
Welcome to the International Skeptics Forum, where we discuss skepticism, critical thinking, the paranormal and science in a friendly but lively way. You are currently viewing the forum as a guest, which means you are missing out on discussing matters that are of interest to you. Please consider registering so you can gain full use of the forum features and interact with other Members. Registration is simple, fast and free! Click here to register today. 
10th November 2022, 03:33 AM  #161 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001


__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

10th November 2022, 03:43 AM  #162 
Illuminator
Join Date: Oct 2009
Posts: 4,731

No, it doesn't.
In your calculation, a photon with 10 eV at B loses 4 eV to drop to 6 eV by the time it gets to C, while a second photon with 9 eV at B loses 3 eV to drop to the same 6 eV by the time it gets to C. If both events you refer to as B are the same, and both events you refer to as C are the same (which is something we could reasonably assume in a scientific presentation, but all bets are off when the presenter has a long and also recent history of using exactly the same letter to mean completely different things in consecutive sentences), then your calculation is inconsistent with an expanding universe. That means any conclusions you may attempt to draw from your calculation have nothing to do with an expanding universe. 
10th November 2022, 08:59 AM  #163 
Penultimate Amazing
Join Date: Jun 2005
Location: Way way north of Diddy Wah Diddy
Posts: 33,760

I am probably being needlessly obtuse here, but it's hard to get behind a theory when it seems ordinary arithmetic doesn't work.
So maybe I'm misunderstanding the issue of percentages here, so correct me if I am. We have a photon with a certain amount of energy. The exact amount seems irrelevant, as long as someone can measure it. It travels a certain distance. The exact distance seems irrelevant, as long as someone can measure it. We determine that a photon with energy n, when it travels a distance x, loses 50 percent of that energy. The exact cause of that loss seems irrelevant, as long as someone understands what it is. The choice of a distance that corresponds to a 50 percent loss is essentially arbitrary, based, one assumes, on long study of the rate of loss. At the point we just measured, the photon now has an energy of n/2. In the next distance of x, one would, I think, expect that the energy of that photon would be halved again, becoming n/4. Yet in your statement, this is not the case. The photon loses ALL its energy, and is effectively extinguished. Now maybe this is true, and maybe the rate of loss is not constant, but varies in some way, but the statement above,
Quote:

__________________
I love this world, but not for its answers. (Mary Oliver) "There is another world, but it's in this one." (Paul Eluard) 

10th November 2022, 09:23 AM  #164 
Master Poster
Join Date: Nov 2020
Posts: 2,998


10th November 2022, 09:24 AM  #165 
Master Poster
Join Date: Nov 2020
Posts: 2,998


10th November 2022, 09:29 AM  #166 
Master Poster
Join Date: Nov 2020
Posts: 2,998


10th November 2022, 10:32 AM  #167 
Master Poster
Join Date: Nov 2020
Posts: 2,998


10th November 2022, 12:09 PM  #168 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001

Equations are descriptive. They work under certain circumstances, but it's easy to use them wrong, and you're using them wrong. Photons don't know how much energy they are emitted with. Hell, there isn't even a single value for that, it's reference frame dependent. The fact that E_{emit} appears in some equation does not mean that the photon itself keeps track of that. That's not how any of this works.

__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

10th November 2022, 01:25 PM  #169 
Illuminator
Join Date: Oct 2009
Posts: 4,731

Some people identify mathematics with arithmetic or calculation, but that's only a tiny part of what mathematics is about. Mathematics is about finding out what follows from what postulates, and about formulating postulates that are of some interest (usually because they correspond at some level to some situation that arises in the real world) and tracking down their often surprising consequences.
Mathematics is also about learning to think abstractly. By thinking abstractly, we can simplify our thought processes, leaving us less vulnerable to the mistakes we might make by pursuing a more concrete and more complicated process. We have an example of that here. A calculation that relies on mainstream physics instead of Helland physics. Your calculations are wrong. Your calculations are wrong because they are based on Helland physics. Your calculation assumes photons behave as you think they behave, which is not how photons behave according to mainstream physics. You started out by assuming photons behave in a way that is inconsistent with mainstream physics. It should come as no surprise that such calculations yield results that are inconsistent with mainstream physics. The only conclusion that can be drawn from the inconsistency of your calculation with mainstream physics is that Helland physics is inconsistent with mainstream physics. You knew that at the outset, when you started by assuming mainstream physics is wrong about the behavior of photons. Your calculations based on Helland physics are mere obfuscation. You begged the question (in the original meaning of that phrase) by assuming mainstream physics is wrong, and then you relied on that assumption while embarking upon calculations designed to show that mainstream physics is wrong. We don't need numbers to understand what's wrong with your calculation. In mainstream physics, a photon that starts out at event B with energy X does not arrive at event C with the same energy as another photon that starts out at event B and follows the same world line to C. Mathematically, the function that describes red shifts along any particular world line between events B and C is not manytoone: You can't have two different starting energies end up at C with the same energy. That last paragraph shows how much easier it is to think mathematically than to limit yourself to grade school arithmetic. 
10th November 2022, 05:56 PM  #170 
Master Poster
Join Date: Nov 2020
Posts: 2,998


10th November 2022, 06:00 PM  #171 
Master Poster
Join Date: Nov 2020
Posts: 2,998

False.
My calculations are standard mainstream stuff. If you think I'm wrong, prove it. Here's the chart. You put what you think is right. Code:
? A B C ?? First photon A (d=0, z=0, E=12 eV) B (d=?Gly, z=?, E=? eV) C (d=? Gly, z=1, E=? eV) Second photon B (d=0, z=0, E=9 eV) C (d=? Gly, z=?, E=? eV) 
10th November 2022, 10:12 PM  #172 
Illuminator
Join Date: Oct 2009
Posts: 4,731

In mainstream relativity and electromagnetism, the following is true:
For any events B and C connected by a specific null geodesic W, and for any photon that departs from B and travels via W to C (without interacting with other particles etc), the relationship between the energy of that photon at B and its energy at C is described by a onetoone mathematical function.Your calculation assumes photons violate that fact about mainstream relativity and electromagnetism. Your calculation is therefore based upon your againstthemainstream brand of physics, which we might as well refer to as Helland physics. QED The specific numbers will depend upon the spacetime geometry and the specific world line W that represents a null geodesic from B to C. Your obsession with numbers at the expense of insight obscures the simple fact that two photons going from B to C via W cannot start out with different energies at B yet end up with the same energy at C. By the way, that simple fact is easily proved using the time reversal of B, C, and W. Two photons that start out with the same energy and follow the same world line can't end up with different energies at the end of that world line unless they interact with some outside influence. 
11th November 2022, 03:57 AM  #173 
Master Poster
Join Date: Nov 2020
Posts: 2,998


11th November 2022, 06:11 AM  #174 
Illuminator
Join Date: Oct 2009
Posts: 4,731

ben m is no longer around to defend himself, but jonesdave116 is still here.
As I noted previously, jonesdave116 got confused by your habit of using exactly the same letter (e.g. "d") to represent completely different things, even in consecutive sentences. From what you wrote in the quotation above, and from things you have been writing throughout this thread, I suspect you have confused yourself as well. Allow me, however, to note that you believe you are discussing these things in the context of red shift resulting from spatial expansion, which implies general relativity. That is why I have been careful to speak of events B and C rather than positions B and C, and why I have been careful to speak of some particular world line W (because there may be multiple null geodesics connecting events B and C). Even if you adopt the idealized simplifying assumption of an FLRW spacetime, the red shift is not uniform along W because the Hubble parameter H is not constant (because the scale factor a(t) is not a constant). To perform a proper calculation requires you to compute the value of a definite integral involving a(t). Even if you use approximations, how the red shift varies along W depends upon whether you are assuming a matterdominated or energydominated FLRW spacetime. 
11th November 2022, 06:40 AM  #175 
Master Poster
Join Date: Nov 2020
Posts: 2,998

Yep.
You can use this interactive version of LCDM to see the difference between matter and dark energy by adjusting the parameters. https://mikehelland.github.io/hubble...other/lcdm.htm If redshifts are caused by an expanding universe, then gravity plays a role in that by reigning it in a bit. Since that is observationally incorrect, dark energy is employed to push it back. Of course, if light just redshifts, none of that is right. That's not to say general relativity has a flaw. Just the FLRW metric does not match reality. Does it have any purpose outside cosmology, BTW? 
11th November 2022, 07:13 AM  #176 
Illuminator
Join Date: Oct 2009
Posts: 4,731

In FLRW models of an expanding universe, gravity acts over time to reduce the second derivative of the scale factor a(t). In some FLRW models, where the matterenergy density of the universe exceeds a certain critical value, gravity will eventually make the first derivative of a(t) go negative, ultimately resulting in a Big Crunch.
The first derivative of a(t) is not negative at the present time, and observational evidence suggests the FLRW parameters that most closely fit the universe as we know it predict the first derivative of a(t) will never go negative. That of course remains to be seen, but I don't expect to be around as the universe dies from heat death (or collapses into a Big Crunch, if that's what you think will happen). You don't know what you're talking about. What I wrote above is true even of FLRW models for which the cosmological constant (dark energy) is zero. If we consider arbitrary spacetime manifolds instead of limiting ourselves to idealized solutions such as FLRW, then the variation in red shift of a photon traveling from some event B to some event C along some null geodesic W can be just about anything you like. There are, however, a few fundamental constraints:
ETA: In that sentence, Mike Helland is telling us that, if we start with Helland physics instead of mainstream physics, then we reach conclusions that are inconsistent with mainstream physics. The reason for that is obvious: Helland physics is inconsistent with mainstream physics. 
11th November 2022, 07:45 AM  #177 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001

You missed the point, which is that equations don't make reality. E_{emit} being in an equation doesn't mean that the photon actually carries that information. It doesn't. And you were using the equations wrong anyways.
Now, I don't know if any of your numbers are right, and I frankly don't care. But your claim of a contradiction was plainly wrong. So let's go through some numbers again. I'm not going to use d or z values here, we don't need them to see where you screwed up. I will use your energy values, though Photon 1 starts at event A (I'm calling it an event because that identifies it as a specific point in both space and time), with an energy of 12 eV. It then travels to event B, where it has an energy of 10 eV. Then it travels to event C, where it has 6 eV. Moving from A to B decreases energy by 16.7 %. Moving from B to C decreases energy by 33.3% of the energy it had at A, but that doesn't matter. What's happening between B and C has no access to any information about what happened at A. Between B and C, energy decreases by 40% of the energy it had at A. Photon 2 starts out at event B and travels to event C. It starts with 9 eV, and experiences the same red shift as photon 1. How much does its energy decrease? You wanted to use 33.3%, but this is wrong. Again, 33.3% was what you calculated as the percentage of the energy at A, but photon 2 didn't start at A, it started at B. You can't use 33.3% here and apply it to photon 2, that makes no sense. You have to use the equivalent, which is 40%, not 33.3%. So it will decrease its energy by 40%, not 33.3%, same as photon 1 when measured from event B, which is the proper way to do it. So its energy will decrease from 9 eV to 5.4 eV. As expected, photon 2 has 10% less energy than photon 1 both at event B and at event C. If you don't **** up the math (which you did), there won't be any contradiction. Note that NONE of this required making ANY assumptions about expansion rates, distances, times, or anything of the sort. 
__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 08:16 AM  #178 
Master Poster
Join Date: Nov 2020
Posts: 2,998


11th November 2022, 08:20 AM  #179 
Master Poster
Join Date: Nov 2020
Posts: 2,998


11th November 2022, 08:39 AM  #180 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001

I just did the math. You ****** up. You can't use the same percentage applied to two different things (energy at A and energy at B) and expect them to match up. Of course that's going to cause inconsistencies.
ETA: OK, let's do this the other way around. Photon 2 goes from 9 eV at B to 6 eV at C, a decrease of 33.3%. Fine. Photon 1 goes from 12 eV at A to 10 eV at B. Then it goes from B to C. It should decrease by 33.3% from B to C, just like photon 2. But not 33.3% of 12 eV, 33.3% of 10 eV. So it will end at C with an energy of 6.7 eV. At both B and C, photon 2 has 10% less energy than photon 1. No contradiction, if you don't **** it up. You ****** it up. 
__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 09:24 AM  #181 
Illuminator
Join Date: Oct 2009
Posts: 4,731

I've done the math:Those posts show the hard part of the math. The derivation of equations from the Friedman equations yields the definite integral I mentioned several posts above, ultimately yielding this equation for the redshift of a photon going from event B at time t_{B} to event C at time t_{C} in the FLRW coordinates:
1 + z = a(t_{C}) / a(t_{B}) = λ(t_{C}) / λ(t_{B})as derived in that same Wikipedia article. Astute observers will observe that the red shift given by that equation does not depend upon the frequency a photon might have had at any event prior to B. The red shift depends only upon the photon's frequency at B (λ(t_{B})) and at C (λ(t_{C})), whose ratio depends in turn only upon the value of the scale factor at B (a(t_{B})) and at C (a(t_{C})). The scale factors a(t_{B}) and a(t_{C}) are determined by the spacetime geometry, and are completely independent of which photons we might be discussing. From that it follows that the red shift given by that equation is the same for all photons traveling from event B to event C along a null geodesic. Which means two photons that have different energies at B cannot have the same energy at C. Which means Mike Helland's calculation is incorrect, no matter much he may stamp his feet and insist he's right. Mike Helland's calculation is incorrect because it is based upon Helland physics, as opposed to mainstream physics. Mike Helland hasn't done the math, and doesn't know enough physics and math to understand the mathematics laid out in the links I provided above. That's why Mike Helland insists upon using numbers instead of equations and general principles of mathematics and physics. He does know how to use a calculator. He just doesn't know enough math to tell whether he's feeding correct numbers into that calculator. 
11th November 2022, 11:25 AM  #182 
Master Poster
Join Date: Nov 2020
Posts: 2,998


11th November 2022, 11:29 AM  #183 
Master Poster
Join Date: Nov 2020
Posts: 2,998


11th November 2022, 12:03 PM  #184 
Master Poster
Join Date: Nov 2020
Posts: 2,998

Here's the problem.
You receive 2 photons, both 6 eV. One of them from a z=0.5 source. The other from z=1. What energy were they emitted with? What distance did they travel? And.... what energy did they have when they met up? Code:
? A B C ?? First photon A (d=0, z=0, E=? eV) B (d=? Gly, z=?, E=? eV) C (d=? Gly, z=1, E=6 eV) Second photon B (d=0, z=0, E=? eV) C (d=? Gly, z=0.5, E=6 eV) 
11th November 2022, 12:36 PM  #185 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001

Who said it had a z of 1? I didn't. I never said anything about z before, but see below.
I said it had a 12 eV starting energy and 10 eV at the meetup point, because that's numbers you used when trying to show a conflict. I'm not going to bother calculating distances, they aren't necessary to disprove your claimed inconsistency. And they are model dependent, but consistency shouldn't be. If photon 2 has a z of 0.5 and an energy of 6 eV at C, then it had an energy of 9 eV at B. If photon 1 has an energy of 6 eV at C, then it also had an energy of 9 eV at B. If its z is 1, then at A, it had an energy of 12 eV. This means that at B, it had a z of 0.33. Now here's where you're likely to run into confusion. You seem to be under the wrong impression about how z changes. If z for photon 2 increased by 0.5 when traveling from B to C, then any photon traveling from B to C should have z increase by 0.5, so that would make photon 1 go from z = 0.33 to z = 0.83. But that's not how it works, at all. The change in z doesn't have to be the same for each of them. It won't be, because z's don't add. z will change from 0.33 to 1.0 over that same distance. 
__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 12:45 PM  #186 
Master Poster
Join Date: Nov 2020
Posts: 2,998


11th November 2022, 12:55 PM  #187 
Master Poster
Join Date: Nov 2020
Posts: 2,998

jonesdave. It was the basic stipulation of the problem.
Quote:
Lookback time * c at z=0.5 is 4.66 Gly. So the first and second photon traveled 4.66 Gly together. That leaves 7  4.66 = 2.33 Gly the first photon traveled alone. And it was z=0.33 when it met the second photon? Lookback time * c at z=0.33 is 3.5 Gly. 4.66 + 3.5 > 7 Doesn't add up. 
11th November 2022, 01:49 PM  #188 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001

Because you're still doing it wrong. The quantity z is model independent, meaning its definition doesn't depend on how fast the universe is expanding. But the relationship between z and distance is NOT model independent. It depends on how fast the universe expands, and that's not constant in time. The relationship between z and distance that you're using is valid for z's calculated today. But the z you're using, 0.33, isn't a z that's valid today. It's a z from 4.66 billion years ago. You would need to use a different relationship between z and distance if you want to calculate how far photon 1 traveled between A and B based on z.
You keep using equations that you don't actually understand, and so don't realize when you're using them wrong. 
__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 01:55 PM  #189 
Master Poster
Join Date: Nov 2020
Posts: 2,998

I understand pretty well.
If a photon travels for a billion years at the speed of light, it traveled 1 billion light years. The source of the photon was less than that at the time of the emission. And it was greater than that when the photon was received. That doesn't change anything though. A photon that travels for 2.33 billion years will have a z=0.2. Not z=0.333. Try filling out the chart. 
11th November 2022, 02:15 PM  #190 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001


__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 02:26 PM  #191 
Master Poster
Join Date: Nov 2020
Posts: 2,998

So what you're saying is, this is right to you?
Code:
? A B C ?? First photon A (d=0, z=0, E=12 eV) B (d=3.5 Gly, z=0.33, E=9 eV) C (d=7 Gly, z=1, E=6 eV) Second photon B (d=0, z=0, E=9 eV) C (d=4.66 Gly, z=0.5, E=6 eV) 
11th November 2022, 02:33 PM  #192 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001

No, it's not right. There's still a contradiction in there. You think that means that there's something wrong with the theory. In point of fact, it means you ****** up.
Again, distance vs. z relationship TODAY is different than it was in the past. I haven't bothered doing the distance/time calculations, but assuming that you did them right for photon 2 (since the calculations were done for today, that's more likely to be correct), then this is what they should be: Code:
?
A B C
??
First photon
A (d=0, z=0, E=12 eV)
B (d=2.33 Gly, z=0.33, E=9 eV)
C (d=7 Gly, z=1, E=6 eV)
Second photon
B (d=0, z=0, E=9 eV)
C (d=4.66 Gly, z=0.5, E=6 eV)

__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 02:37 PM  #193 
Master Poster
Join Date: Nov 2020
Posts: 2,998


11th November 2022, 02:53 PM  #194 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001

NO! That is EXACTLY what I'm telling you is WRONG.
God damn it, Mike, how many times do I have to tell you? You CANNOT use an equation which is only valid TODAY for something long in the past. 4.66 billion years ago, the relationship between z and distance/age was DIFFERENT than it is today. 
__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 02:58 PM  #195 
Master Poster
Join Date: Nov 2020
Posts: 2,998

Ok.
But you're confident an observer at point B would received a photon from point A at z=0.333? Let's say 7 billion years ago 2 photons left point A. One of them stops at point B 4.66 billion years ago. The other continues to point C and gets there today. Is the trip between point A and B uniform for both photons? 
11th November 2022, 03:13 PM  #196 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001


__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 03:18 PM  #197 
Master Poster
Join Date: Nov 2020
Posts: 2,998

Because it traveled for 2.33 billion years, and lost 25% of its energy (at z=0.333).
But if it traveled that same distance and was received today it would have lost just 16.66% of its energy (at z=0.2). Since the universe is expanding faster now than in those times... they should have lost less energy in the past than now. Not adding up.
Quote:
You say the z's don't need to be equal. Kinda bailing on the whole consistency thing eh? 
11th November 2022, 03:38 PM  #198 
Penultimate Amazing
Join Date: Jun 2003
Posts: 53,001

YOU came up with those ages, not me. The ages are model dependent. I don't know what model you're using. I don't know if that model is accurate. I don't know if that model produces acceleration.
What I do know is that you aren't handling red shifts correctly when there's more than one step.
Quote:
Quote:

__________________
"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

11th November 2022, 03:48 PM  #199 
Master Poster
Join Date: Nov 2020
Posts: 2,998


11th November 2022, 03:58 PM  #200 
Master Poster
Join Date: Nov 2020
Posts: 2,998

Let's add another step. X:
Code:
7 A B C 2.334.66 A B X C 2.33 First photon A (d=0, z=0, E=12 eV) B (d=2.33 Gly, z=0.2, E=10 eV) X (d=4.66 Gly, z=0.5, E=8 eV C (d=7 Gly, z=1, E=6 eV) Second photon B (d=0, z=0, E=9 eV) X (d=2.33 Gly, z=0.2, E=7.5 eV_ C (d=4.66 Gly, z=0.5, E=6 eV) 
Thread Tools  

