is something that people devote a lot of time and equipment to measuring, with some fine satellite instruments, and it still could be exactly 1.000000 (perfectly flat space)
or it could be as large as 1.04 (positively curved space expanding from a point)

Either way it is the Big Bang. It is just that it has always been known that the BB COULD have started from infinite space extending in all directions. In some sense that is the simpler scenario. Although infinite space is hard for many people to imagine.

If it was infinite when it began expanding then it is infinite now.

If it was finite ( like a point) when it began expanding then it is finite now (somehow closed on itself)

Because 1.02 is so close to 1, and for a bunch of other reasons, cosmologists typically talk as if Omega is exactly 1 and as if the universe is exactly flat-----it is tantalizingly close and if it is not exactly flat it is very odd that it could be so close.
So most of them give up and when they give a talk they just say its flat. But there is this uncertainty. (which is always going to rear its ugly head until the issue is completely settled)
 
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  • #29
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Marcus,

Thanks. When I first mentioned to a friend, an EE master, about that temperature, chemical reaction and nuclear reaction actually change the mass. he told me I am out of minds. When I searched thru Internet to show him the doucument about the nuclear binding energy, he took the nuclear reaction one, but he still can't take the other two.

Now you stright this out for me. I am happy that you verified that I am on track.

Only one Q left. I have mentioned about spinning a top with high speed shall also add mass to it. Is there other complicate issues here that prevent this from happening?

The next one is a little long shot. This mass-energy equation implys that by binding photons or certain subparticles in a closed box with a certain dynamic in a closed box, the box would appear to carry a mass to the outside observers and the mass would be related to the dynamic instead of the original rest mass of these unseen objects. Is there any consensus in the mainstream Physicists about this idea? When I read about two quarks can form a particle that measured less mass than their combined mass due to their internal dynamics. This seems to imply what I just mentioned. Is it correct?

By the way, thank you for the info. about that flat timespace and the cosmological constant. When I have time, I will definitely take a look of it. Any way, I might need to straight out some clouds in my GR perception before I can fully understand that paper. Janus has answered me a question. The cloud is getting a little clearer. I hope soon that will be clear to me.

Ranyard, by the way, I beleive I have browsed that experiment in the Physic World. I would guess it got somethings to do with condensate and quantum state because I can't remember the detail. Not surprisingly, as I was told, Quantum effect does not live very well with SR. At a very low energy environment, quantum effect or certain subpartical forces could come into play, I think. Sorry that I am not too interested in that yet. I am more attracted to high energy, high speed and cosmology at the point.

Dave, get back to you a bit. About the imaginary experiment, I purposely to make you see that the traveller actually only spend 30 years to arrive at a star 300 light years away from us. You will think that I violate the light pseed maximum. I did not. The traveller is not even moving relative to himself. He is seening the star approching him at a speed less than light speed, because the 300 light years distance to us is much less than 30 light years to him. Do some more sketch and math. in the Minkowski Diagram. If you still have problem understand me, I will try to do the math. for you.

One thing I tried to emphasize in that example is that a misconception of nobody can not exceed light speed making space travel impossible is wrong. While we are trying to accelerate an object to higher and higher speed, the object will become heavier and heavier, you will have to add more and more energy into it to add just one bit of speed to it. The difficulty is exponentially growing. Some unseen truth here is that the traveller lives also in a slower and slower clock to us and our distance is shorter and shorter to him. This really ends up he can get to a star 300 light years away in, said one second to him, and much more than 300 years seen by us. I tried to exaggerate the effect. Hope the mainstream expert will not be bothered by that. Marcus, if I am not correct, please correct me.

This is another long shot. When extending that thought, to the photon itself, if photon has a clock, the time is at rest foreever while it travels. If you heared about the Bell experiment in trying to find out who is right about Uncertainty Interpretation, Eienstein or Heisenberg. Einstein argued there would nothing that could travel faster than light. I wonder this interpretation of light actually travel in a rest clock to itself would help.
 
  • #30
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I have asked a few questions here. Either nobody has answers or nobody seem to be interested.

Any way, getting back to the original question, Just look at the stars moving away from us according to cosmalogist. Will their temperature drop to their own observations? NO.

The so-call temperature equation is to be used by us measuring from here. To measure somethign not physically touchable is already a question. I think the point is still in what you are using to measure it.

The relative speeds of a group of molecules or particles in a enclosed box in a moving object will be constant to the moving observer.

There are some more fundamental issues relating to the temperature, the mass or energy and thermodynamics. I believe there are some secrets there waiting for us to decipher. That's the original reason I came to visit this thread.
 
  • #31
David


Originally posted by marcus
but maybe this is not perfect for your needs so I hope.....somebody else has a better online reference for GPS and the GR effect on time.
I hate to disappoint you, but this is not an effect on “time”, it’s just effect on the particular type of clock that is used. Study Einstein’s 1911 theory and you’ll see what I’m talking about.

This is an “electrodynamical” effect on atoms. Their internal harmonic oscillation rates slow down under strong gravity conditions and they speed up under low gravity conditions. That’s all that happens.

Pendulum clock work in just the opposite way. They slow down in low gravity and they speed up in high gravity. This is a large moving mass mechanical effect. The slowing of atomic clocks is an electrodynamical effect. Lorentz was the first to work on these ideas in his 1895 book, "Versuch einer Theorie der Elektrischen und Optischen Erscheinungen in bewegten Körpern".

That book was the beginning of modern relativity theory.

A mechanical effect in a pendulum clock works a certain way because basically only a gravitational field is involved. But an atom works differently because not only gravity but other fields are involved on the small scale, such as the electric and magnetic fields and even smaller fields.

With atomic clocks, this has become known as “time dilation” but it is merely a vibration rate change for the atoms in the clock. They speed up just as much as they slow down. Their vibration rates are altered by gravitational fields. That’s all.

Your own personal biological time isn’t figured in atomic time, it’s figured in “thermodynamic time”. Look up [biology thermodynamic time] on Google and read about what the biologists call “time”.

However, if your teacher or professor demands that you call an atomic clock rate slowdown “time dilation”, you’d better play along with him or he might give you a bad grade.
 
  • #32
David
Originally posted by Sammywu
I have asked a few questions here. Either nobody has answers or nobody seem to be interested.

Any way, getting back to the original question, Just look at the stars moving away from us according to cosmalogist. Will their temperature drop to their own observations? NO.

The so-call temperature equation is to be used by us measuring from here. To measure somethign not physically touchable is already a question. I think the point is still in what you are using to measure it.

The relative speeds of a group of molecules or particles in a enclosed box in a moving object will be constant to the moving observer.

There are some more fundamental issues relating to the temperature, the mass or energy and thermodynamics. I believe there are some secrets there waiting for us to decipher. That's the original reason I came to visit this thread.

The first secret you need to decipher is that the Kinematical part of the 1905 Special Relativity theory is wrong. There is NO physical effect due only to “relative motion”. There is NO clock or time slowdown due only to relative motion. There is NO temperature changed due only to relative motion.

Einstein corrected his big mistake in 1918 when he added a gravitational field to the k frame in the 1905 theory.

Of course “relative motion” does NOT lower any temperature. If that were true, then all the galaxies that are moving at “c” relative to the earth would be frozen solid and they would not emit light and we would not be able to see them.
 
  • #33
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David, Your reasoning is actually very interesting and convicing. Would you mind just explain the so-called constant light speed with your theory?
 
  • #34
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David, By the way, I have mentioned I am a layman. I don't have a professor to teach me. I just try to know whether I misunderstood what I read. So, if you can prove your theory can explain some fundamental experiments, I will truely appreciate it.
 
  • #35
David
Originally posted by Sammywu
The traveller is not even moving relative to himself. He is seening the star approching him at a speed less than light speed, because the 300 light years distance to us is much less than 30 light years to him. Do some more sketch and math. in the Minkowski Diagram.
There IS NO TIME DILATION due only to RELATIVE MOTION. It’s impossible, because “relative motion” puts no physical “force” on anything.

Things that are far apart and relatively moving don’t even know the other things are moving “relative” to them.

This is just a big urban legend and a form of “magic” in science, due to a mistake Einstein made in his 1905 SR paper.

Einstein corrected his big 1905 error in a paper he wrote in 1918. In 1918 he found he needed to add a gravitational field to the 1905 theory and the 1905 clock had to be turned into an atomic clock, since the same effect won't work on a mechanical clock.

You can find his 1918 paper in this modern book at any big university library:

"Dialogue about Objections to the Theory of Relativity"

"Dialog über Einwände gegen die Relativitätstheorie" Die Naturwissenschaften 6 (1918)


Published now in the new book:

"The Collected Papers of Albert Einstein, Volume 7:
The Berlin Years: Writings, 1918-1921."
 
  • #36
David
Originally posted by Sammywu
David, Your reasoning is actually very interesting and convicing. Would you mind just explain the so-called constant light speed with your theory?


The 1905 Einstein “constant” speed of light theory said this:

“light is always propagated in empty space with a definite velocity c”

But this turned out to be wrong. He learned in 1911 that light speed can change at different places in space. He also said so in his 1916 book. See page 76 of the Crown press version of “Relativity: The Special and General Theory”.

In 1911 he learned that light speed can change due to light passing through a strong gravitational field. Also, an atomic clock can change rates and slow down in a strong gravitational field.

So, if you measure the local speed of light inside a gravitational field with an atomic clock resting in that same field, you will measure “c” for the local speed of light. That is becaue in a gravitational field, the light slows down as the rate of the clock slows down, and the light speeds up as the rate of the clock speeds up. So an atomic clock (but not any other kind) will always measure “c” for the “local” speed of light, at the clock. But if that same clock measures the speed of light moving someplace else, away from that local gravitational field, then that clock will measure other rates other than “c”, either slightly faster or slightly slower.

So, all the speculating about what happens to clocks in SR theory is wrong, and it has been wrong for 98 years.

Read that 1918 paper and you’ll see what I’m talking about. Also, read his 1911 gravitational redshift paper, which is GR theory and it is ok.

Gravity does not slow down “time”, it slows down atomic clocks. It speeds up pendulum clocks. It affects different kinds of clocks in different ways.

Relative motion doesn’t slow down any clocks. (1905 SR theory is wrong)

Acceleration does slow down atomic clocks. (1911 GR theory is correct)

Acceleration might or might not slow down other kinds of clocks, depending on what kind of clock it is. (Classical clock experiments and observation, see “Harrison’s chronometer”.)

Human time is “thermodynamic time”. (IE heat energy time, not atomic energy time. See any biology thermodynamic time website.)
 
  • #37
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Daid, Please tell me why scientist believe light speed would not change relative to the observer's speed. Any experiment and its detail.
 
  • #38
David
Originally posted by Sammywu
Daid, Please tell me why scientist believe light speed would not change relative to the observer's speed. Any experiment and its detail.
This is a little difficult to explain. My explanation is not a standard one, but it matches reality and it matches the improvements Einstein made in his theory, and the improvements started in 1911. The improvements became known as the "General Theory" of relativity.

Einstein’s original 1905 light speed postulate is wrong: “light is always propagated in empty space with a definite velocity c”. That is wrong and he changed his postulate in 1911. It is wrong because in 1905 he thought of space as being "empty", and he did not consider the effect a gravity field has on the speed of light.

His improved 1911 Law of light speed is right, as far as I can tell, but he never phrased it in a single sentence, and it is a little difficult to understand.

I will try to state it here, in two sentences:

1: Light speed measured by an atomic clock will be measured at “c” at the clock, where ever the clock is located, even in a strong gravitational field, because when light speed slows down in a gravity field, so does an atomic clock, so an atomic clock is incapable of measuring a local change in the speed of light, at the place where the clock is located.

2: But, an atomic clock can measure light speed changes in different parts of space, if the light waves/photons are somewhere else, somewhere other than where the clock that measures their speed is located.

This means that if we put an atomic clock at the surface of the earth, it will measure “c” for the light waves/photons that hit or pass right by that clock. And if we think of an atomic clock at the surface of the sun, that atomic clock will measure “c” for the light that hits or passes right by that clock.

But if we put an atomic clock on the moon, and if we could use that clock on the moon to measure the speed of light: 1) traveling in space between the earth and the sun, 2) at the surface of the earth, 3) at the surface of the sun, and 4) at the surface of the moon, because of the gravitational field at the moon, and the atomic clock located at the moon’s surface, here is how the moon clock will measure those different speeds of light:

Atomic clock resting on surface of moon measures:

1) light speed in space, the fastest local-area speed for light

2) light speed at the earth, a slower speed for light

3) light speed at the sun, an even a slower speed for light

4) light speed at the moon and at the clock, a faster speed than at the earth and sun, but not as fast as light in local deep space

Here is a website where a young physics student tries to explain this. The student’s drawing is just about the same as Einstein’s 1911 drawing. Notice the two different speeds for different points along a wavefront of a light beam passing near the sun, c’dt and cdt. The “distant time” means the atomic clock that measures this speed must be well away from the gravitational field of the sun, or the clock will slow down at the same rate the light speeds slow down:

http://66.102.7.104/search?q=cache:...ht+slows+down+physics+near+sun&hl=en&ie=UTF-8

As Einstein brilliantly deduced in the 1911 paper, this clock/light slowdown phenomenon is caused by the strange effect of an atomic clock slowing down in places (in gravitational fields) where the local speed of light slows down. So, if the local atomic clock slows down in a strong gravitational field, and the local speed of light slows down in the same strong gravitational field, then that clock won’t notice the light speed slow-down, because the clock has slowed down too.

But if that clock can be used to measure the speed of light somewhere else, such as moving between two points in space, well outside of that local gravitational field, then that clock inside the field will measure a faster speed of the light between the two points, as long as those points are far away from any strong gravitational field.

So, the first 1905 postulate is not correct, because light does change speed as it moves from place to place. It travels the fastest when the waves/photons are a long way from a strong gravitational field, and it travels slowest when it passes through a strong gravitational field.

But this phenomenon is often misunderstood, since atomic clocks are used to measure the exact speed of light, because atomic clocks are the most accurate. Atoms, which emit the light in the first place, slow down their internal harmonic oscillation rates when they are subjected to strong gravity, and that is why an atomic clock will measure “c” as the “local” speed of light at the clock that measures the local speed.

This is very confusing, since his 1911 paper is not very clear and is also confusing, and people get the original 1905 postulate mixed up with his 1911 Law.

Even many physics professors seem to think the 1905 “postulate” is correct, but it isn’t. His 1911 “Law” is correct.

Some people get mad at me when I say, “Einstein made a mistake in 1905”, but he corrected his own mistake in the 1911 paper and in his 1918 paper. I guess he got tired of trying to explain the difference between the 1905 postulate and the 1911 Law, so he never wrote very much about the difference after 1918.

I just discovered this recently. There is a new paper about it, published in the European Journal of Physics, titled “Einstein and the Twin Paradox”. That tells about his 1918 correction. Also, Wolfgang Pauli wrote a relativity book in 1921, and he tells about the change and the 1918 Einstein correction to the 1905 theory. These are the only two places I’ve ever seen mention of Einstein’s 1918 correction.

I’ve ordered a copy of his 1918 paper, but it hasn’t arrived yet.

What I’m telling you now was known among many physicists and professors in the 1920s, but the information seems to have been lost or forgotten or neglected over the years. Now, everybody who reads his 1905 paper thinks the 1905 postulate is correct, but it’s not. The 1911 Law is correct, but that paper is much more complicated, so not many people understand it. I had to study that 1911 paper, and compare it with the 1905 paper, for more than 10 years before I began to understand the subtle differences in what he was saying in the two papers.

But if you ask some professors or some physicists, they will say I am wrong. That’s because they are not aware of his 1918 correction to the 1905 theory. But if you read that young student’s website, you will see that he explains the slowdown of light near the sun, in terms of a “distant clock”. Unfortunately, he doesn’t explain why a distant clock needs to be used.
 
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  • #39
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David, This is my part of calculation.
Assume v=c*sinA. T=T'*(1/sqrt(1-v^2/c^2))=T'*(1/cosA), X/T=v. X=280 light years, T is the static observer's time, T' is the mover's time. T'=30 years. so 280c/(30/cosA)=c*sinA. 280/30*cosA=sinA. tanA=sinA/cosA=280/30. sinA=280/sqrt(280^2+30^2)=0.9943. So if the mover's speed is 0.9943c relative to the static observer, the mover will arrive at a star 280 years far away in 30 years in the mover's time. cosA=30/sqrt(280^2+30^2)=0.1065. T=30/0.1065=281.6901. To the static observer, the mover will arrive at the star after 281.6901 years. It's not 300 years in my question. Sorry. I threw out some figures just want to show the mover's time is actually less than 280 years.

So, the static observer will believe the mover moving in a speed less than c. To the mover, it did not move but the start moved to him, the distance is 280*0.1065=29.82 light years. So, the star is moving toward him in the speed of 29.82c/30=0.9943c. None of each sides violate the maximum light speed and they are exactly the same magnitude but different direction.

Hope I did not messup the calculation.

It's my understanding of SR. Maybe I am wrong. The mass is now m0/0.1065=9.3897m0. The mass was increased mare than 8 times of rest mass. E=mc^2=9.3897m0*c^2. The Energy required to push a rest spaceship to such speed will be at least 8.389m0*c^2. I did my part of math. As I have stated, maybe you are right. From your model, how will it look like? Can you answer my last question also.
 
  • #40
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Daid, Do not forget about muon phenomenon and Theo... experiment.
 
  • #41
David
Originally posted by Sammywu
Daid, Do not forget about muon phenomenon and Theo... experiment.
Muon phenomenon is due to acceleration and motion through the earth’s fields. It has nothing to do with SR “relative motion”.

Lorentz predicted similar phenomena due to motion of atoms and particles through fields as early as 1895. He even predicted mass increase due to “acceleration” in 1904.

The Muon phenomenon is NOT due only to “relative motion”.

Same with the Ives-Stilwell experiment of 1938. Their electrons were accelerating AND moving through the earth’s gravitational field.

Hafele-Keating experiment. The clocks were MOVING THROUGH the earth’s gravitational field. That’s why Westbound clock speeded up and Eastbound clock slowed down. Einstein in 1905 prediced ONLY SLOWDOWN in both directions of motion. That was wrong.
 
  • #42
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David, My final say about this.

My calculation in last reply violated principle of relative motion. If 280 years of static observers is 30 years of mover, then 30 years of movers shall be 280 years of the static observer. Agreed.

Check the other experiment, the 3-light-second-long rocket and the 5-light-second-long tunnel ( I changed it now from 4 second to 5 second, easier to calculate. I hat calculation ).

First event A, the front of the rocket reaches the open end of the tunnel.

Second event B, the rear of the rocket reaches the open end of the tunnel. The light beam was sent at the point from the rear of the rocket or/and the open end of the tunnel.

Third event C, The front of the rocket reaches the other end of the tunnel. At the same time, the light beam reaches the fron ot the rocket and this end of the tunnel.

So what we can be ceratin is the light shall have travelled three seconds for the rocket, because if you are in the rocket, you see the light travel from the rear to the end for 3 light seconds. No ambiguity here. You are a static observer and you knoe it's built with 3 light years long.

Now, if you sit at the close end of tunnel, you know the light travelled for 5 seconds. No ambiguity here, either.

That means T'=TcosA. 5=3cosA. cosA=3/5. sinA=4/5. T' is the rocket's time, and T is the tunnel's time.

v=c*sinA. The required rocket's speed is 4/5c relative to the tunnel.

Now, let's discuss the interval between event A and event B. This interval represent the time for the rocket passing through the open end of the tunnel. If you, working for the tunnel, installed a gate here, you open the gate when the front of the rocket arrived and shut the gate to cut the rocket at the last moment. Since the speed is 4/5c to you and the rocket is 3 light-second long as you already know as part of the experiment's participant. 3c/(4/5c)=15/4=3.75. The rocket will need 3.75 seconds to go through the gate. All you need to do is close the gate after 3 seonds to cut the rocket into two pieces.

No. the rocket has shrunk to you also. The 3 light-second rocket will appeared to you only 3c*(3/5)=9/5*c=1.8c. It will pass the gate in 1.8c/(4/5c)=9/4=2.25 seconds.

I hope I did not do this wrong. It usually took me a month to check through the thought of this experiment. You have to draw an event shadow in the Minkowski diagram to visualize how this works.

This is the best I can do in writing without Minkowski diagram. If you are not interested in what I say here. I guess our paths just do not cross. Thanks for your lesson, any way.
 
  • #43
David
Originally posted by Sammywu
David, My final say about this.
Ok.
 
  • #44
Equivalence between internal energy and einstein energy

After I read all of this discussion, I recall a question I posted several months ago, about the connections between the thermodynamic internal energy and the relativistic rest energy. Specifically, it is the thermodynamic internal energy U equal to the rest Einstein´s energy at rest ( E= m c2)?. Is E= U?.







jeff said:
The key thing to realize is that the principle of relativity alone can't determine the precise form of thermodynamical relations in a moving frame. In particular, how the temperature of moving bodies should change under lorentz transformations is really a matter of convention. As a simple example, I'll demonstrate the freedom one has in choosing how to handle temperature relativistically by considering an emitting body whose spectrum is isotropic and follows planck's law

f(E,T) ~ (eE/T ± 1)-1

where pμ = (E,p) is the emitted particle four-momentum, the Boltzmann constant is taken as unity, and ± refers to emitted bosons and fermions respectively. For an emitting body moving with velocity v, this can be written covariantly in terms of the product of pμ with either a "4-temperature" Tμ ≡ Tγ(1,v)] or an inverse 4-temperature βμ ≡ T-1γ(1,v) which in the rest frame are just (T,0) and (1/T,0) respectively. We may then express E/T covariantly as either

E/T = pμβμ or pμTμ/TνTν.

We then have three ways - equally valid from the standpoint of SR - to define the temperature, each determining how it changes under lorentz transformations:

1) T ≡ 1/β0 ⇒ T' = γ-1T.

2) T ≡ T0 ⇒ T' = γT.

3) T ≡ (TμTμ)½ or (βμβμ) ⇒ T' = T.
 
  • #45
Chronos
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If you walk behind hoofprints, what do you expect to find? Advice: don't kick the fresh ones. If you wish to 'correct' the Einstein equations, at least use the ones near and dear to our hearts... i.e., the ones that actually apply. That said, I do appreciate the insights on particle physics. Pottery magicians, go figure.
 
  • #46
pervect
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Iraides Belandria said:
After I read all of this discussion, I recall a question I posted several months ago, about the connections between the thermodynamic internal energy and the relativistic rest energy. Specifically, it is the thermodynamic internal energy U equal to the rest Einstein´s energy at rest ( E= m c2)?. Is E= U?.
Since our last discussion on thermodynamics & relativity, another poster has pointed out

http://lanl.arxiv.org/abs/gr-qc/9803007

which looks like it addresses the topic in some detail. I haven't really studied the whole paper very closely, but I think it might be of interest to you.

There are a few things the author of the above says that still puzzle me a bit - for instance, I'm not quite sure how entropy gets turned into a current, since it isn't conserved. But it seems reasonably straightforwards to me that thermal energy should be treated like any other form of enregy, with a stress-energy tensor, as the author suggests.

Personally, though, I find it just as easy to use the old-fashioned non-Lorentz-invariant defintion of temperature, with the appropriate restriction of using the concept only n the frame where it applies. (This wouuld be the frame that's comoving with the fluid element.) That's the approach that MTW uses, for instance, in their discussion of thermodynamics in stellar interiors, which I've already mentioned.
 
  • #47
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David, you are wrong about your claims about SR. First, you are claiming that one of the most experimentally accurate theories in modern science is "wrong." You are claiming that SR is wrong and GR is right. They are both right, SR is ONLY to be used in an inertial referenece frame, i.e. one without any acceleration, gravitation, or rotation (or one where there are no fictitous forces such as centrifugal). GR is more general (hence the general relativity), and applies anywhere. When there is free space (devoid of any mass-energy) light DOES propogate at c. You seem to be under the impression that SR is corrected by GR, but is actually generalized. You cannot employ GR, without accepting the postulates and theory of SR>
 
  • #48
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Also, you seem to think that time dilation is a result of a "force." This is not true in either SR or GR. Time dilation is a result of the warping of 4-D space in order to account for its true, world line. In SR, this simply means that, heuristically, "time must slow down so that the speed of light can be invariant." In GR this effect is further augmented by a massive objects warping of space through the EFE's. There is no "force" acting on an object to dilate it's relative time." You often quote physicists, yet you do not understand their work. You simply reject their tried-and-true formulas and equations and substitute poorly formulated replacements.
 
  • #49
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David said "So an atomic clock (but not any other kind) will always measure “c” for the “local” speed of light, at the clock."

This is wrong. Your wristwatch would measure c just like the atomic clock. All clocks are equivalent in SR and GR. Your growing beard is a clock no different than an atomic clock to SR.
 
  • #50
Vanadium 50
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Most of this thread is 7 years old.
 

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