Hubble Deep Field showing galaxies up to 10 billion light-years distant from Earth.

Is it possible that when we look into the cosmos that we are seeing into the past?

We hear all the time that we are looking into the past when we look out into space. But we can’t definitively say that! In the following I’ll explain why.

Astronomers say that because the speed of light is a finite value (c = 299,792.458 km/s ) it takes light 1 year to travel a distance of 1 light-year. On the surface of it that seems very reasonable.

That means that light leaving the star alpha Centauri, which is 4.3 light-years away, took 4.3 years to get to Earth and thus the information in that light is 4.3 years old by the time it gets to Earth. Thus they say we are looking back in time — into the past. And for distant galaxies this means we are looking back in time even billions of years.

But is that correct?

How can you know that to be true? Wouldn’t you have to measure the speed of the incoming light from the stars? How could you measure that one-way speed?

All speed of light measurements that have ever been performed have measured a two-way (or round-trip) speed by reflecting a light/laser beam from a rotating mirror or some such apparatus. That technique gives only the average speed over the outbound and inbound paths. See below for an example.

Note: Other techniques, even so-called ‘one-way’ speed of light measurements, assume that the one-way speed is the same in all directions. That means the one-way speed is assumed to be equal to the two-way speed and as a result they do not make a true one-way measurement.

This may seem strange to some, but the one-way speed of light has never been and cannot be measured! That is a fact of the physical laws that govern this universe. As a result, you cannot know the incoming speed of light from the stars. And if you don’t know the incoming speed of light how can you say how long it takes to get to Earth?

Now, let’s look at this from a wider perspective.

No geologist would believe that the rock layers, or the fossils in them, are in the past. He might believe that the fossils are evidence of past life but no one can see into the past and see living dinosaurs, for example.

However, the evolution story critically needs billions of years of unobserved past geological history–called ‘deep time’–for the slow and gradual changes they believe occurred in the Earth since its alleged formation 4.6 billion years ago. That time is needed for so-called biological evolution to have occurred. But it has never been observed while it is happening.

No one has ever invented a time machine. We just don’t have any access to the past despite messages in the plethora of time travel movies nowadays. We cannot see into the past in the rock layers on Earth. The past is gone forever. It cannot be observed!

No biologist, no matter how strong his conviction that biological evolution has occurred over the past 3.8 billion years of Earth history, would believe any living creature he observes now on Earth is in the past. He only studies different species now in the present. He can only conjecture about the past evolution story but he cannot see into the past to observe it happening.

No one has ever invented a time machine. We just don’t have any access to the past. We cannot see into the past history of life on Earth. The past is gone forever. It cannot be observed!

The same problem exists in cosmology. It also needs billions of years of deep time for the cosmic evolution story, which allegedly started in a big bang about 13.8 billion years ago.

It also needs the unobserved past.

Astrophysicists assume galaxies at a certain distance are representative of all galaxies at some past epoch of time. But this is an assumption — not a measurement of the past.

No one has ever invented a time machine. We just don’t have any access to the past. We cannot see into the past. Even in the cosmos the past is unobservable! It is gone forever!

When we look out into space, even with the biggest telescopes, we are seeing the galaxies now. We are seeing them as they appear to us now, not as they were at some past moment of time. We see them in real time now.

But you say: the galaxies are billions of light years away. How can we see them as they are now? Doesn’t light take billions of years to get to Earth?

But … how can you know that?

This is what I was explaining above. You cannot make any such implied statements. It leads to a logical fallacy.

Without stating it, you assume the inward one-way speed of light is the same as the measured two-way speed. You assume it is isotropic — the same speed in all directions. Hence based on the measured speed c, with the assumption that it is the same in all directions, you incorrectly conclude that light from the galaxies must take billions of years of travel time to get to Earth, but without ever measuring it.

I accept that the distances to the galaxies are essentially correct. No argument there. But a light-year is the distance that scientists have calculated that light would travel at speed c. If the inbound light is not travelling at speed c, then the light could cover much more distance than calculated with this assumption. In fact, if the inbound speed is infinite then the light from the stars would arrive at the Earth instantaneously.

But it is important to remember that the one-way incoming speed of light cannot be measured.

And if you don’t know the incoming speed, you cannot know the travel time.

From the physics of Einstein we have learnt that to know the travel time of light from the stars we must know the incoming speed. And thus if we don’t know the incoming speed–it has never been measured–we cannot know the travel time.

However, also from the Einstein we have learnt that we are free to choose any value for the one-way speed of light between 1/2c and infinity. There is a rule here: the average round-trip speed must be equal to c, because that is what is always measured.

Thus the apologetics is finished.

Einstein’s physics tells us that it is perfectly valid to choose an infinite incoming speed of light. As such there is no starlight travel time. Thus it follows that we are seeing the stars and galaxies now in real time. And there is no way to refute this. No experiment has ever been, or will ever be, devised to prove otherwise.

There is one final question:

What is the language of the Bible?

Does the language of the Bible imply that there is no light travel time? If so, it follows that the incoming one-way speed of light is infinite and there is no travel time.

The main issue here for biblical creationists is the creation of the stars on Day 4 of Creation Week. Reading Genesis 1:14-15

When creating the sun. moon and the stars, God said, ‘let there be’ lights in the expanse of heavens. The important expression here is ‘let there be’ which is followed by ‘it was so’. This language implies as soon as God spoke the lights (especially important here is the stars) were visible from Earth. The expression ‘it was so’ does not connote billions of years of travel time for the light to reach Earth, but rather it was instantaneous.

This point is strongly made in Psalm 33:9

As soon as God spoke ‘it was done’. He commanded and ‘it stood fast’. There is no delay. And all creation is viewed within an Earth-centric frame of reference.

God created the whole creation in the present moment we call ‘now’. Isaiah 48:7 makes this point.

When God was creating He says He did not do it a long time ago but ‘now’.

Finally looking at 2 Peter 3:7

The subject here includes the heavens, which we see ‘now’. It is not referring to the heavens as they were some million or billion years ago, due to the delayed light signal coming from those distant sources.


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37 responses to “Can we see into the past?”

  1. Edoardo Roncelli Avatar
    Edoardo Roncelli

    Thank you for your article dr. Hartnett.

    In my ignorance about the matter, I imagine now the evolutionist and skeptic’s opposition, built on the ‘verified delay time’ in the communications among interplanetary probes and earth control centers. For example, I take from the page appearing on http://www.spaceacademy.net.au the following times:
    Earth-Mars 55 – 378 million km 3 – 21 minutes
    Earth-Jupiter 590 – 970 million km 33 – 53 minutes
    Earth-Pluto ~5800 million km 5 hours
    Earth-Nearest Star ~40 million million km 4 years

    In to reply a skeptic, is it right to apply the principle you expose in the article, in other words as “the average round-trip speed must be equal to c, because that is what is always measured”, we could assume a very low speed of light from the earth to the probe, but an almost infinite speed for the waves coming from the probe to the control center?

    May you and your family enjoy a beautiful 2019 in Christ.

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    1. These delay times are calculated using the distance and the assumed isotropic speed of light c equal to approximately 300,000 km/s. But the answer to your question is yes, because we cannot measure the one-way speed, we can choose it. The round-trip average speed must be c which is what is always measured.

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  2. gary302@reagan.com Avatar
    gary302@reagan.com

    Sincerely, I say “Thank You!”

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  3. Gideon , this is amazing ! Two reasons. No. 1 just today I had a , quantum leap , of thinking about the universe and the time constant ‘c’ in the Einstein equation of fame , e=mc2 , .. and No. 2 , thinking of atomic matters and words used to describe things , and the spoken Word , of the Light before Sun , Moon and stars , day 4 ..
    I had been conversing with a chap about the assumptions made by many who do not comprehend Einsteins theory , and his own doubt about the “greatness” , of his work ..
    As you suggest , the Universe is vastly huge , and yet as we develop better and better viewing methods , it would appear that the universe we see , may not be all there is, … now this for me gets VERY INTERESTING .. as I think I have a good grasp of the size .. parsecs .. = distance light travels in a year .. from scifi , (bear with me ) ,. . .the drawback of travel in space is time v distance , and that becomes not ONLY a speed issue , but a vector issue .. . So back to travel . If one takes a scifi improbability , inertialessness , .. hang on , it gets bumpy .. in the near neighbourhood of a galaxy , kne would ‘travel’ a bit like a car in the city , say 60 kmh or the old 35mph , out in the country or rural or on a highway one might do 80-100kmh or about 50-60 mph .. then you have the autobahns and the Nevada no-mans-land and as Oz used too , the ‘unlimited’ , other than equipment limit value say 300kmh or about 200mph .. now transfer those numbers to parsecs and in scifi its near enougn to making a ‘trading’ system workable for near galactic centres .. but still means no contact beyond about 400 parsecs in a normal life span for a human , , and then a further scifi jump cryofreeze , cellular stasis , for journeys up to 1000 parsecs . .. we can ‘see’ beyond that “distance” today ! .. (?).. , but for scifi , whereby a real physical limitation is ignored for sake of a good story . . The idea that mankind ‘could’ not only populate but discover , ‘other’ , lifeforms makes for a good story. .. back to Light and time and distance .. math , dist x time = speed, change in speed =acceleration , where the change is speed x time =accel . , momentum ks ALWAYS conserved and for the , scifi , inertialessness bit , the momentum had to be dealt with at each end , destination , using massive shock absorbing webs, ,. .anyway it popped into my head /mind that all light is photons , and these impact Light receptors at retina interface .. thjs all light only exists at interface signal pickup .. Light is invisible “until” ,it manifests on a receiver .. the darkness comprehendeth it NOT ..

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  4. Consider a deep space satellite. It’s clock was sunchronized to earth’s before it was launched. Now, many years later, it sends a signal. The signal is time stamped with its own clock, naturally. The signal is received here, and a difference is noticed between the time stamp in the signal and the time stamp of received signal on earth. The time stamp of the received signal is NOT the same as the time stamp IN in the signal. The incoming speed is therefore not infinite.

    It would seem a bit specious to me that the act of moving the satellite earlier from Earth to its now distant location say beyond Pluto causes it to be “higher” in the gravitational well of the sun (which it is), and so this has its time to get internally readjusted so that when its time stamp is received here, we do truly see an apparent delay.

    What am I missing?

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    1. To assume that the distant clock is still synchronised with the Earth clock after moving it out into space is the same as assuming the speed of light is isotropic. That means you assume the speed of light to be the same in all directions and equal to c to prove it is equal to c. Totally circular. What you describe is called ‘slow clock transport’. It assumes the SR time dilation term is zero if you move the clock slowly. But the term only is small if you assume the ESC and isotropic speed of light. Under ASC and anisotropic speed of light the time dilation term is non-zero and proportional to the distance of separation. This is explained in detail in Lisle’s new book. I’ll post a review of that book very soon.

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      1. Just read your review of Lisle’s book. In that post, near the end, you say:
        //What we call ‘now’ here on Earth is ‘now’ everywhere else in the universe.//
        This means that the LIGO chirp, when it was heard, was the actual instant/moment when two black holes spiraled into each other, howsoever far they may be?
        This means that when the supernova 1987a was seen on earth, in 1987, that was the actual instant/moment it, happened howsoever far that object was?

        If so, then how would you address the reality of the different time stamps we would see to the situation in my first para of my OP?
        Don’t space scientists actually have to wait to get the signal from a spacecraft which is say near Mars, refer the recent Insight mission, or the earlier Curiosity mission? Why does it not happen in real time?

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      2. The best answer to this is to read the full details in chapter 17 of Lisle’s new book.
        The answer to your first two questions is yes. The only way to observe these events is by receiving a signal from them. We observe them happening when we receive a signal them. In the case of the gravity wave it is not light but propagates the same as light. Under ESC it travels at c and is isotropic but under ASC it is anisotropic and travels toward us at infinite speed.

        Your next question on time stamps is similar to what I answered previously. One must assume a synchrony convention to analyse these measurements. In the case of satellites out near Mars or any other so-called ‘one-way’ measurement they usually assume isotropy of the speed of light and thus all the delay is due to the travel time r/c where r is the distance from source to Earth receiver. That means they assume the SR time dilation term on Earth clocks is zero which for low relative velocities with v << c it is true. But the time dilation term only is small if you assume the ESC and isotropic speed of light. Under ASC and anisotropic speed of light the time dilation term on Earth clocks is non-zero and proportional to the distance of separation and equal to r/c. In both cases one would expect a delay of r/c — under ESC is it travel time of the light and under ASC it is due to time dilation. Under ASC it is the time dilation term that accounts for the difference in time stamps. But it does happen in real time. Just the satellite's clock is calculated to run slower that Earth clocks, and they obviously are not synchronised.

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      3. BTW, thank you for informing of Jason Lisle’s book!! It is excellent and I’m already at Ch7. Looking forward to Ch 17-19! Very well written book, and easy to read, and clearly from a Biblical Creationist perspective.

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  5. Dehne McLaughlin Avatar
    Dehne McLaughlin

    Read Jason Lisle’s book just before your new post on one way speed of light arrived. Appreciate your article on this matter and the analogy with geology and evolution. Jason’s chapter on time travel almost entertaining..not bad for a physics book.

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  6. Dr. Hartnett,
    [I composed this comment yesterday, before you published your latest post. It is still relevant, although your post today and your response to Vincent confirms that the answer to my last question is that the Lorentz factor as I calculated it is only valid for an isotropic speed of light (ESC).]
    I am a mechanical engineer with some background in physics, robotics, and control systems. In my line of work with road survey systems, we use laser rangefinders, doppler lasers, and radar systems, among other technologies. The possibility that the speed of light could be anisotropic is not something I ever considered until being introduced to your writing some years ago.
    Your earlier model, which posited time dilation effects in an expanding early universe, seemed to be on the right track from my layman’s perspective and made more sense to me than adopting the anisotropic synchrony convention (ASC). I’m curious if you found problems with your earlier model and abandoned it for that reason, or if you simply found the ASC more convincing. Would you consider your earlier model still to be valid (under ESC)?
    In any case, I took some time over the holidays to read up on the history of the Einstein Synchrony Convention (ESC) and to review my physics textbooks from years past. I had recalled (incorrectly, as it turns out) that the Michelson–Morley experiment proved that the speed of light was isotropic; in reality, it proved that the two-way speed of light is isotropic. I also learned that assuming the one-way speed of light is the same as the two-way speed is simply done by convention and has not been proven by experiment. That said, I agree with your other readers who have commented that it will take more than stating “we are free to choose a synchrony convention” to gain wide acceptance of this proposed major shift to an accepted convention, especially because it is being advanced by creationists who have a motivation to solve the starlight time travel problem!
    One problem is that there isn’t a good reason to expect that light would travel instantaneously towards the observer and at half c away from the observer, c being the accepted speed of light. [You addressed this today to some extent.] If I look at the equations used for laser range-finding, velocity measurement from Doppler lasers, or radar signal processing, they continue to work as long as the average two-way speed of light is c. In other words, the ESC vs ASC debate doesn’t affect what we’re doing with these sensors. That said, up until now, there has been no reason to think that the speed of the electromagnetic signal from the emitting device to the object being measured is half c, while the reflection back to the emitter travels at infinite speed, as ASC would suggest. It seems that it should be possible to design an experiment to test this, but admittedly I cannot think of one and apparently far greater minds have not done so.
    Let’s take a practical engineering example that will illustrate the difference between ESC and ASC: communicating with a rover on the surface of Mars. We know that the signals must cover a distance of at least 55 million km when Mars is closest to the Earth. At the accepted speed of light c, this implies a one-way travel time of 3 minutes (55,000,000 km/300,000 km/s = 183 seconds) under ESC. Let’s think through some scenarios where mission control on Earth wants to ask the rover what time it is. We’ll ignore all signal processing delays and assume the distance between mission control and the rover is such that the two-way travel time of light is exactly 6 minutes.
    Let’s assume for the moment that it is possible to synchronize the clock on the rover with an Earth-based clock at mission control (I’ll return to this later because we know that this is not possible to do without assuming a synchrony convention first). So if the clocks were somehow – magically – synchronized, then if we send a signal from Earth to the rover at 12:00 UTC to query the rover’s current time, under ESC it will take 3 minutes for the query to get from Earth to the rover, arriving at 12:03 UTC according to the rover’s (and Earth’s) clock. The rover responds instantaneously with “12:03 UTC” (its current time). This response takes another 3 minutes to get back to mission control. At 12:06 UTC on the Earth clock, mission control will receive the signal from the rover saying that it is “12:03 UTC.” Under ESC, everything makes sense because we expected the signal to be delayed 3 minutes in reaching mission control.
    Now let’s continue pretending that clock synchronization is in place and see what would happen under ASC. At 12:00 UTC, mission control sends the query to the rover. The signal takes twice as long to get to the rover, so it’s not until 12:06 UTC that the rover receives the signal and responds with its current time, “12:06 UTC.” The return signal travels at infinite speed and arrives back at mission control at 12:06 UTC, saying that it is “12:06 UTC.” Again, this is what we would expect under ASC because we “know” that the return signal travels instantaneously. So now to determine whether ESC or ASC reflects the true physics, we “only” need to find a way to synchronize the clocks.
    To do that, let’s have mission control tell the rover what time it is and instruct it to reset its onboard clock to that time. At 12:00 UTC, mission control will tell the rover that it is exactly 12:00 UTC. So how do we program the rover’s software to handle this incoming signal? Do we have the rover set its clock to the exact time it receives at the moment it receives it (ASC), or do we try to compensate for the assumed one-way travel time and add 3 minutes to whatever time is sent by mission control (ESC)? Well, to synchronize the clocks it seems we need to “know” the one-way travel time, as you have been saying. If ASC is valid, then the signal travel speed will be infinite from the perspective of the rover (because it’s an incoming signal); therefore, let’s program the rover to set the rover’s clock exactly to the received time when it is received. From the Earth’s perspective, under ASC we assume that signals take 6 minutes to get to the rover, and that signals from the rover reach Earth instantaneously. Therefore, based on how we programmed the rover, to set the rover’s clock we need to tell the rover that it is “12:06 UTC” at 12:00 UTC to account for the expected delay for the outbound time set command to reach the rover. We know that when the rover receives “12:06 UTC” it will be 12:06 UTC on mission control’s clock also, and then the clocks will be synchronized. To test that the clocks are synchronized, at 13:00 UTC we will send a new signal to the rover asking what time it is. It will take the signal 6 minutes to reach the rover, at which time the rover will instantaneously respond with “13:06 UTC” which will match our time. ASC is validated! Except, it isn’t, because we built the assumption about ASC into the synchronization process by telling the rover it was “12:06 UTC” when we set its time.
    So can we outsmart ourselves and not make any assumptions about ESC or ASC when synchronizing the clocks? Let’s try. We program the rover to set its clock exactly to the instructed time when the signal is received, as we did above. This time, at 12:00 UTC we send the Earth time of “12:00 UTC” without any attempted compensation because we don’t want to assume anything. We know the rover will set its clock to 12:00 UTC when it receives the signal. Under ESC, that will happen at 12:03 UTC according to our clock, and under ASC it will happen at 12:06 UTC. At 13:00 UTC, we will ask the rover what time it is. Let’s think through what will happen. If ESC is “correct,” the rover will have set its clock to “12:00 UTC” when Earth’s clock was at 12:03 UTC – it will be three minutes behind. When we query the rover’s time at 13:00 UTC, it will take the signal 3 minutes to get to the rover, arriving at 13:03 UTC according to mission control. The rover will then respond with “13:00 UTC” as its current time, and this signal will take another 3 minutes to get back to mission control, arriving at 13:06 UTC. At first glance it would appear that the rover is 6 minutes behind, but we will understand that the rover is really 3 minutes behind the Earth-based clock because it would have sent the “13:00 UTC” signal at 13:03 UTC in Earth time. If on the other hand ASC is “correct,” the rover will have set its clock to “12:00 UTC” at 12:06 UTC as logged by mission control. When we query the current time at 13:00 UTC, the query will take 6 minutes to reach the rover, at which time the rover will reply “13:00 UTC,” that signal reaching us instantaneously at 13:06 UTC. This is the SAME RESULT we get under ESC! The conclusion is that we simply cannot tell from this type of experiment whether ASC or ESC is “correct.” They both look the same in this round trip experiment.
    There is a totally different approach we can take: we can synchronize the clocks before the mission begins, when the rover is still on Earth near mission control. We know from special relativity’s time dilation effect (confirmed by the Hafele–Keating experiment) that a moving clock will slow down. By the time the clock arrives on Mars, it will be behind the Earth-based clock. However, this is where I get lost because it doesn’t appear that the effect of time dilation will be significant. The ratio v/c is only 0.0000877 at typical rocket velocities (say 26.3 km/s), making the Lorentz factor for time dilation about 0.99999999615. This will introduce less than a tenth of a second of error in the rover’s onboard clock over a 254 day travel time from Earth to Mars. It suggests that a clock traveling on a rocket can be considered a slow-moving clock. I know there is an additional effect from gravitational time dilation, but I believe that would make the clock sync error even smaller because the effect will be in the opposite direction. The rocket is moving further away from the sun, and Mars’ gravity is less than Earth’s, so the clock will run FASTER, countering the slight slow-down due to relativistic time dilation. When the rover arrives on Mars, it seems its onboard clock will basically still be in sync with Earth’s clock. Now we are back to the above scenario where the clocks are “magically” synchronized. We can proceed to test ASC vs ESC simply by asking the rover what time it is. It will respond with a time that is either zero or 3 minutes different from Earth time, confirming that either ASC or ESC is “correct.” What am I missing? The only way this is wrong is if the time dilation due to special relativity and/or gravitation does not work the way I assume above when we are in ASC, and this somehow leads to a situation where the clock sync error is greater. [As noted above, your post from today addresses this issue, but a practical example demonstrating that the effect will truly take us back to an equivalent situation with ESC would help tremendously.]
    Best regards,
    Michael

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    1. It seems to me that you would do well to buy and read Lisle’s book “The Physics of Einstein”, the subject of my Review in the following post.

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      1. Thank you, Dr. Hartnett. Your answers to reader questions are helpful, and you’ve easy convinced me to order the book.
        I wondered further if you had any comment on my other question, perhaps lost in my long message: “Your earlier model, which posited time dilation effects in an expanding early universe, seemed to be on the right track from my layman’s perspective and made more sense to me than adopting the anisotropic synchrony convention (ASC). I’m curious if you found problems with your earlier model and abandoned it for that reason, or if you simply found the ASC more convincing. Would you consider your earlier model still to be valid (under ESC)?”

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      2. I have moved Lisle’s ASC well above my adaptation of Carmeli’s cosmology to YEC cosmogony. I no longer consider Carmeli’s approach very promising. The reasons for this are: Carmeli never found a full 5D cosmology for the whole universe. I laid out a sketch in my book of what I hoped we could find but instead as I worked on his theory I found several internal inconsistencies. (His Cosmological Special Relativity theory contradicts his Cosmological General Relativity theory. And I determined that his CSR theory is plain wrong.) Hence I eventually gave up on his theory. Secondly, I came to believe that the Scriptures do not describe an expanding universe and in fact the physical evidence can just as well be used to describe a static universe. That is, the evidence is equivocal. Humphreys was convinced by me that the Scriptures don’t describe expansion though Lisle still believes that, which he mentions in his book. If the universe is static, which I now believe it is, then Carmeli’s model is not applicable anyway.

        There is another problem for Carmeli-Hartnett time-dilation cosmology/cosmogony. It relates to the Curse. This is something I realised recently in a discussion with Russ Humphreys. Read “The effects of the Curse visible in the cosmos present another biblical creationist starlight travel-time problem”.

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  7. Jason Lisle,
    If you are reading this post and the comments, would you care to post your comments posted by artaxerxes99 and me?
    I realize there is a “propositional” and mathematical perspective where the ASC seems to be accurate. We all have had to go through these paradigm shifts, whether it be of motion itself, things concerning the ether, time and length dilation, etc, etc. That is agreed. We could therefore also take it to be true that ASC is the convention to use, and that that is the language of the Bible. All this is agreed.
    Yet, there is something deeply and disturbingly unsatisfying about saying all incoming light is infinite in speed and outgoing is 1/2c such that the inevitable and practical time computations that will need to be done turns out to c.
    For ASC to be true in reality, physically that is, not merely as a convention, it looks like there is a change is the property of space relative to the source of light and its destination in the eye/sensor. In other words, consider light coming from the sun to the earth or from some black holes colliding to LIGO. Here the light could be consider as incoming, therefore infinite. But then if we consider the satellite around Mars, or around Jupiter, or even further, could we not say that a signal sent from earth to the satellite, outgoing to us, is incoming to the satellite, and so infinite in speed? This make the definition for “incoming” relative to the destination detector/eye/sensor.
    Something is not jiving. Care to comment?

    Liked by 1 person

    1. Hello Vincent. I am happy to try to answer your questions.

      You say, “Yet, there is something deeply and disturbingly unsatisfying about saying all incoming light is infinite in speed and outgoing is 1/2c such that the inevitable and practical time computations that will need to be done turns out to c.”

      Two things to consider here. First, intuition just isn’t reliable in areas in which people have little experience. To people who have not studied relativity, it may indeed feel “unsatisfying” that the universe behaves in the way it does. But the universe still behaves that way. To my thinking, this is one of the ways that God humbles us, and reveals the superiority of His mind (Isaiah 55:8-9).

      Second, the alternative to ASC also has its counter-intuitive elements. For example, under ESC, an outgoing beam of light travels at “c” relative to a stationary observer. What will an observer in a rocket traveling at ½ c in the same direction of the beam see? Our intuition expects him to see the beam moving only ½ c faster than himself. But in fact, he will see it as traveling c faster than himself. Moreover, a rocket traveling in the opposite direction also see the beam moving at speed c, not 1.5c as our intuition might expect. Physics often challenges our expectations.

      You say, “For ASC to be true in reality, physically that is, not merely as a convention,…”

      Let me stop you there, because both ASC and ESC are conventions by which we assign coordinates to events in spacetime. According to Einstein, neither is more “physical” or “real” than the other. It’s a bit like asking whether centimeters or meters is the physical, “real,” or “correct” unit of length. You are free to use either, and you can convert from one to the other. You will get a different number, but it will have the same physical meaning.

      You say, “This make the definition for “incoming” relative to the destination detector/eye/sensor.”

      Yes! Both ASC and ESC are observer-based. Each observer is allowed to stipulate how the one-way light moves relative to himself, and synchronize clocks accordingly. So if we had a hypothetical settlement on Mars, they could use the ASC system and would consider incoming signals to be of infinite speed and outgoing signals at 1/2c. In communicating with Earth, both observers on Earth and Mars would agree on the total time it takes to send a signal from Earth to Mars and back. But they would disagree on which leg of the trip is the instantaneous one, and there is no experimental way to tell.

      And you asked me to comment on artaxerxes99’s questions as well. His discussion of using ASC or ESC to synchronize clocks between Earth and Mars by radio/light transmission is correct; there is no way to distinguish which system is “correct”, any more than we can do an experiment to measure whether meters or centimeters is correct. Then he goes on to consider what would happen if we synchronized the clocks while the rover is on Earth, and then moved it to Mars. This is the slow clock transport method. He assumes that time-dilation is negligible, and this is where the problem occurs.

      “What am I missing?” The answer is that artaxerxes99 has used the ESC version of the time-dilation equation. By assuming ESC, this invalidates the experiment. Only under ESC will the time-dilation between Earth and Mars be so small. The full time-dilation equation depends on the choice of epsilon (the one-way speed of light) as shown in John Winnie’s 1970 papers. The equation is also listed in (17.1) in my book: The Physics of Einstein. Under ESC epsilon = ½ and the second term drops to unity. But under ASC, epsilon = 1, and so you get a different answer.

      Artaxerxes99 says, “The only way this is wrong is if the time dilation due to special relativity and/or gravitation does not work the way I assume above when we are in ASC, and this somehow leads to a situation where the clock sync error is greater.”

      Yes! That is exactly right. The time-dilation under ASC will be different. Under ASC, the Mars rover’s clock will tick slower on the journey than it would under ESC, and according to equation 17.1 it will lose about 3 minutes. So under ESC or ASC you get the same answer for any physically measurable quantity. Under ESC, time dilation is negligible, the Mars rover clock is still essentially synchronized with Earth, but we see it as three minutes behind because it takes the light three minutes to get from Mars to Earth. Under ASC, the Mars rover clock ticks slower on the journey so that it is three minutes behind Earth’s clocks when it arrives on Mars. It’s light/radio travels instantly to Earth, and we see the clock as three minutes behind because it really is.

      I hope that helps. God bless.

      – Jason Lisle

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      1. Thank you, Jason, John, for your comments.

        I have been able to purchase the Kindle version of the book (located in India) and looks like Ch 17 is the important one. Will need to also grasp what epsilon is. Was not aware of the factor in my earlier years of the study of Relativity.

        The upshot if I understand correctly of what you both are saying is that, for any observer, in any part of the universe, the speed of incoming light is infinite! Is this correct?

        If so, then how did Maxwell compute the speed of light to be the finite product of the electric permittivity and magnetic permeability? There must be something inherently ESC in his equations (as he was before Einstein). Admittedly, the level of mathematics there is beyond me, so I hope either of you can please suggest how the permittivity and permeability of free space can be modified by an “ASC factor”. Perhaps this is already in the book Jason has written, or you can point to a link where someone has explained it?

        When the supernova 1987a exploded, we on earth saw it instantly. Ergo, a photon (many photons) from there traveled here at infinite speed. A different photon (many photons) from the diametrically opposite side of the exploding star went in the 180 degree, opposite direction, at an infinite speed to terminate on an hypothetical object, let’s say the same distance as the earth was from 1987a. And so we can consider 4*PI steradian surface being “lit” by individual photons, each having traveled through free space at infinite speed. If so, how is the permittivity and permeability being modified to make this true?

        Looking forward to now reading the book!!

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      2. Vincent,

        //The upshot if I understand correctly of what you both are saying is that, for any observer, in any part of the universe, the speed of incoming light is infinite! Is this correct?//

        Yes, that is the ASC version of SR. But if we make a biblical model there is only one location, the Earth.

        //If so, then how did Maxwell compute the speed of light to be the finite product of the electric permittivity and magnetic permeability? There must be something inherently ESC in his equations (as he was before Einstein).//

        Correct again. Generally Maxwell’s equations are solved by closed integrals. This means the two-way speed of light.

        //Admittedly, the level of mathematics there is beyond me, so I hope either of you can please suggest how the permittivity and permeability of free space can be modified by an “ASC factor”. Perhaps this is already in the book Jason has written, or you can point to a link where someone has explained it?//

        It is discussed in the book. There are generalised Maxwell’s equations but they are not shown.

        //When the supernova 1987a exploded, we on earth saw it instantly. Ergo, a photon (many photons) from there traveled here at infinite speed. A different photon (many photons) from the diametrically opposite side of the exploding star went in the 180 degree, opposite direction, at an infinite speed to terminate on an hypothetical object, let’s say the same distance as the earth was from 1987a. And so we can consider 4*PI steradian surface being “lit” by individual photons, each having traveled through free space at infinite speed. If so, how is the permittivity and permeability being modified to make this true?//

        Those constants of the vacuum are calculated assuming (implicitly) the two-way speed of light or more specifically the isotropy of the speed of light. I think reading the chapters 17-19 of Lisle’s book will cover most of your questions.

        Liked by 1 person

      3. Thank you for your response, Dr. Lisle. It is clear that you and Dr. Hartnett are doing important work, and maybe you have even come upon something transformational. I will read your book and then hope to have more to say on this topic.
        Perhaps it is possible to say that the one-way speed of light is “undefined.” The assertion, “I am seeing the distant stars as they are now,” becomes impossible to contradict. One’s conviction about whether one sees in the stars and galaxies the past or the present moves into the realm of metaphysics or faith.
        Michael

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      4. You are quite correct. The one-way speed of light is undefined. So, if we choose Earth as the point of reference we can stipulate it to have an infinite incoming speed with respect to the Earth observers. That creates the special conditions we need to say we observe the stars as they are now. We define a universal ‘now’ this way. I agree it is metaphysics but that is also important.

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  8. Reader says, “A different photon (many photons) from the diametrically opposite side of the exploding star went in the 180 degree, opposite direction, at an infinite speed to terminate on an hypothetical object”
    But he missed it. Light would move away from the object – opposite earth’s line of sight – only at 1/2 c. And this is precisely why Lisle’s ASC universe is not young. By the time light reaches earth with infinite speed *it has already traveled for billions of years in the opposite direction*. Light travel time in an ESC and ASC universe are *exactly the same duration*. Both views of our universe are old. The ASC universe is *not young*.

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    1. You are quite correct in that the reader you quote misunderstood the ASC. Nevertheless one can still say the universe is young. We define the special frame of reference at the Earth. This is consistent with Genesis creation. It is irrelevant what is happening to photons travelling outward away from the observer. Only those photons we can see are relevant and those reach Earth instantly after emission. So we do see the stars in real time and only about six thousand years have past done their creation. The universe is young not billions of years old.

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      1. Thanks for the reply; however, the difficulty is not resolved on your end. Your response is based on phenomenology and mine is based on the science of light travel time in the universe. Moreover, the universe is single and has a single age. Lisle’s paradigm must make the claim that the universe has an ancient ESC age and simultaneously a mere day’s-old ASC age. This is quite an impossible situation given the physics involved.

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      2. Randy

        Actually your response is based to an implicit assumption that the speed of light is isotropic and equal to c. You beg the question by using isotropy as your starting premise. You cannot just state that the ‘universe … has a single age’. You must define your frame of reference and your choice of coordinates. If there is one lesson relativity theory has taught us, it is that ‘all is relative’. Different inertial observers record different timings of the same events and would measure different ages due to relativistic time dilation effects.

        It is not an impossible situation. It is what it is. It does not depend on personal preferences. Besides Special Relativity is not intuitive, quite the opposite. Depending on which synchrony convention you choose you will determine a different age not only of the universe but also for any object in it. Based on ESC and the Earth’s motion around the sun one would determine the age of a celestial object, like a galaxy for example, to be wildly different when determined at two different times of Earth orbit, 6 months apart. This is because the earth would be moving towards the object for one measurement and away from it for the second. That changes the sign of the Doppler term and hence the age of the object quite significantly. But under the ASC there is no difference in age as it does not depend on motion but only on distance.

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      3. You wrote, “It is not an impossible situation. It is what it is. It does not depend on personal preferences. Besides Special Relativity is not intuitive, quite the opposite. Depending on which synchrony convention you choose you will determine a different age not only of the universe but also for any object in it.”

        Of course I staunchly disagree with the idea that a different choice of convention actually changes the age of the universe. But I can see you want to avoid the issue of light travel time, so let me answer your question directly with a simple gedanken experiment.

        To prove that time dilation has nothing whatever to do with the age of the universe, we will take a hypothetical ESC ride on an accelerating earth which moves toward every galaxy *simultaneously* at the speed of light. Time dilation says our passage of time is zero in our frame of reference. But how do the peculiarities we witness in our frame affect the *isotropic* propagation of light from galaxies towards earth and away from earth? None whatever. So the age of the universe has not changed just because we personally experience time dilation. We can naively claim a universe with zero age if we desire, but that won’t change its actual age.

        Now lets perform the same experiment in an ASC view. We are going to stipulate a light angle of theta = 0 at our location and claim an infinite speed of light from every galaxy directly towards earth. Time dilation says our passage of time is zero in our ASC location. But how do the peculiarities we witness in our location affect the *anisotropic* propagation of light from galaxies towards earth and away from earth? None whatever. So the age of the universe has not changed just because we personally experience time dilation. We can naively claim a universe with zero age if we desire, but that won’t change its actual age.

        You rightly stated, “It does not depend on personal preferences,” because a personal preference in either view might very well claim a young universe. But an actual scientific claim – completely outside of personal preferences – would return a very old universe based on light propagation from distant galaxies, whether *anisotropic* or *isotropic* – it just simply does not matter.

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      4. Randy,

        My responses in line below.

        //To prove that time dilation has nothing whatever to do with the age of the universe, we will take a hypothetical ESC ride on an accelerating earth which moves toward every galaxy *simultaneously* at the speed of light.//

        I don’t see how that is possible. An accelerating frame is not an inertial frame and you would introduce gravity through the equivalence principle. Also to move ‘toward every galaxy *simultaneously* at the speed of light’ is impossible regardless of whether you could reach near speed of light c. Light from galaxies in front would be blueshifted well past gamma wavelengths and light from galaxies behind would be redshifted way down past ULF radio wavelengths.

        // Time dilation says our passage of time is zero in our frame of reference.//

        Now you assume an inertial Earth observer moving at c. Of course that is impossible but even if it was time dilation of Earth clocks still occurs just differently when compared to source galaxies in the direction of motion or the opposite direction. There is a sign change in the SR time dilation term. This is standard SR Doppler effect.

        //But how do the peculiarities we witness in our frame affect the *isotropic* propagation of light from galaxies towards earth and away from earth? None whatever. //

        You assumed the isotropic speed of light. You said so by assuming ESC. As such you have the cart be for the horse.

        //So the age of the universe has not changed just because we personally experience time dilation. //

        Not so. If you calculate the age of blueshifted galaxies or redshift galaxies using ESC SR time dilation term you get different answers.

        //We can naively claim a universe with zero age if we desire, but that won’t change its actual age.//

        You really need to read the book “The Physics of Einstein” because you completely missunderstand Special Relativity.

        //Now lets perform the same experiment in an ASC view. We are going to stipulate a light angle of theta = 0 at our location and claim an infinite speed of light from every galaxy directly towards earth. //

        That is not possible because we observe galaxies all around us.

        //Time dilation says our passage of time is zero in our ASC location. //

        That is also wrong. Under ASC an extra term of order r/c, where r is the distance to the source (a galaxy), is included in the time dilation equation.

        //But how do the peculiarities we witness in our location affect the *anisotropic* propagation of light from galaxies towards earth and away from earth? None whatever.//

        Again you have it backwards.

        // So the age of the universe has not changed just because we personally experience time dilation.//

        Age is what we measure; it to be based on the travel time of light. Under ASC there is no travel time and so the age of the galaxies is only about 6000 years. It has been about 6000 years since the first light from them arrived at the Earth. Under ESC the travel time is millions and billions of years.

        // We can naively claim a universe with zero age if we desire, but that won’t change its actual age.//

        You naively believe that age is a property of the universe that we just need to discover. But it is not. It requires the correct starting assumptions (from the Genesis account) and the biblically consistent synchrony convention to interpret the data. From that we can determine age. Since there is no travel time of light the age agrees with the Biblical account or about 6000 years. The universe is young.

        //You rightly stated, “It does not depend on personal preferences,” because a personal preference in either view might very well claim a young universe.//

        I probably was not clear on what I meant there. By personal preference I meant that one has some right to decide which synchrony convention is the absolute truth of the universe. There is no such thing. Only by understanding from Scripture that the Bible uses the ASC can one decide which it is that we should use. In principle, from SR we can choose any convention we like, but the Bible tells us we should use the ASC.

        // But an actual scientific claim – completely outside of personal preferences – would return a very old universe based on light propagation from distant galaxies, whether *anisotropic* or *isotropic* – it just simply does not matter.//

        You are totally wrong. You have no understanding of relativity theory, even in it most common form, where Einstein chose/stipulated the speed of light to be isotropic. Until you thoroughly read Jason’s new book I will not be responding to any further comments from you, because it would seem that you a) do not know what you are talking about and b) you have made no attempt to understand the physics involved.

        Liked by 1 person

    2. Actually, I DID mean to say that at each point on a 4*PI steradian virtual sphere of radius = distance from earth to SN 1987a, if there were an observer at each of those points like there was one on the earth, the photons would necessarily be incoming to EACH observer on that 4*PI ster sphere at infinite speed.
      I was NOT intending to say that we on earth observed the various photons hitting each point on that sphere. Or the point on the opposite side from us of SN 1987a. I WAS intending to say or at least imply, that at every point in the universe, ALL incoming photons/signals must necessarily be infinite with ASC. This is not an issue of, if there is no one in the forest, did a falling tree make a sound. It did, there was simply no one or sensor to hear it. It has to do with something physically happening.
      I further disagree that the ASC universe is not young. The universe , let alone the earth, IS young. This is clearly seen from the Holy Bible. Of course, people will disagree, but that is simply because of an interpretation issue.

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      1. Vincent,

        I understand your point now. But I would say one must pick a frame of reference, in our case it is the Earth, and stick to that frame of reference for any analysis. But for each of your hypothetical observers around SN 1987a each could assume the incoming speed to be infinite within his own frame of reference. Each would be free to choose the ASC for their frame of reference. Thus they would agree on the age of the SN provided they are all equi-distant as you imagined. But that still says nothing about the isotropic speed of light.

        I agree with you. The universe is young and the ASC model gives us a clear basis for that.

        Liked by 1 person

      2. I have been gradually seeing my paradigm shifting to ASC having read your work and Jason’s from quite a long time back, of course, along with the work of others. Thank you all.

        Of course, while you, Jason, and other biblical creationist scientists must be rigorous in your equations, as best as can be, and I don’t have that capacity, not at your levels, I do understand these things up until the point you all stay away from tensors :-).

        This said, and seeing that ASC is starting to make far more sense as I understand it more, my primary point or focus of understanding is what if I were “on” a photon travelling from a source to a destination. Granted, this is going to get complicated because we soon have to deal with spatial separations and time, and I understand that ASC is the way WE on earth can understand what is going on. We are NOT on the photon.

        Without being facetious at all, neither wanting to cop out, we know, by definition, that God is omnipresent, and that means he is infinitely AT every Planck point (a sphere with radius of the Plack length, the smallest we can sensibly speak of) in the universe, and so necessarily is the reference for defining synchonization in the universe. Granted, WE dont know things due to our infinitesimalness. Because God is truth, when he says anything, it IS true. And so, as you point out, we know that light reached the earth, even from the stars, the same 4th day.

        This means that on the 4th day when he created the Sun and Moon and all the stars, gazillions upon gazillions of photons (of light, gamma ray, etc, etc) moved outwards from zillions upon zillions of stellar objects. These photons are actual quanta of energy that are travelling in a direction such that they are incoming to EVERY Planck point along its propagation path starting at its source to as far as the edge of the universe.

        This therefore MUST mean that a photon (quanta of energy) propagates at infinite speed relative to every Planck point along its direction of propagation. As you’ve indicated, the incoming speed is infinite, so may we say that at EVERY point in the universe, all incoming photons to THAT point are travelling at infinite speed? Would you agree with this?

        This is like saying, a photon which moved from the surface of the Sun to a sensor on SOHO reached SOHO as instantaneously soon as it “left” the surface of the Sun. Another somewhat “closeby” and adjacently positioned photon which also “left” the Sun’s “surface” at the same instant as the first photon, reached Earth and your eye at the same instantaneous moment it and the previous photon left the Sun. Do you think this is what is happening in reality, in principle?
        (We wont get into details that we dont directly look into the Sun etc, etc, or the photon which entered my eye was not the same photon that physically exited the Sun, but was the last one in a chain of absorption and emission.)

        We will now need to understand all stellar observations (red shifting, etc, etc) with the ASC paradigm of infinite incoming speed, because that IS what is happening on Earth. Thoughts?

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      3. We cannot say “what is happening in reality”. That is trying to define an absolute one-way speed of light. We cannot know what it ‘actually’ is, nor is it important, since we are free to choose it. This statement will remain true until someone makes a genuine one-way speed of light measurement. But that in my opinion is highly unlikely, but I suppose we should not rule it out because we may not have thought of everything. Nevertheless our current understanding of Special Relativity rules it out.

        I think you should remember that ASC or ESC or whatever synchrony convention is chosen it is a choice of coordinate system like choosing a unit of measurement. It does not matter which you choose the physics remains unchanged. But when you choose one convention you must also choose a frame of reference, and stick to it. You seem to be wanting to describe a sort of universal frame — the way you describe what is happening at every Planck length step throughout the universe. So one chooses the convention that simplifies the physics best. If ESC helps you understand redshift use that. Converting to ASC will not change the physics. But when you change to a different convention you have to also use the appropriate equations for that convention. Lisle’s has the fully generalised SR equations in his book, and those for ASC. They are not the same as those for standard ESC Special Relativity.

        So what is relevant for us, is what we observe at the Earth. That is the important frame of reference and the only one we can make measurements from. Under ASC the incoming speed of photons is infinite. They arrive from cosmic sources without any time lag but that does not mean that there is not time dilation of our clocks relative to the cosmic source clocks. There is, just no travel time. So is the case of your SOHO and sun illustration. Observers at different distances may receive the photons instantly but they experience different amounts of time dilation under ASC. Under ESC they also would determine a time difference but they would put it down to differences in light travel time and not time dilation. The measurements give the same value of time difference depending on their relative distances from the Sun but the interpretation of what the cause is depends on the choice of timing convention. And as I said we cannot say what is ‘really’ happening, which is the true interpretation. We just can’t know.

        I considered galaxy redshifts under a static universe model and discussed ESC and ASC within that model. See Speculation on Redshift in a Created Universe.

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  9. Hi John, but is there a reason, other than the language of appearanbce in Scripture, to believe that the one way speed of light could be different than the measured two-way? Surely we are not able to measure the one-way speed but that surely does not mean that we can choose it willy-nilly; if one guy chooses (1/2)x c and the other choose infinity surely both cannot be right.
    Is this approach not effectively a cop-out?

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    1. You can choose any value of the one-way speed you like between 1/2c and infinity. But that means the average speed round-trio speed must be c. The ASC chooses infinite speed towards observer, therefore 1/2c away from observer, and c at 90 degrees to direction of source. Because it cannot be measured the one-way speed does not really tell us anything meaningful about physics. Regardless of which value you choose, within the rules, the physics will be unchanged. It is not a cop-out. Einstein chose isotropy — c in all directions but stated himself that it was a mere stipulation. Why isotropic? There is no physical reason to choose that except some innate belief in symmetry but there is no reason why this should be true, nor any reason why it should not be true. That is just the way it is.

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  10. Fascinating concept indeed – best explanation I’ve seen! Thanks

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  11. Hello Dr. Hartnett,

    First, I’m thankful you seem to be feeling better.

    Second, I’ve tried to at least read through all the posts here before posting a question, although I have not YET read Dr. Lisle’s book.

    Just two questions:

    Question 1:

    You said in your second to last comment,

    “And as I said we cannot say what is ‘really’ happening, which is the true interpretation. We just can’t know.”

    Artexerxes99 said, “The assertion, ‘I am seeing the distant stars as they are now,’ becomes impossible to contradict. One’s conviction about whether one sees in the stars and galaxies the past or the present moves into the realm of metaphysics or faith,” to which you agreed.

    You said, “I probably was not clear on what I meant there. By personal preference I meant that one has some right to decide which synchrony convention is the absolute truth of the universe. There is no such thing. Only by understanding from Scripture that the Bible uses the ASC can one decide which it is that we should use. In principle, from SR we can choose any convention we like, but the Bible tells us we should use the ASC.”

    Under ESC, there is a time-travel problem.
    Under ASC, there is not. So for those who believe the Bible, it would seem ESC is TRULY wrong. It’s not that we “should” use ASC because God “prefers” it. Rather, we MUST use it to be consistent with Scripture (which admittedly is a statement of God’s preference).

    We cannot “prove” which is correct without resorting to faith. Among those who believe the Creator’s account, faith is precisely what we are using. We then can, at least to ourselves, discern which is correct.

    Is this true?

    Question 2:

    Is it possible to see the edge of the visible universe expanding? If so, would that contradict ASC?

    Thank you, and please feel free to respond with, READ THE BOOK! I plan to anyways.

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    1. Q1: I agree. Based on the biblical account, not physics, we can say yes.
      Q2: Is it possible to see the edge of the visible expanding universe? I don’t know. I personally don’t anymore believe the universe is expanding. However if we are talking about seeing the edge of all visible galaxies, if it was possible, I can’t see how that could contradict the ASC or the ASC model. You can’t contradict a convention, but you might observe some structure that contradicts the ASC model’s age of the universe, like some structure that is more than 7000 years old. Even so even that would be difficult to prove.

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  12. Hmmmm, if the ASC is true, would there be some way to detect that, by using distance? If two events occurred at the same time, but different distances away from us, then their light should reach us at the same time, if the speed of light is infinite. So we set an experiment, with, say, a long straight cable, perpendicular to our line of sight. One end of the cable is much closer to us than the other end. Place a computer at the middle of the cable, and at t=0, send a signal to each end of the cable to turn on a light. If the lights appear simultaneously to us, then ASC is true, otherwise it is not. Dr Hartnett, is there any reason this experiment wouldn’t work?

    Of course, the cable doesn’t even need to be perpendicular to us. In fact, if it slants away from us at quite a steep angle, that might make it even easier to measure accurately. Of course if the speed of light depends on the gravitational field, then this won’t work at all. Cheers, Garry.

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    1. Garry,

      To start with is you say ‘two events occurred at the same time’ you impose the condition that the clocks at each end are synchronised. That requires the assumption of the isotropy of the speed of light. This issue is all about synchronisation of clocks separated by a distance. So to synchronise distant clocks you need to send a light signal to the most distant end from the end where you are. Thus your experiment becomes a measurement of the round-trip speed of light. So there is a very good reason why this will not work.

      Gravitational fields are not relevant. The effects we are discussing are totally due to special relativity.

      I suggest you read the following:
      1. Einstein’s physics says there is no biblical creationist starlight travel-time problem
      2. New cosmologies converge on the ASC model
      3. Update on the ASC model and the one-way speed of light
      4. Jason Lisle defends his ASC model

      And if you can buy and read Jason Lisle’s book “The Physics of Einstein”

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