What if Newton was not wrong?

quant

Registered Senior Member
He was wrong about certain features of the universe such as universal time and was not aware of relativistic effects but this does not upend his domain.

What if Newton were not wrong? What if he was correct in stating that both time and space were absolute? Look for example at the case where someone goes to meet someone on a Wednesday at a café in New York. A week later he returns to the same Café at the same time, again on a Wednesday, to meet the same person. As far as he is concerned nothing has changed he has returned to the same place on the same day of the week, at the same time to meet the same person. We are aware that during that time interval; the earth has been rotating on its axis at a speed of 1600 km/h approx. apart from that the earth has also been speeding around the sun at a speed of something like 107,000 km/h and at the same time the sun has been tracing a path through the Milky Way Galaxy at 514,000 km/h and the Milky Way Galaxy leaves them all in the shade by moving around the Universe at 2,000,000 Km/h. So nothing is the same, nothing is as it was. The first question is how can that be? What strange force causes events on earth to remain synchronized in spite of the huge distances and times that have taken place in the interim? The second thought that occurs is, is that it doesn’t really matter what has moved, or how far or how fast it has moved; because the aether remains stationary and unchanging. This means that all positions can be plotted with reference to the aether, which acts like a Universal frame of reference. “Great Supposition you say!” But, I ask you to consider the question of Dark Matter, according to recent research, and before the crazy theory of Dark Energy came along, it was calculated using sophisticated instrumentation that Dark Matter constitutes 90% of all matter in the Universe. Here is a quote from the Department of Energy USA: “Dark matter makes up about 85 percent of the total matter in the universe, accounting for more than five times as much as all ordinary matter. Dark matter played an important role in the formation of galaxies and the evolution of the universe.” Although here the estimate is given at 85% and not 90%.

That aside, consider the properties of Dark Matter, it has such low interaction with matter, that it is estimated that it can travel through a block of lead a light year thick without experiencing any interaction whatsoever and vice-versa. At the same time Dark Matter exerts a pervasive gravitational force. But the truly incredible property of Dark Matter is that it offers zero interaction with any type of electromagnetic radiation; everything from Radio-waves to Gamma rays can travel without the slightest interference from one side of the Universe to the other. Amazing. Just as amazing is the fact that these are identical (not taking into consideration the farcical luminiferous aether concept) to the properties the so scorned aether was once thought to possess. The Ancients might have been smarter than we thought. If you would like to read more about this theory, consider reading "Redefining the Electron" available on Amazon.
 
What if Newton were not wrong? What if he was correct in stating that both time and space were absolute? Look for example at the case where someone goes to meet someone on a Wednesday at a café in New York. A week later he returns to the same Café at the same time, again on a Wednesday, to meet the same person. As far as he is concerned nothing has changed he has returned to the same place on the same day of the week, at the same time to meet the same person. We are aware that during that time interval; the earth has been rotating on its axis at a speed of 1600 km/h approx. apart from that the earth has also been speeding around the sun at a speed of something like 107,000 km/h and at the same time the sun has been tracing a path through the Milky Way Galaxy at 514,000 km/h and the Milky Way Galaxy leaves them all in the shade by moving around the Universe at 2,000,000 Km/h. So nothing is the same, nothing is as it was. The first question is how can that be? What strange force causes events on earth to remain synchronized in spite of the huge distances and times that have taken place in the interim? The second thought that occurs is, is that it doesn’t really matter what has moved, or how far or how fast it has moved; because the aether remains stationary and unchanging. This means that all positions can be plotted with reference to the aether, which acts like a Universal frame of reference. “Great Supposition you say!” But, I ask you to consider the question of Dark Matter, according to recent research, and before the crazy theory of Dark Energy came along, it was calculated using sophisticated instrumentation that Dark Matter constitutes 90% of all matter in the Universe. Here is a quote from the Department of Energy USA: “Dark matter makes up about 85 percent of the total matter in the universe, accounting for more than five times as much as all ordinary matter. Dark matter played an important role in the formation of galaxies and the evolution of the universe.” Although here the estimate is given at 85% and not 90%.

That aside, consider the properties of Dark Matter, it has such low interaction with matter, that it is estimated that it can travel through a block of lead a light year thick without experiencing any interaction whatsoever and vice-versa. At the same time Dark Matter exerts a pervasive gravitational force. But the truly incredible property of Dark Matter is that it offers zero interaction with any type of electromagnetic radiation; everything from Radio-waves to Gamma rays can travel without the slightest interference from one side of the Universe to the other. Amazing. Just as amazing is the fact that these are identical (not taking into consideration the farcical luminiferous aether concept) to the properties the so scorned aether was once thought to possess. The Ancients might have been smarter than we thought. If you would like to read more about this theory, consider reading "Redefining the Electron" available on Amazon.
You mean the book by this guy?:
Dr Dilip D James profile image

Dilip D James.

I can't seem to find anything about this fellow's credentials. He seems to have written a number of books and papers, none peer-reviewed, so far as I can see, about some variant of the Electric Universe (crank) hypothesis.

Do you know any more about him and can you explain why we should take him seriously? If he's an Electric Universe proponent, my guess is he may be an electrical engineer by background. Am I close?


P.S. I'll make a separate reply to your question about the New York café.
 
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What if Newton were not wrong? What if he was correct in stating that both time and space were absolute? Look for example at the case where someone goes to meet someone on a Wednesday at a café in New York. A week later he returns to the same Café at the same time, again on a Wednesday, to meet the same person. As far as he is concerned nothing has changed he has returned to the same place on the same day of the week, at the same time to meet the same person. We are aware that during that time interval; the earth has been rotating on its axis at a speed of 1600 km/h approx. apart from that the earth has also been speeding around the sun at a speed of something like 107,000 km/h and at the same time the sun has been tracing a path through the Milky Way Galaxy at 514,000 km/h and the Milky Way Galaxy leaves them all in the shade by moving around the Universe at 2,000,000 Km/h. So nothing is the same, nothing is as it was. The first question is how can that be? What strange force causes events on earth to remain synchronized in spite of the huge distances and times that have taken place in the interim? The second thought that occurs is, is that it doesn’t really matter what has moved, or how far or how fast it has moved; because the aether remains stationary and unchanging. This means that all positions can be plotted with reference to the aether, which acts like a Universal frame of reference. “Great Supposition you say!” But, I ask you to consider the question of Dark Matter, according to recent research, and before the crazy theory of Dark Energy came along, it was calculated using sophisticated instrumentation that Dark Matter constitutes 90% of all matter in the Universe. Here is a quote from the Department of Energy USA: “Dark matter makes up about 85 percent of the total matter in the universe, accounting for more than five times as much as all ordinary matter. Dark matter played an important role in the formation of galaxies and the evolution of the universe.” Although here the estimate is given at 85% and not 90%.

That aside, consider the properties of Dark Matter, it has such low interaction with matter, that it is estimated that it can travel through a block of lead a light year thick without experiencing any interaction whatsoever and vice-versa. At the same time Dark Matter exerts a pervasive gravitational force. But the truly incredible property of Dark Matter is that it offers zero interaction with any type of electromagnetic radiation; everything from Radio-waves to Gamma rays can travel without the slightest interference from one side of the Universe to the other. Amazing. Just as amazing is the fact that these are identical (not taking into consideration the farcical luminiferous aether concept) to the properties the so scorned aether was once thought to possess. The Ancients might have been smarter than we thought. If you would like to read more about this theory, consider reading "Redefining the Electron" available on Amazon.
Your question about the New York café is strange. It's almost as if you don't understand anything about special relativity. The speeds at which the people involved move with respect to the café are negligible compared to the speed of light. That is why their experience fits with Newtonian physics.

If all of them are moving, collectively, at huge speed relative to something else, that affects nothing, for them. It would be an observer moving with that something else who might see length contraction or time dilation effects, if the relative speed were a significant fraction of c.

There is no role for an aether in any of this.
 
If all of them are moving, collectively, at huge speed relative to something else, that affects nothing, for them. It would be an observer moving with that something else who might see length contraction or time dilation effects, if the relative speed were a significant fraction of c.
Pinball1970, leaving aside your conjectures on the merits or demerits of the author for the moment and taking a look at your comments on Einstein. OK, let us look at the ideas behind relativity. The first point you have to understand is that physical objects follow Galilean transformations: Suppose that Car A is going down the road at 75 km an hour and that car B is approaching from the opposite direction also travelling at 75 km an hour. What would happen? Using Galilean transformations it is possible to state that relative to car A, car B is approaching at 150 kilometres per hour. Similarly if car A and car B are travelling in the same direction and car B overtakes car A at 110 kilometres per hour. Using Galilean transformations we can say that car B is departing relative to the location of car A at a speed of 35 kilometres per hour. As you can see Galilean transformations add and subtract, it is as simple as that. However, when it comes to the speed of waves, everything changes, the speed of a wave is independent of the movement of any observer towards or away from the source, regardless of whether the source itself is moving forward or away from the observer. Sound familiar? Yes, Einstein describes the constancy of the speed of light in exactly the same words! So, solids move in a certain manner and immaterial objects like waves move in another manner. The speed of a wave depends solely on the properties of the medium it is travelling through. (This is where the aether, Dark Matter or a medium comes into the picture; the existence of such Dark Matter, aether or medium offers the perfect explanation for the constancy of the speed of light.). Einstein’s rather convoluted thinking was to try to explain why light or photons (particles) behaved like waves while travelling. Since photons were particles they should follow Galilean transformations. Why then did light behave like a wave travelling at a constant speed regardless of the speed of any observer or their movement towards or away from the source of the light? The special relativity postulate of the constancy of the speed of the light was formulated to explain this discrepancy. As such relativity is on pretty shaky ground. The ‘crank’ electromagnetic Universe theory that you refer to explains why and how light has the properties of being both particle like and wave-like very simply. It is a symbiosis of a wave and a particle. As such it can travel as both wave and particle, follow the inverse square law etc., etc.,

What Einstein in effect says is that the faster one goes, the slower time passes. Therefore, for a photon, that travels at the speed of light, time does not exist! From the photons point of view time always stands still! Which is all very well providing one ignores the fact that waves travel in exactly the same way without all the mumbo jumbo.
 
Pinball1970, leaving aside your conjectures on the merits or demerits of the author for the moment and taking a look at your comments on Einstein. OK, let us look at the ideas behind relativity. The first point you have to understand is that physical objects follow Galilean transformations: Suppose that Car A is going down the road at 75 km an hour and that car B is approaching from the opposite direction also travelling at 75 km an hour. What would happen? Using Galilean transformations it is possible to state that relative to car A, car B is approaching at 150 kilometres per hour. Similarly if car A and car B are travelling in the same direction and car B overtakes car A at 110 kilometres per hour. Using Galilean transformations we can say that car B is departing relative to the location of car A at a speed of 35 kilometres per hour. As you can see Galilean transformations add and subtract, it is as simple as that. However, when it comes to the speed of waves, everything changes, the speed of a wave is independent of the movement of any observer towards or away from the source, regardless of whether the source itself is moving forward or away from the observer. Sound familiar? Yes, Einstein describes the constancy of the speed of light in exactly the same words! So, solids move in a certain manner and immaterial objects like waves move in another manner. The speed of a wave depends solely on the properties of the medium it is travelling through. (This is where the aether, Dark Matter or a medium comes into the picture; the existence of such Dark Matter, aether or medium offers the perfect explanation for the constancy of the speed of light.). Einstein’s rather convoluted thinking was to try to explain why light or photons (particles) behaved like waves while travelling. Since photons were particles they should follow Galilean transformations. Why then did light behave like a wave travelling at a constant speed regardless of the speed of any observer or their movement towards or away from the source of the light? The special relativity postulate of the constancy of the speed of the light was formulated to explain this discrepancy. As such relativity is on pretty shaky ground. The ‘crank’ electromagnetic Universe theory that you refer to explains why and how light has the properties of being both particle like and wave-like very simply. It is a symbiosis of a wave and a particle. As such it can travel as both wave and particle, follow the inverse square law etc., etc.,

What Einstein in effect says is that the faster one goes, the slower time passes. Therefore, for a photon, that travels at the speed of light, time does not exist! From the photons point of view time always stands still! Which is all very well providing one ignores the fact that waves travel in exactly the same way without all the mumbo jumbo.
I'm not Pinball.

Photons are the quanta of light radiation. As such they have both wavelike and particle-like properties. I know you think QM is nonsense but that's because, probably being an electrical engineer of some sort (?), you have not been taught how QM works. Whereas, as a physical chemist, I have. So I know it is far from nonsense. Indeed QM, along with statistical thermodynamics, is almost the entire basis of physical chemistry. You cannot even explain the Periodic Table without it.

Einstein did not say, in effect, that the faster one goes the slower time passes. Special relativity says that time, for a system moving rapidly with respect to an observer, passes more slowly from that observer's viewpoint. From the viewpoint of the system itself, time passes at the normal rate. Time passes at different rates, depending on the frames of reference, according to the relative motion between the system observed and the observer.

At rates of relative motion <<c, the effect is negligible, which results in effectively Galilean relativity and Newtonian dynamics, both of which assume absolute rates of time and lengths in space. At rates of relative motion that are a significant fraction of c, these assumptions no longer apply, as shown by such experimentally observed phenomena as atmospheric muon lifetimes, or the decay rates of particles in accelerators. You may not like it but we've observed it.
 
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. Therefore, for a photon, that travels at the speed of light, time does not exist! From the photons point of view time always stands still! Which is all very well providing one ignores the fact that waves travel in exactly the same way without all the mumbo jumbo.
Special relativity is not mumbo jumbo, it has been tested and verified experimentally, by 1000s of scientists over the last 119 years. The extension, General relativity has also been tested experimentally over the last 108 years.
 
“The facts of physics do not oblige us to accept one philosophy rather than the other...the laws of physics in any one reference frame account for all physical phenomena, including the observations of moving observers. And it is often simplest to work in a single frame, rather than to hurry after each moving object in turn...You can pretend that whatever inertial frame you have chosen is the ether of the 19th century physicists, and in that frame you can confidently apply the ideas of the FitzGerald contraction....It is a great pity that students don't understand this. Very often they are led to believe that Einstein somehow swept away all that went before. This is not true. Much of what went before survived the theory of relativity, with the added freedom that you can choose any inertial frame of reference in which to apply all those ideas.”
― John S. Bell
 
“The facts of physics do not oblige us to accept one philosophy rather than the other...the laws of physics in any one reference frame account for all physical phenomena, including the observations of moving observers. And it is often simplest to work in a single frame, rather than to hurry after each moving object in turn...You can pretend that whatever inertial frame you have chosen is the ether of the 19th century physicists, and in that frame you can confidently apply the ideas of the FitzGerald contraction....It is a great pity that students don't understand this. Very often they are led to believe that Einstein somehow swept away all that went before. This is not true. Much of what went before survived the theory of relativity, with the added freedom that you can choose any inertial frame of reference in which to apply all those ideas.”
― John S. Bell
I would like to add that the same applies to quantum mechanics except perhaps to an even greater extent. Quantum mechanics did not sweep away all that went before, far from it. In fact I would go as far as to state that the only worthwhile aspects of quantum mechanics are those based on empirical observations, such as Bohr's model of the atom, light spectra and Planck's experiments with black body radiation.
 
Special relativity is not mumbo jumbo, it has been tested and verified experimentally, by 1000s of scientists over the last 119 years. The extension, General relativity has also been tested experimentally over the last 108 years.
Pinball 1970. I t should be stated that I have no wish to escalate this difference of opinion into a major argument. Yes, clocks everywhere change time with gravity (or acceleration). Very true. But it is also true that it was possible (still is) to detect Cavendish's Universal gravitational constant using just a torsion balance and weights. For what its worth.
 
Pinball 1970. I t should be stated that I have no wish to escalate this difference of opinion into a major argument. Yes, clocks everywhere change time with gravity (or acceleration). Very true. But it is also true that it was possible (still is) to detect Cavendish's Universal gravitational constant using just a torsion balance and weights. For what its worth.
If you want to talk about quantum mechanics you need to start a separate thread.
 
“The facts of physics do not oblige us to accept one philosophy rather than the other...the laws of physics in any one reference frame account for all physical phenomena, including the observations of moving observers. And it is often simplest to work in a single frame, rather than to hurry after each moving object in turn...You can pretend that whatever inertial frame you have chosen is the ether of the 19th century physicists, and in that frame you can confidently apply the ideas of the FitzGerald contraction....It is a great pity that students don't understand this. Very often they are led to believe that Einstein somehow swept away all that went before. This is not true. Much of what went before survived the theory of relativity, with the added freedom that you can choose any inertial frame of reference in which to apply all those ideas.”
― John S. Bell
I could not have put this better although I do not know about Fitzgerald.
John Bells work should have got him the Noble but he died relatively young.
 
Pinball 1970. I t should be stated that I have no wish to escalate this difference of opinion into a major argument.
The thread is 200 posts long so most of this has been covered. The OP was a response to another poster who claimed Newton had been overthrown.
 
Pinball1970, leaving aside your conjectures on the merits or demerits of the author for the moment and taking a look at your comments on Einstein. OK, let us look at the ideas behind relativity. The first point you have to understand is that physical objects follow Galilean transformations: Suppose that Car A is going down the road at 75 km an hour and that car B is approaching from the opposite direction also travelling at 75 km an hour. What would happen? Using Galilean transformations it is possible to state that relative to car A, car B is approaching at 150 kilometres per hour.
Do you know how to calculate the relative speed in this example using special relativity? What is the answer in that case?
However, when it comes to the speed of waves, everything changes, the speed of a wave is independent of the movement of any observer towards or away from the source, regardless of whether the source itself is moving forward or away from the observer. Sound familiar?
It's not true that the speed of waves is independent of the movement of the observer towards or away from the source. Try googling "Doppler effect".

I assume you've had the experience of hearing a police car with a siren going past you? The tone of the siren drops as the car goes past. Have you ever stopped to consider why that is?
Yes, Einstein describes the constancy of the speed of light in exactly the same words!
Light also exhibits Doppler shifts. (Though, to get the right answers with light we need to calculate the relativistic Doppler shift. Galileo/Newton gives the wrong answers.)
(This is where the aether, Dark Matter or a medium comes into the picture; the existence of such Dark Matter, aether or medium offers the perfect explanation for the constancy of the speed of light.).
Does it? Please explain.
Einstein’s rather convoluted thinking was to try to explain why light or photons (particles) behaved like waves while travelling.
What are you referring to, exactly? Which publication of Einstein's are you thinking of?
Since photons were particles they should follow Galilean transformations.
No. Photons travel at the speed of light and the Galilean transformations give the wrong answers at those speeds.

All this has been extensively tested experimentally. Are you aware of this?
Why then did light behave like a wave travelling at a constant speed regardless of the speed of any observer or their movement towards or away from the source of the light?
Well, Einstein explains it in his 1905 paper on relativity. Have you read that? It's freely available on the internet.

Also, every good introductory text on special relativity explains it - in many cases in a way more easily understood than Einstein's 1905 paper. (After all, we've had more than 100 years to work out how best to teach this stuff.)

However, you don't actually need to read anything to understand the answer to your question. The constancy of the speed of light is a postulate in Einstein's theory. It is an assumption. The assumption leads, along with one other assumption, to the entire theory.

The question of whether the theory of relativity is correct or not is, of course, not one that can be resolved by appealing to assumptions. It must be tested experimentally. Luckily for you, we have over 100 years of rigorous tests, all of which show that the theory of relativity works very nicely in circumstances where Galilean relativity demonstrably fails, thank you very much.
The special relativity postulate of the constancy of the speed of the light was formulated to explain this discrepancy.
Not exactly. One important motivation for the theory was the fact that Maxwell's equations of electromagnetism predict a constant speed of light, which is contrary to what we would expect if the Galilean transformations were true. In contrast, the theory of relativity is entirely consistent with Maxwell's equations.
The ‘crank’ electromagnetic Universe theory that you refer to explains why and how light has the properties of being both particle like and wave-like very simply. It is a symbiosis of a wave and a particle. As such it can travel as both wave and particle, follow the inverse square law etc., etc.,
What's the relevance of any of that to the theory of relativity? It sounds like you're talking about quantum mechanics, now.
What Einstein in effect says is that the faster one goes, the slower time passes.
That's a very imprecise, oversimplified statement of one result for one special case of the theory. But, okay.
Therefore, for a photon, that travels at the speed of light, time does not exist!
More accurately, a reference frame that travels at the speed of light does not exist.
From the photons point of view time always stands still!
Since the reference frame of a photon cannot exist, the photon can't really be considered to have a point of view. Never mind that the photon is not an observer.
Which is all very well providing one ignores the fact that waves travel in exactly the same way without all the mumbo jumbo.
They do not. The descriptions of how waves travel are different in Newtonian and relativistic physics, in certain testable respects. All the tests show that, in the competition, relativity "wins".
 
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That's a very imprecise, oversimplified statement of one result for one special case of the theory. But, okay.
Perhaps a little more detail is required.
Einstein's equation for time dilation, derived from his theory of relativity, expresses how time is experienced differently for observers in relative motion. The equation is:

t' = t x sqrt(1 - (v^2c^2)

Where:

( t') is the time interval measured by a moving observer (the proper time).

( t) is the time interval measured by a stationary observer.

( v) is the relative velocity between the observers.

( c) is the speed of light in a vacuum.

Considering that two planets A and B are 10 light years apart as seen by an observer on earth. Let us see how speed affects 5 spaceships, (a), (b),(d), (e) and (f) all travelling from Planet B towards Planet A. The respective speeds of the spaceships are (a) = 0.5c, (b) =(0.6c), (d) =0.7c , e = 0.8 c and f = 0.9c then the following equation will give how long each of these spaceships will travel to reach earth:

The time taken for each spaceship to travel to earth as seen by an observer on earth would be as follows:-

a) Traveling at 0.5c it would take 20 years

b) Would take 16.666 years

d) Would take 14.2 years

e) Would take 12.5 years

f) Would take 11.111 years

For an observer on the space ship using Einstein's equation for time dilation, derived from his theory of relativity, expresses how time is experienced differently for observers in relative motion. The equation is:

t' = t x sqrt(1 - /(v^2}(c^2))

For spaceship a : t' = 20 x sqrt(1 -/ (0.5c^2} x (c^2)) = 20 x 0.866 = 17.32 years

For spaceship b : t' = 16.66 x sqrt(1 -/ (0.6c^2)(c^2) = 16.66 x 0.64 = 13.32 years

For spaceship d : t' = 14.2 x sqrt{1 - / (0.7c)^2)(c^2) = 14.2 x 0.51 = 10.41 years

For spaceship e : t' = 12.50 x sqrt{1 - /(0.5c^2)(c^2) = 12.50 x 0.866 = 17.32 years

For spaceship f : 11.11x sqrt{1 - /(0.9c)^2)(c^2) = 12.50 x 0.436 = 4.84 years

In each case for a person on earth a different time in years would have passed to that experienced on the space ships. While less time would have passed for the individual travelers depending on the speed of their spaceships, the faster the ship the less time taken for the journey. Time varies in special relativity, it is no longer constant, each traveler experiences a different time. So, if the clock on the spaceship (f) is measuring time properly according to an observer moving with the clock, how can we account for the fact that the observer on the ship seems to cover a distance of 10 light years in 4.8 years, which would imply that they’re traveling at a speed of 2.08c? That absolutely cannot be true. For one thing, one of the implications of relativity is that nothing can travel faster than c, the speed of light in vacuum. c is the ultimate speed limit in the universe. For another, two observers will always agree on their relative velocities. If the person on the Earth sees the spaceship moving at 0.9c, the observer on the spaceship agrees that the Earth is moving at 0.9c with respect to the spaceship (and because the other planet B is not moving relative to the Earth), everyone’s in agreement that the relative velocity between the spaceship and planet is 0.9c. So, distance is velocity multiplied by time and we know the velocity and time measured by the observer on the spacecraft is 0.9c and 4.8 years. This implies that they measure a distance for the trip of 4.32 light-years, much smaller than the 10 light-year distance measured by the observer on the Earth. The idea is that light does not experience time, since the faster you go through space the slower you go through time and vice-versa. The journey would be instant for you but to an outside observer (assuming they were standing still) would see your journey take over four years.

This is good, we have been able to calculate the speeds, times and distances for five spaceships, BUT consider if there were 1000 space ships instead of just 5 spaceships, travelling this time in both directions between the two planets, all at different speeds, how many different bits would space split into? The answer is 1000! (One thousand factorial) or a number bigger than all the atoms in the Universe. Is such a situation tenable?
 
quant:
Einstein's equation for time dilation, derived from his theory of relativity, expresses how time is experienced differently for observers in relative motion. The equation is:

t' = t x sqrt(1 - (v^2/c^2)

Where:

( t') is the time interval measured by a moving observer (the proper time).

( t) is the time interval measured by a stationary observer.

( v) is the relative velocity between the observers.

( c) is the speed of light in a vacuum.
Like I said, this is a special case. Specifically, it applies where t' is a proper time interval between two events in spacetime, as you have (more or less) said.
Considering that two planets A and B are 10 light years apart as seen by an observer on earth.
We're assuming that A and B are approximately stationary as seen by the observer on Earth?
Let us see how speed affects 5 spaceships, (a), (b),(d), (e) and (f) all travelling from Planet B towards Planet A. The respective speeds of the spaceships are (a) = 0.5c, (b) =(0.6c), (d) =0.7c , e = 0.8 c and f = 0.9c then the following equation will give how long each of these spaceships will travel to reach earth:

The time taken for each spaceship to travel to earth as seen by an observer on earth would be as follows:-

a) Traveling at 0.5c it would take 20 years

b) Would take 16.666 years

d) Would take 14.2 years

e) Would take 12.5 years

f) Would take 11.111 years
Yes.
For an observer on the space ship using Einstein's equation for time dilation, derived from his theory of relativity, expresses how time is experienced differently for observers in relative motion. The equation is:

t' = t x sqrt(1 - (v^2}/(c^2))

For spaceship a : t' = 20 x sqrt(1 -/ (0.5c^2} x (c^2)) = 20 x 0.866 = 17.32 years

For spaceship b : t' = 16.66 x sqrt(1 -/ (0.6c^2)(c^2) = 16.66 x 0.64 = 13.32 years

For spaceship d : t' = 14.2 x sqrt{1 - / (0.7c)^2)(c^2) = 14.2 x 0.51 = 10.41 years

For spaceship e : t' = 12.50 x sqrt{1 - /(0.5c^2)(c^2) = 12.50 x 0.866 = 17.32 years

For spaceship f : 11.11x sqrt{1 - /(0.9c)^2)(c^2) = 12.50 x 0.436 = 4.84 years
Yes.
In each case for a person on earth a different time in years would have passed to that experienced on the space ships. While less time would have passed for the individual travelers depending on the speed of their spaceships, the faster the ship the less time taken for the journey.
Yes. Of course, from the perspectives of the travellers on the spaceships, their time is running at the normal rate. The reason the journey takes less time, according to them, is that the distance between planets A and B is shorter than 10 light years. So, they don't have as far to travel as the Earth observer says.

Also, it's worth noting that, during the journeys, from the perspectives of the people on the spaceships, clocks on Earth that run slower than their own clocks on their spaceships.
Time varies in special relativity, it is no longer constant, each traveler experiences a different time. So, if the clock on the spaceship (f) is measuring time properly according to an observer moving with the clock, how can we account for the fact that the observer on the ship seems to cover a distance of 10 light years in 4.8 years, which would imply that they’re traveling at a speed of 2.08c? That absolutely cannot be true.
See above. You might be forgetting length contraction.
For one thing, one of the implications of relativity is that nothing can travel faster than c, the speed of light in vacuum.
Yes. And nothing with non-zero rest mass can travel at the speed of light.
For another, two observers will always agree on their relative velocities. If the person on the Earth sees the spaceship moving at 0.9c, the observer on the spaceship agrees that the Earth is moving at 0.9c with respect to the spaceship (and because the other planet B is not moving relative to the Earth), everyone’s in agreement that the relative velocity between the spaceship and planet is 0.9c.
Yes.
So, distance is velocity multiplied by time and we know the velocity and time measured by the observer on the spacecraft is 0.9c and 4.8 years. This implies that they measure a distance for the trip of 4.32 light-years, much smaller than the 10 light-year distance measured by the observer on the Earth.
Yes. That's length contraction.
The idea is that light does not experience time, since the faster you go through space the slower you go through time and vice-versa. The journey would be instant for you but to an outside observer (assuming they were standing still) would see your journey take over four years.
If we plug v=c into your equation for time dilation, the equation says t'=t times zero, which might seem fine until you try to invert it: t = t'/zero. Division by zero tells us that there is a problem. The problem is that we can't have a reference frame that travels at v=c.

Nevertheless, we can choose a velocity that is almost c, and in that case there's no problem. We get t'=t times (something very small), and t'=t/(something very small), but the maths doesn't explode.
This is good, we have been able to calculate the speeds, times and distances for five spaceships, BUT consider if there were 1000 space ships instead of just 5 spaceships, travelling this time in both directions between the two planets, all at different speeds, how many different bits would space split into? The answer is 1000! (One thousand factorial) or a number bigger than all the atoms in the Universe. Is such a situation tenable?
This is the first time you have mentioned space "splitting into" parts? What do you mean? There's nothing about that in the maths.
 
BUT consider if there were 1000 space ships instead of just 5 spaceships, travelling this time in both directions between the two planets, all at different speeds, how many different bits would space split into? The answer is 1000! (One thousand factorial) or a number bigger than all the atoms in the Universe. Is such a situation tenable?
Are you suggesting that the Many Worlds model of quantum mechanics applies here? I don't think it does.

Perhaps it may help if you understood the model better. Here is a very approximate i.e not especially accurate, explanation:

In quantum mechanics it is axiomatic that, for a sub-atomic system, any properiy that can be observed/measured is a quantum mechanical operator. And simple linear algebra states that every such operator can be associated to objests called eigenvectors to which are in turn associated multiple eigenvalues. These latter eigenvakues are, in QM, the real-valued measurements.of the state

Now experiment shows that repeated meaurements of the exact same system in the exact some state in the exact same way will likely produce a different eigenvelue each time. The average value of many such mearements is called the "expectation value" of this operator.

But the "collapse of the wave function" model suggests that, having as it were "chosen" an eigenvalue, no other eigenvalue is any longer available. The rough definition of expection vakue given above suggests this cannot be true unless to each quantum system one can associate multiple wave functions, each with a different, single eigenvalue.

Does this sound to you like the sort of world in which you are likely to find spaceships?
 
It's not true that the speed of waves is independent of the movement of the observer towards or away from the source. Try googling "Doppler effect".

I assume you've had the experience of hearing a police car with a siren going past you? The tone of the siren drops as the car goes past. Have you ever stopped to consider why that is?
Unless you accept the fundamental fact that waves are different and solids are different, there is way in which one can make any kind of comment on special relativity. Bringing the Doppler shift into this is if you will forgive me saying so speaking out of the wrong end.
 
Are you suggesting that the Many Worlds model of quantum mechanics applies here? I don't think it does.

Perhaps it may help if you understood the model better. Here is a very approximate i.e not especially accurate, explanation:

In quantum mechanics it is axiomatic that, for a sub-atomic system, any properiy that can be observed/measured is a quantum mechanical operator. And simple linear algebra states that every such operator can be associated to objests called eigenvectors to which are in turn associated multiple eigenvalues. These latter eigenvakues are, in QM, the real-valued measurements.of the state

Now experiment shows that repeated meaurements of the exact same system in the exact some state in the exact same way will likely produce a different eigenvelue each time. The average value of many such mearements is called the "expectation value" of this operator.

But the "collapse of the wave function" model suggests that, having as it were "chosen" an eigenvalue, no other eigenvalue is any longer available. The rough definition of expection vakue given above suggests this cannot be true unless to each quantum system one can associate multiple wave functions, each with a different, single eigenvalue.

Does this sound to you like the sort of world in which you are likely to find spaceships?

The many-worlds interpretation posits that the wave function never collapses. Instead, all possible outcomes of a quantum measurement exist simultaneously in a superposition. When a measurement occurs, the universe "splits" into branches, each representing a different outcome. Therefore, repeated measurements do not contradict Many Worlds Interpretation; rather, each measurement results in a new branching of the universe where each possible eigenvalue is realized.

The Many Worlds Interpretation of quantum mechanics remains consistent with the mathematical framework of quantum mechanics. The formalism of operators, eigenvalues, and expectation values remains unchanged; it's the interpretation of these mathematical entities that differs. The many-worlds interpretation provides a way to account for the apparent randomness of measurements without invoking wave function collapse.

These arguments bring me back to the original question as to whether a science such as quantum mechanics represents reality. I don’t think it does.
 
Not exactly. One important motivation for the theory was the fact that Maxwell's equations of electromagnetism predict a constant speed of light, which is contrary to what we would expect if the Galilean transformations were true. In contrast, the theory of relativity is entirely consistent with Maxwell's equations.
Which is the reason that James Clerk Maxwell was still thinking of an aether like medium, when he was literally on his death bed. Since the existence of such a medium would explain the constancy of the speed of light and much else.
 
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