David Levy

Thanks, but that isn't my question. The questions are as follow: As SPECIAL relativity applies locally in flat space – please specify the distance range which is considered as locally. Is it 1 Mpc? 100 Mpc? or xMpc? On the other hand, from which distance we consider it as SPECIAL relativity? I can't understand why there is no distance range?

Thanks That was very clear to me. However, this doesn't answer my question. Do I need to explain the question?

Thanks So, Lorentz Transforms are part of SPECIAL relativity that only applies locally in flat space, while the expansion of space is described by GENERAL relativity. Can you please specify the distance range for SPECIAL relativity and GENERAL relativity? In other words, what is the maximal distance range that it is considered as SPECIAL relativity and therefore Lorence transformation is applicable? – (Which means velocities don't add linearly) From what distance range it is considered as general relativity? (Which means velocities add linearly - Every individual Mpc expands at the same rate 70 km/sec/Mpc)

Please try to answer the following contradiction: In one hand it is stated that: "Every individual Mpc expands at the same rate 70 km/sec/Mpc" Hence, the speed increases very linearly: At 1 Mpc the speed is 70 Km/sec At 10 Mpc the speed is 700 Km/sec At 100 Mpc the speed is 7,000 Km/sec At 1,000 Mpc the speed is 70,000 Km/sec At 10,000 Mpc the speed is 700,000 Km/sec and so on… However, on the other hand based on Lorentz Transformations mathematics the speed increase isn't linearly Can you please explain this contradiction?

In the following article it is stated: http://www.iflscience.com/space/why-universe-accelerating/ "We know that our universe is expanding at an accelerating rate, but what causes this growth remains a mystery. The most likely explanation is that a strange force dubbed “dark energy” is driving it." So, the expansion is based on some sort of power/force/energy. We must find the source for that energy Thanks That is excellent description for what we see. However, what is the real cause for this phenomenon? Let's look at the example which Janus has used: So, let's use the rockets as follow: B is an observer with his own clock passing A at the rear of a rocket moving at 0.6c relative to A, C is a projectile fired by B at 0.6c relative to himself towards the front of the rocket. He fires the projectile at the moment he is passing A. D is a projectile fired by C at 0.6c relative to himself towards the front of the rocket. He fires the projectile at the moment he is passing A. E is a projectile fired by D at 0.6c relative to himself towards the front of the rocket. He fires the projectile at the moment he is passing A. …. M is a projectile fired by L at 0.6c relative to himself towards the front of the rocket. He fires the projectile at the moment he is passing A. Hence. At t=0 we get: A B C D E F G H I J K L M At t=1 we get: A-B-C-D-E-F-G-H-I-J-K-L-M At t=3 we get: A---B---C---D---E---F---G---H---I---J---K---L---M Hence, if the expansion works as rockets over rockets, than we have a simple solution. Now we need to find the source for those rockets and/or the requested energy for the expansion.

Now we understand the difference between "Moving away" and "receding". Hence, the far end galaxy is receding from us at a speed which is greater than the speed of light. However, as we discuss on relativity - it is clear that the outcome is that the relative speed between us and this galaxy is faster than the speed of light. So, why this semantic is so important for our scientists? If I understand it correctly: Based on the current hypothesis - nothing can move faster than a speed of light. So in order to bypass that "nothing can move faster" we call it receding. Hence, we can keep with our hypothesis that nothing can move faster than the speed of light while we justify the simple evidence that there are galaxies which are moving away from us at a speed which is greater than the speed of light. By now, I assume that I understand the basis for this decision. We claim that the expansion isn't considered as some force or power. So as there is no need for force, there is no room for "moving away" only a "receding". Therefore, by adding this simple word - "receding" instead of "moving away", we have bypassed this contradiction and now we can hold the stick from both sides. In one hand - we can claim that nothing can move faster than the speed of light, while on the other hand we can justify why galaxies are receding from us at a speed which is greater than the speed of light. And now - for the main question about the expansion: How could it be that the matrix expansion of space comes for free? If I want to make even one step - I need to set power. So how could it be that the nature carries galaxies at a speed which is greater than the speed of light for free - without any need for power? Don't you think that there must be a power source for that expansion?

Excellent!!! I fully agree with your brilliant example. Yes, yes - yes! So, we are not moving faster than the speed of light but with regards to that far end galaxy we recede away from them at a speed faster than the speed of light. Don't forget that everything is relative. Hence, instead of using the word "moving" away, we need to use the word "recede" away. I have no problem with that. Now we can be friend again. No more war! One simple word, same meaning - bring peace to our universe.

So at any location in the whole universe galaxies will never ever gain a speed greater than c. This is based on special relativity Therefore, when we look at our nearby space, all the galaxies must move at a speed which is lower than the speed of light. However, If we look at the horizon, we see galaxies which are moving away from us at a speed which is close to the speed of light. Never the less, if we could be there we should see a similar space view as we see from our milky way galaxy. Hence, as stated: "Which means that it is a local limit (in flat space, with no gravity, in inertial frames of reference)." So far so good. Now, let's focus on general relativity by the following example: Let's assume that our galaxy is just standing at our position (with regards to the nearby space aria). 40 Billion Light years away - there is a galaxy which also just stands at its local space aria. However, due to the expansion, the volume between the two galaxies increases dramatically. Hence, based on a simple calculation, the two galaxies are actually moving away from each other at a speed which is greater than the speed of light. That is based on my simple common sense. However, based on kinematic motion this is impossible. I really can't understand why.

Thanks Great answer Fully Agree! Also fully agree. So, due to general relativity (such as cosmological expansion), there is no speed limit of speed of light and therefore, galaxies could move at a speed which is higher than the speed of light. Did I understand you correctly?

Great article! However, there is a contradiction, as you have stated: In one hand it is stated: that that galaxies which are located at a distance of over 13.7 Billion light years should move faster than a speed of light: "This is our freaky friend, the Hubble Constant, the idea that for every megaparsec of distance between us and a distant galaxy, the speed separating them increases by about 71 kilometers per second. Galaxies separated by 2 parsecs will increase their speed by 142 kilometers every second. If you run the mathatron, once you get out to 4,200 megaparsecs away, two galaxies will see each other traveling away faster than the speed of light. How big Is that, is it larger than the Universe? The first light ever, the cosmic microwave background radiation, is 46 billion light-years away from us in all directions. I did the math and 4,200 megaparsecs is a little over 13.7 billion light-years.There’s mountains of room for objects to be more than 4,200 megaparsecs away from each other. Thanks Universe?!?" While on the other hand it is stated: "I stand with Einstein when I say that nothing can move faster than light through space, but objects embedded in space can appear to expand faster than the speed of light depending on your perspective. "Light emitted by the galaxies is moving towards us, while the galaxy itself is traveling away from us, so the photons emitted by all the stars can still reach us. These wavelengths of light get all stretched out, and duckslide further into the red end of the spectrum, off to infrared, microwave, and even radio waves. Given time, the photons will be stretched so far that we won’t be able to detect the galaxy at all. In the distant future, all galaxies and radiation we see today will have faded away to be completely undetectable. Future astronomers will have no idea that there was ever a Big Bang, or that there are other galaxies outside the Milky Way. Thanks Universe." So, it is clear that we want to hold the stick in both sides simultaneously. In one hand we claim that nothing can move faster than the speed of light but on the other hand we are asking for some help from our dear "expansion" as it is stated: "but objects embedded in space can appear to expand faster than the speed of light depending on your perspective" So, we say yes and no simultaneously.. Hence, although it's quite difficult for us to say yes or no – it's time to give direct answer. Not just to me, but mainly to yourself. Than with the expansion or without - somehow they must move faster than the speed of light with reference to our prospective. This must be embedded in our formula. How can we say that the formula is correct "but... There is no room for "but". Just "yes" or "no" - please! If due to the expansion some galaxies can move faster than a speed of light depending on our perspective - than please say yes and show it in an updated formula! We MUST add the impact of the expansion to our formula.

Thanks I'm not sure that I fully understand your answer with regards to the expansion. So, please advice if the following is correct: 1. The expansion has no impact this formula. Hence, the formula is fully updated for our current universe. 2. Therefore, there is no galaxy in the whole universe which is moving away from us at a speed which is faster than the speed of light (even if it is located 40 or 100 Billion Light years away from us. Yes or no

Thanks I will read the articles as advised. However, with regards to the expansion; This formula had been developed over than 100 years ago. At that time people consider the universe as quite compact size. They didn't have any clue about the BBT or the Expansion. Therefore, I assume that they took it for granted that nothing can move faster than the speed of light. However, with all of our current knowledge, could it be that the formula is not updated for our current universe? Do we have an idea how the expansion impact this formula? Could it be that due to the expansion there are some galaxies at the far end of the Universe which are moving faster than the speed of light and therefore we can't see them?

Thanks for the explanation. It is clear that I need to improve my knowledge in relativity - and I will use your excellent advice. However, I have discovered an issue which seems to me as some sort of contradiction. Would you kindly offer a direct answers to my questions (I have only got an answer to no 4)? With regards to question n. 4. Are you sure that "No 4 is not based on negative k or curvature of any form." In the article it is stated: "If κ < 0, then we set {\displaystyle c=1/{\sqrt {-\kappa }}}... which becomes the invariant speed, the speed of light in vacuum. This yields κ = -1/c2 and thus we get special relativity with Lorentz transformation" So what can we understand from κ < 0 or κ = -1/c2?

Thanks However, your answer isn't fully clear to me. So let me ask the following questions: 1. Please advice if the following formula is for constant velocity (0.6c)? 2. Do you agree that this formula is based on Lorentz transformations? 3. Without Lorentz transformations, can we prove this formula based on Rapidity or some other transformations? 4. Is it correct that Lorentz transformations is based on negative K (κ < 0)?

Do appriciate your support. If I understand it correctly, the following formula is based on Lorentz transformations. However, Lorentz transformations is based on a negative K. As K must be positive, could it be that there is an error in this formula?

Please see the following article: https://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations#Hyperbolic_rotation It is stated: Define this constant as δ(v)/v γ(v)= κ, where κ has the dimension of 1/v2. Lorentz transformations If κ < 0, then we set {\displaystyle c=1/{\sqrt {-\kappa }}}... which becomes the invariant speed, the speed of light in vacuum. This yields κ = -1/c2 and thus we get special relativity with Lorentz transformation Only experiment can answer the question which of the two possibilities, κ = 0 or κ < 0, is realised in our world. The experiments measuring the speed of light, first performed by a Danish physicist Ole Rømer, show that it is finite, and the Michelson–Morley experiment showed that it is an absolute speed, and thus that κ < 0. Question: If K has the dimension of 1/v2 than by definition it must be a positive no. κ < 0 means a negative no. Sorry - there is no way to convert 1/v2 to a negative no. Not experiment and not any imagination!!! They have to prove how could it be that Dimension of 1/v2 could represent a negative no. If K can't be a negative no by definition, than, how could it be that based on Lorentz transformations κ < 0? Without Lorentz transformations there is no room for the following formula: studiot, on 20 Apr 2017 - 7:09 PM, said: So, could it be that the above formula which is based on Lorentz transformations is unrealistic?

Perfect explanation. I'm not sure that I fully understand the time selections, but I'm sure by 100% that it is correct. It is clear to me that you are the expert. Actually all is about the same formula with different variation: By using the standard time dilation equation: We actually get at the end the same result as by using the v: So, the speed is relative, the time is relative and even the distance is relative. It is clear that I need to get better understanding about this unique formula. Can you please highlight an article about it?

Thanks It's fascinating example. It's quite difficult for me to trace all the time selections, so let me start with the following questions: By consider things according to B. Why B front side rocket has the same clock as it's back side although the rocket is 0.6 light sec long? Why you don't add (0) to C? So, why the starting point is not as follow: A(0) B(0)____|(0.6) C(0) With regards to factor: It is stated: "..and because A has a relative motion with respect to B, B measures A"s clock as running slow by a factor of 0.8." How did we calculate this factor? Why it is only valid between A to B? What about the factor between B to C?

O.K. I will read as advised. However, Would you kindly advice if both are correct: If we look from B point of view, the speed V (ac) between A to C is 1.2c and therefore the distance had been increased by S (ac) = 1.2c * t1. If we look from C point of view, the speed V (ac) between A to C is 0.88c and therefore the distance had been increased by S (ac) = 0.88c * t1.

Thanks for you support Sorry, but I ask the same question as I do not get a direct answer. That is correct. I focus on absolutes However, before discussing about relativity would you kindly answer the following: 1. Do you agree that with regards to B point of view, the relative speed between A and C is 1.2c? Yes or no 2. If so, do you agree that based on B point of view and t1 (time frame) the distance S (ac) between A to C had been increased by 1.2c * t1? Yes or no If the answers to the above are - yes, let's move to relativity: O.K. So based on relativity, the view from C isn't the same as the view from B. With regards to - Distance. If we look from B point of view, the speed V (ac) between A to C is 1.2c and therefore the distance had been increased by S (ac) = 1.2c * t1. If we look from C point of view, the speed V (ac) between A to C is 0.88c and therefore the distance had been increased by S (ac) = 0.88c * t1. I had the impression that distance by definition must be absolute. So, which one is the correct answer? I still don't understand how could it be that due to relativity both are correct.

O.k. The mathematics is clear. However, I still don't understand the logic. I would like to verify the correlation with the following formula: S = V * T S = Distance V = Velocity T = Time. So, let's look at the following example: The relative speed between B to A and B to C is 0.6c. Therefore, after t1 the distance between B to A and B to C should be increased by: S (ba) = S (bc) = S1 = 0.6 c * t1. As BA vector is on the same line as BC, than by definition the distance between C to A should be increased by: S (ca) = S (ba) + S (bc) = 2 * S1 = 1.2 c * t1. It took t1 (time) for C and A to increase their distance by S (ca) Therefore - during t1 their relative speed is: V (ca) = S (ca) / t1 = 1.2c Simple and clear. Do you see any error with that calculation? However, based on your mathematics - the relative speed between A to C is: V (ca) = 0.88 c. Therefore, after t1 the increased distance between A and C is: S (ca) = 0.88 c * t1. That can't represent the real increased distance of S (ca) = 1.2 c * t1. Can you please explain this enigma?

O.K. The space is expanding in between us and them. Hence, there are two options: 1. The expansion increases the relative speed (above c) between us and them and therefore we can't see them. 2. The expansion doesn't increase the relative speed between us and them and therefore we must see them. Please choose one.

Well, we are living in one Universe. The expansion is an important section of that universe. Therefore, it must be included in the formula of speed. We can't just use a formula which doesn't take in account the expansion effect. So let me ask again: Do you agree that there are galaxies beyond D? If so, why we can't see them? Why we can't assume that – Due to the expansion some galaxies are moving at the speed which is higher than c and therefore we can't see them?

One more question. If we look left we can see that D galaxy moves almost at the speed of light. We don't see any further galaxies. So, there are two options: 1. There are no galaxies beyond D 2. There are other galaxies but they are moving at a speed which is faster than the speed of light and therefore we can't see them. Which one is correct?

O.K. Let me ask you the following: If the speed between A and C is 0.88235 c, please prove by mathematics how could it be that the speed between B to A and B to C is 0.6 c.