The Half Life of CO2 in Earth’s Atmosphere – Part 1

Posted on September 22, 2014 by Euan Mearns
Original link:  http://euanmearns.com/the-half-life-of-co2-in-earths-atmosphere-part-1/ 

• Sequestration of CO2 from the atmosphere can be modelled using a single exponential decay constant of 2.5% per annum. There is no modelling need to introduce a multi time constant model such as the Bern Model.
• The Bern model, favoured by the IPCC, uses four different time constants and combining these produces a decay curve that is not exponential but also matches atmosphere to emissions.
• The fact that both single exponential decline and multi-time constant models of emissions can be made to fit atmospheric evolution of CO2 means that this approach does not provide proof of process. Either or neither of these models may be correct. But combined, both of these models do provide clues as to the rate of the CO2 sequestration processes.

Single time constant, 2.5% per annum, exponential decline model gives an excellent fit between emissions (LH scale, coloured bands) and actual atmosphere (RH scale, black line). This confirms Roger Andrew’s assertion from a couple of weeks ago that it was possible to model sequestration of CO2 from the atmosphere using a single decline constant. The Blue wedge at bottom is the pre-1965 emissions stack that is also declined at 2.5% per annum. The half life of ~27 years is equivalent to a residence time for CO2 of 39 years, slightly but not significantly different to Roger’s result.

A couple of weeks ago Roger Andrews had a post called The residence time of CO2 in the atmosphere is …. 33 years? that stimulated a lot of high quality debate and for me a lot of new information came to light. This is the first part of an X part series of posts aimed at summarising what we know, aiming to zero in on “the truth” about CO2 sequestration rates from the atmosphere.

In this post (Part 1) I look at a single time constant exponential decline model, compare this with Roger’s model and the Bern model favoured by the IPCC and the climate science community. The Bern model uses 4 different time constants from fast to slow and infinity and this post illustrates how this works. I am not a mathematician and prefer visual illustration of mathematical equations.

This post has been significantly delayed since I could not get my XL model to produce the same results as Roger’s. Our models now agree but may still be providing slightly different results.

In Part 2 I will discuss the Atomic bomb 14C data and the proportional reservoir growth model put forward by Phil Chapman.

Why half life is important

We hear all the time form the climate science community that even if we stop burning fossil fuels (FF) today the CO2 we have already produced will still be in the atmosphere for centuries to come. We have already lit a long slow burning fuse that will lead us to climate Armageddon. How much of this is actually true?

What we kind of know for sure is that in 1965 the mass of CO2 in the atmosphere was roughly 2400 Gt (billion tonnes) and today (2010) it is roughly 2924 Gt. That is an increase of 524 Gt. And we also know that we have added roughly 1126 Gt of CO2 to the atmosphere through burning FF and deforestation (emissions model from Roger Andrews). And so while Man’s activities may have led to a rise in CO2 the rise is only 46% of that expected from our emissions. Earth systems have already removed at least 54%. How is this reconciled with the warnings of climatic meltdown?

To understand this requires understanding of the very complex carbon cycle, but in short, some of our emissions have been dissolved in ocean water and some have been taken up by enhanced forest and plant growth. Both of these enhanced uptakes are brought about by the increased partial pressure of CO2 in the atmosphere.

Understanding exponential decline and half life

In the context of atmospheric CO2, imagine a slug of CO2 added to the atmosphere, like manmade FF emissions, and how it may decline via sequestration into the oceans and trees. If the initial slug is absorbed by 5% in the first year, and 5% of the remaining 95% the following year and so on then the decline curve would be like that shown in Figure 1. The half life is the time it takes for 50% of the initial slug to be removed. In the case of 5% per annum decline it turns out that the half life is about 13 years (t1 in Figure 1). After another 13 years (t2) another 50% of what was there after t1 is removed and so on. As a rule of thumb, after 5 half lives have past there is hardly anything left of the original slug.

Figure 1 This chart illustrates how a pulse of 13.3 billion tonnes (Gt) of CO2 injected into the atmosphere in 1965 would decay if 5% of the remaining CO2 is removed each successive year. After 13 years (t1) 50% of the pulse has been sequestered. 50% of the remainder is sequestered in the following 13 years (t2) and so on.

The residence time is defined as follows:

Half life / 0.693 = Residence time

My XL spread sheet model has the exponential decline rate as the main input variable where:

P2 = P1*r
P1 = initial amount
P2 = amount remaining after 1 year
r = the annual decline rate. For example, for annual decline of 5% r=0.95

My spread sheet gives the same result as the general decline formula:

P(t) = P0*e^-rt
P0 = initial amount
P(t) = the amount remaining after time – t
t = time in years
r = the decay rate

It also allows me to estimate half life from the output. Therefore in this discussion I will stick to using decline rate and half life as illustrated in Figure 1 and where possible avoid using the more abstract residence time term.

Single time constant, multi pulse model for the atmosphere

This may sound complicated but I hope to make it simple to understand. Roger already laid the groundwork with a chart that shows the same as Figure 2. In Figure 2, the single pulse declining at 5% per annum (Figure 1) is the layer labelled as (1) in 1965 (Figure 2). The next year there is a new pulse (2) that declines at the same rate and the next year another pulse (3) and so on. The size of each annual pulse equals emissions for that year. So we have multiple pulses but they all decline at the same rate of 5% per annum. After 13 years, half of pulse one is gone and so forth. In the 16 years shown in Figure 2 a total of 289 Gt of CO2 is added to the atmosphere but sequestration has removed 70 Gt meaning that only 210 Gt remain, that is the height of the 1980 column.

Figure 2 In his earlier post, Roger produced a chart near identical to this and one reason for reproducing this here is to show that we are both singing from the same spread sheet. The pulse shown in Figure 1 is that labeled as number (1) on the chart. The next year there is a new pulse, scaled to the emissions model, that also decays at 5% and so forth. Because of sequestration into the oceans and biosphere the amount of CO2 left in the atmosphere is always much lower than the amount we have added.

We can now expand this model to a full time series, 1965 to 2010 and adjust the exponential decline rate that the model uses to produce a best fit between the model and the observed evolution of CO2 in the atmosphere (Figure 3). The atmosphere model is based on 750 Gt C in the atmosphere in 1998 (IPCC Grid Arendal) when the atmosphere had 367 ppm CO2. The C content of the atmosphere is then projected backwards and forwards from that date in proportion to annual CO2 concentrations from Mauna Loa. The data are then converted to Gt CO2 by multiplying by 44/12 (the molecular weight of CO2 / atomic weight of carbon).

Figure 3 The model is now expanded to include all years from 1965 to 2010. The black line (right hand scale) is the atmosphere based on observed CO2 at Mauna Loa. The decline rate was adjusted to give this “best fit”. Notably 1126Gt CO2 has been added but only 516 Gt remains and this fits the overall observation of CO2 sequestration reducing emissions by 54%. In detail, the fit of the emissions to the atmosphere is not as good as that achieved by Roger.

It was at this point that I encountered the first problem trying to reconcile my model with Roger’s model. The fit of additions to atmosphere is nothing like as good as that achieved by Roger and the half life yields a residence time of  18.8 years somewhat different to Roger’s 33 years. The problem with the model shown in Figure 3 is that it is built on a flat baseline that does not account for the decline (sequestration) of pre-1965 emissions.
Building in decline to the pre-1965 emissions produces an excellent fit of emissions and the actual evolution of the atmosphere (black line) with a half life of 27 years equivalent to a residence time of 39 years. Closer to but not exactly the same as Roger’s result (Figure 4).

Figure 4 Single time constant, 2.5% per annum, exponential decline model gives an excellent fit between emissions (LH scale, coloured bands) and actual atmosphere (RH scale, black line). This confirms Roger Andrew’s assertion from a couple of weeks ago that it was possible to model sequestration of CO2 from the atmosphere using a single decline constant. The Blue wedge at bottom is the pre-1965 emissions stack that is also declined at 2.5% per annum. The half life of ~27 years is equivalent to a residence time for CO2 of 39 years.

A major conclusion of this post, therefore, is that emissions can be fitted to the observed evolution of the atmosphere using a single time constant model that has a 2.5% per annum decline rate. This credit really has to go to Roger Andrews if no one else has achieved this before. To achieve this fit, it is essential to have a model where the longer term emissions also decline. In my model, the emissions are initiated in 1910.

At this point it is important to stress that matching emissions to observations assumes that all of the rise in atmospheric CO2 comes from emissions. As we shall see in Part 2, the atomic bomb 14C data suggests a much more rapid decline of 7% per year that yields a half life of ~5 years  that creates the need for some of the increase in CO2 to come from other sources. I hope to show why the bomb data give a false picture.

This leads into consideration of the Bern Model which has multiple time constants. If it is possible to get a good model fit using a single time constant why use 4? Doing so has lead to much debate on sceptic blogs since  it is difficult to conceptualise why different processes should discriminate between different parts of the overall CO2 budget. For example Willis Eschenbach writing on WUWT:

So my question is, how do the sinks know the difference? Why don’t the fast-acting sinks just soak up the excess CO2, leaving nothing for the long-term, slow-acting sinks? I mean, if some 13% of the CO2 excess is supposed to hang around in the atmosphere for 371.3 years … how do the fast-acting sinks know to not just absorb it before the slow sinks get to it?

The Bern Model

I have not found it easy to find information on the Bern model simply through Google. And it is worth declaring that until a few weeks ago I had barely heard of it. I have this from Clive Best via email:

AR4 page 213 of WG1 defines the BERN model as
a0 + sum(i=1,3)(ai.exp(-t/Taui)) , Where a0 = 0.217, a1 = 0.259, a2 = 0.338, a3 = 0.186, Tau1 = 172.9 years, Tau2 = 18.51 years, and Tau3 = 1.186 years.
The term a0 is the fraction which remains for ever in the atmosphere ( tau = infinity) – roughly 22%

Of course it doesn’t stay in the atmosphere for ever. It is eventually removed through rock weathering and build up of  sediments on the ocean floor. Tau > 1000 years.

This is translated into the following:

Time constant (Tau)   % of annual pulse removed at that rate

1.2 y                                18%
18.5 y                             34%
173 y                              26%
∞                                    22%

The Bern model may therefore be described as a multi pulse multi time constant model. In real terms it says that certain processes will sequester CO2 emissions very quickly, for example solution into ocean water, some act more slowly, for example removal by tree growth and soils and some will act very slowly, for example removal of surface water CO2 into the deep oceans.

Figures  5, 6, 7 and 8 show what these different time slices weighted according to the % of emissions they apply to look like. Note the variable Y-axis scales, the very fast slice accounts for virtually none of the accumulated CO2 growth. These models are built on a flat baseline and so are for illustrative purposes only.

Figure 5 The super fast time constant removes most of annual CO2 additions within 5 years. This is represented by the thin yellow band in Figure 9.

Figure 6 The second time constant of 18.5 years applied to 34% of emissions is the only one that resembles the single time constant, single pulse model (Figure 3). Note this is slightly convex up while the next two charts are concave up and combining the two provides a way of producing the observed linear increase in CO2.

Figure 7 With the spread sheet model I’m using it is difficult to model the t173 year slice so I set the decline to 0.1%. With the 45 year time scale involved from 1965 to 2010 this makes little to no difference. While Figure 5 shows little carry over from one year to the next the T173 slice shows virtually 100% carry over from one year to the next. The concave up style of this slice cancels the convex up style of the T18.5 year slice.

Figure 8 The T∞ slice has decline set to 0 and is virtually the same as the T173 model shown in Figure 7.

Adding the 4 time constant slices together provides the picture shown in Figure 9.

Figure 9 Combing the slices shown in Figures 5, 6, 7 and 8 produces the picture shown here. It is important to understand that this is a picture of what remains, not what went in. Tweaking the input variables of the Bern model or the atmosphere model it should be quite straight forward to produce a better fit. The pre-1965 emissions (underlying decline) are modelled as a single exponential which is an approximation since Bern is not an exponential decline model. It would be a lot of work to adapt my spread sheet to handle the underlying decline in the proper way. Doing so would likely improve the fit. The purpose here is to illustrate how the model works.

So where does this leave our understanding? Since CO2 emissions can be matched to atmosphere evolution using different modelling approaches it is clear that the approach of matching model to observations provides no proof of the underlying process. In the Bern model, 48% of emissions remain in the atmosphere for a long time. I do not believe that the model itself provides any evidence that this is the case.

In this comment to Roger’s post Phil Chapman presented an idea of redistribution of a slug of CO2 between the fast reservoirs. The atmosphere began with 21% of the fast reservoir CO2 and Phil argued that following multiple slugs, once equilibrium was reached, the atmosphere would end up with 21% of the increased amount of CO2 circulating between the fast reservoirs (assuming linear processes). In other words, 21% of emissions will remain in the atmosphere until the slow fluxes have time to remove it. This idea rhymes with the Bern model and I am currently thinking along the lines of a model that does not decline to zero but to 21% above the original baseline.

What about Willis Eschenbach’s enigma? At the moment I think it may be helpful to think about this from a different angle. We seem to know that different processes remove CO2 at different rates. They are all acting simultaneously. Hence, maybe some of the slow processes get to CO2 emissions before the faster processes grab them? But it is possible that sequestration is dominated by fast processes, just that at equilibrium 21% of emissions may remain.

In part 2 I hope to illustrate using simple models why the bomb 14C cannot be used to model CO2 sequestration rates. And I currently believe that for the same reasons natural variations in d13C are unlikely to be useful tracers either. I will also take a closer look at Phil Chapman’s idea (I do not know if this is originally Phil’s idea) and see how this may be incorporated into a refined model.

Half-life

From Wikipedia, the free encyclopedia

Number of half-lives elapsed	Fraction remaining	Percentage remaining
0	1⁄1	100
1	1⁄2	50
2	1⁄4	25
3	1⁄8	12	.5
4	1⁄16	6	.25
5	1⁄32	3	.125
6	1⁄64	1	.563
7	1⁄128	0	.781
...	...	...
n	1/2n	100⁄(2n)

Half-life (symbol t_1⁄2) is the time required for a quantity to reduce to half its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay. The term is also used more generally to characterize any type of exponential or non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life is doubling time.
The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s.^[1] Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.

Probabilistic nature

Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note the consequence of the law of large numbers: with more atoms, the overall decay is more regular and more predictable.

A half-life usually describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states "half-life is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom, and its half-life is one second, there will not be "half of an atom" left after one second.

Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average". In other words, the probability of a radioactive atom decaying within its half-life is 50%.

For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the process. Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.

There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.^[2][3][4]

Formulas for half-life in exponential decay

An exponential decay can be described by any of the following three equivalent formulas:

${\displaystyle {\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}}\\N(t)&=N_{0}e^{-{\frac {t}{\tau }}}\\N(t)&=N_{0}e^{-\lambda t}\end{aligned}}}$

where

• N₀ is the initial quantity of the substance that will decay (this quantity may be measured in grams, moles, number of atoms, etc.),
• N(t) is the quantity that still remains and has not yet decayed after a time t,
• t_1⁄2 is the half-life of the decaying quantity,
• τ is a positive number called the mean lifetime of the decaying quantity,
• λ is a positive number called the decay constant of the decaying quantity.

The three parameters t_1⁄2, τ, and λ are all directly related in the following way:

${\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)}$

where ln(2) is the natural logarithm of 2 (approximately 0.693).

By plugging in and manipulating these relationships, we get all of the following equivalent descriptions of exponential decay, in terms of the half-life:

${\displaystyle {\begin{aligned}N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}}=N_{0}2^{-t/t_{1/2}}\\&=N_{0}e^{-t\ln(2)/t_{1/2}}\\t_{1/2}&={\frac {t}{\log _{2}(N_{0}/N(t))}}={\frac {t}{\log _{2}(N_{0})-\log _{2}(N(t))}}\\&={\frac {1}{\log _{2^{t}}(N_{0})-\log _{2^{t}}(N(t))}}={\frac {t\ln(2)}{\ln(N_{0})-\ln(N(t))}}\end{aligned}}}$

Regardless of how it's written, we can plug into the formula to get

• ${\displaystyle N(0)=N_{0}}$ as expected (this is the definition of "initial quantity")
• ${\displaystyle N\left(t_{1/2}\right)={\frac {1}{2}}N_{0}}$ as expected (this is the definition of half-life)
• ${\displaystyle \lim _{t\to \infty }N(t)=0}$; i.e., amount approaches zero as t approaches infinity as expected (the longer we wait, the less remains).

Decay by two or more processes

Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T_1⁄2 can be related to the half-lives t₁ and t₂ that the quantity would have if each of the decay processes acted in isolation:

${\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}}$

For three or more processes, the analogous formula is:

${\displaystyle {\frac {1}{T_{1/2}}}={\frac {1}{t_{1}}}+{\frac {1}{t_{2}}}+{\frac {1}{t_{3}}}+\cdots }$

Examples

Half life demonstrated using dice in a classroom experiment

There is a half-life describing any exponential-decay process. For example:

• The current flowing through an RC circuit or RL circuit decays with a half-life of RCln(2) or ln(2)L/R, respectively. For this example, the term half time might be used instead of "half life", but they mean the same thing.
• In a first-order chemical reaction, the half-life of the reactant is ln(2)/λ, where λ is the reaction rate constant.
• In radioactive decay, the half-life is the length of time after which there is a 50% chance that an atom will have undergone nuclear decay. It varies depending on the atom type and isotope, and is usually determined experimentally. See List of nuclides.

The half life of a species is the time it takes for the concentration of the substance to fall to half of its initial value.

In non-exponential decay

The decay of many physical quantities is not exponential—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule. In such cases, the half-life is defined the same way as before: as the time elapsed before half of the original quantity has decayed. However, unlike in an exponential decay, the half-life depends on the initial quantity, and the prospective half-life will change over time as the quantity decays.

As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5,730 years. A quantity of carbon-14 will decay to half of its original amount (on average) after 5,730 years, regardless of how big or small the original quantity was. After another 5,730 years, one-quarter of the original will remain. On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is. Perhaps a puddle of a certain size will evaporate down to half its original volume in one day. But on the second day, there is no reason to expect that one-quarter of the puddle will remain; in fact, it will probably be much less than that. This is an example where the half-life reduces as time goes on. (In other non-exponential decays, it can increase instead.)

The decay of a mixture of two or more materials which each decay exponentially, but with different half-lives, is not exponential. Mathematically, the sum of two exponential functions is not a single exponential function. A common example of such a situation is the waste of nuclear power stations, which is a mix of substances with vastly different half-lives. Consider a mixture of a rapidly decaying element A, with a half-life of 1 second, and a slowly decaying element B, with a half-life of 1 year. In a couple of minutes, almost all atoms of element A will have decayed after repeated halving of the initial number of atoms, but very few of the atoms of element B will have done so as only a tiny fraction of its half-life has elapsed. Thus, the mixture taken as a whole will not decay by halves.

In biology and pharmacology

A biological half-life or elimination half-life is the time it takes for a substance (drug, radioactive nuclide, or other) to lose one-half of its pharmacologic, physiologic, or radiological activity. In a medical context, the half-life may also describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value (the "plasma half-life"). The relationship between the biological and plasma half-lives of a substance can be complex, due to factors including accumulation in tissues, active metabolites, and receptor interactions.^[5]

While a radioactive isotope decays almost perfectly according to so-called "first order kinetics" where the rate constant is a fixed number, the elimination of a substance from a living organism usually follows more complex chemical kinetics.

For example, the biological half-life of water in a human being is about 9 to 10 days,^{[citation needed]} though this can be altered by behavior and various other conditions. The biological half-life of cesium in human beings is between one and four months.

Bandwagon effect

A literal "bandwagon", from which the metaphor is derived.

The bandwagon effect is a phenomenon whereby the rate of uptake of beliefs, ideas, fads and trends increases the more that they have already been adopted by others. In other words, the bandwagon effect is characterized by the probability of individual adoption increasing with respect to the proportion who have already done so.^[1] As more people come to believe in something, others also "hop on the bandwagon" regardless of the underlying evidence.

The tendency to follow the actions or beliefs of others can occur because individuals directly prefer to conform, or because individuals derive information from others. Both explanations have been used for evidence of conformity in psychological experiments. For example, social pressure has been used to explain Asch's conformity experiments,^[2] and information has been used to explain Sherif's autokinetic experiment.^[3]

According to this concept, the increasing popularity of a product or phenomenon encourages more people to "get on the bandwagon", too. The bandwagon effect explains why there are fashion trends.^[4]

When individuals make rational choices based on the information they receive from others, economists have proposed that information cascades can quickly form in which people decide to ignore their personal information signals and follow the behavior of others.^[5] Cascades explain why behavior is fragile—people understand that they are based on very limited information. As a result, fads form easily but are also easily dislodged. Such informational effects have been used to explain political bandwagons.^[6]

Origin

The definition of a bandwagon is a wagon which carries a band during the course of a parade, circus or other entertainment event.^[7] The phrase "jump on the bandwagon" first appeared in American politics in 1848 when Dan Rice, a famous and popular circus clown of the time, used his bandwagon and its music to gain attention for his political campaign appearances. As his campaign became more successful, other politicians strove for a seat on the bandwagon, hoping to be associated with his success. Later, during the time of William Jennings Bryan's 1900 presidential campaign, bandwagons had become standard in campaigns,^[8] and the phrase "jump on the bandwagon" was used as a derogatory term, implying that people were associating themselves with success without considering that with which they associated themselves.

In politics

The bandwagon effect occurs in voting:^[9] some people vote for those candidates or parties who are likely to succeed (or are proclaimed as such by the media), hoping to be on the "winner's side" in the end.^{[citation needed]} The bandwagon effect has been applied to situations involving majority opinion, such as political outcomes, where people alter their opinions to the majority view.^[10] Such a shift in opinion can occur because individuals draw inferences from the decisions of others, as in an informational cascade.^{[citation needed]}

Because of time zones, election results are broadcast in the eastern parts of the United States while polls are still open in the west. This difference has led to research on how the behavior of voters in western United States is influenced by news about the decisions of voters in other time zones. In 1980, NBC News declared Ronald Reagan to be the winner of the presidential race on the basis of the exit polls several hours before the voting booths closed in the west.

It is also said to be important in the American presidential primary elections. States all vote at different times, spread over some months, rather than all on one day. Some states (Iowa, New Hampshire) have special precedence to go early while others choose to wait until a certain date. This is often said to give undue influence to these states, a win in these early states is said to give a candidate the "Big Mo" (momentum) and has propelled many candidates to win the nomination. Because of this, other states often try front loading (going as early as possible) to make their say as influential as they can. In the 2008 presidential primaries two states had all or some of their delegates banned from the convention by the central party organizations for voting too early.^[11][12]

Several studies have tested this theory of the bandwagon effect in political decision making. In the 1994 study of Robert K. Goidel and Todd G. Shields in The Journal of Politics, 180 students at the University of Kentucky were randomly assigned to nine groups and were asked questions about the same set of election scenarios. About 70% of subjects received information about the expected winner.^[13] Independents, which are those who do not vote based on the endorsement of any party and are ultimately neutral, were influenced strongly in favor of the person expected to win.^[14] Expectations played a significant role throughout the study. It was found that independents are twice as likely to vote for the Republican candidate when the Republican is expected to win. From the results, it was also found that when the Democrat was expected to win, independent Republicans and weak Republicans were more likely to vote for the Democratic candidate.^[15]

A study by Albert Mehrabian, reported in the Journal of Applied Social Psychology (1998), tested the relative importance of the bandwagon (rally around the winner) effect versus the underdog (empathic support for those trailing) effect. Bogus poll results presented to voters prior to the 1996 Republican primary clearly showed the bandwagon effect to predominate on balance. Indeed, approximately 6% of the variance in the vote was explained in terms of the bogus polls, showing that poll results (whether accurate or inaccurate) can significantly influence election results in closely contested elections. In particular, assuming that one candidate "is an initial favorite by a slim margin, reports of polls showing that candidate as the leader in the race will increase his or her favorable margin".^[16] Thus, as poll results are repeatedly reported, the bandwagon effect will tend to snowball and become a powerful aid to leading candidates.

During the 1992 U.S. presidential election, Vicki G. Morwitz and Carol Pluzinski conducted a study, which was published in The Journal of Consumer Research (1996). At a large northeastern university, some of 214 volunteer business students were given the results of student and national polls indicating that Bill Clinton was in the lead. Others were not exposed to the results of the polls. Several students who had intended to vote for Bush changed their minds after seeing the poll results.^[17]

Additionally, British polls have shown an increase to public exposure. Sixty-eight percent of voters had heard of the general election campaign results of the opinion poll in 1979. In 1987, this number of voters aware of the results increased to 74%.^[18] According to British studies, there is a consistent pattern of apparent bandwagon effects for the leading party.

In microeconomics

In microeconomics, bandwagon effect describes interactions of demand and preference.^[19] The bandwagon effect arises when people's preference for a commodity increases as the number of people buying it increases. This interaction potentially disturbs the normal results of the theory of supply and demand, which assumes that consumers make buying decisions solely based on price and their own personal preference.
Gary Becker has even argued that the bandwagon effect could be so strong as to make the demand curve slope upward.^[20]

In medicine

Medical bandwagons have been identified as “the overwhelming acceptance of unproved but popular ideas”. They have led to inappropriate therapies for numerous numbers of patients, and have impeded the development of more appropriate treatment.

In Lawrence Cohen and Henry Rothschild's exposition The Bandwagons of Medicine (1979) several of these therapeutic misadventures, some of which persisted for centuries before they were abandoned, substituted by another bandwagon, or replaced by a scientifically valid alternative.^[21] The ancient serpent cult of Aesculapius, in which sacred snakes licked the afflicted as treatment of their diseases, is an example of a bandwagon gathering momentum based on a strong personality, in this case a Roman god.^[22]

In sport

Stephen Curry, two-time NBA MVP (2014/15 - 2015/16)

One who supports a particular sports team, despite having shown no interest in that team until it started gaining success, can be considered a "bandwagon fan". One recent example in the United States is the Golden State Warriors, who rose to prominence by winning the 2015 NBA Finals, followed by a record-breaking 73-9 record the following year.^[23] The bandwagon effect can be seen in the statistics of the sales of point guard Stephen Curry's jersey. Curry merchandise sales in the first two weeks of the 2015–2016 season were 453% higher than in the first two weeks of the 2014–2015 season, including a 581% increase in sales of his jersey; his merchandise was a top-seller in 38 of the 50 U.S. states, and the Warriors' merchandise became the best-selling of any NBA team.^[24]

Antimatter

From Wikipedia, the free encyclopedia

In modern physics, antimatter is defined as a material composed of the antiparticle (or "partners") to the corresponding particles of ordinary matter.

In theory, a particle and its anti-particle have the same mass as one another, but opposite electric charge, and other differences in quantum numbers. For example, a proton has positive charge while an antiproton has negative charge. A collision between any particle and its anti-particle partner is known to lead to their mutual annihilation, giving rise to various proportions of intense photons (gamma rays), neutrinos, and sometimes less-massive particle–antiparticle pairs.

Annihilation usually results in a release of energy that becomes available for heat or work. The amount of the released energy is usually proportional to the total mass of the collided matter and antimatter, in accord with the mass–energy equivalence equation, E = mc².^[1]

Antimatter particles bind with one another to form antimatter, just as ordinary particles bind to form normal matter. For example, a positron (the antiparticle of the electron) and an antiproton (the antiparticle of the proton) can form an antihydrogen atom. Physical principles indicate that complex antimatter atomic nuclei are possible, as well as anti-atoms corresponding to the known chemical elements.

There is considerable speculation as to why the observable universe is composed almost entirely of ordinary matter, as opposed to an equal mixture of matter and antimatter. This asymmetry of matter and antimatter in the visible universe is one of the great unsolved problems in physics.^[2] The process by which this inequality between matter and antimatter particles developed is called baryogenesis.

Antimatter in the form of anti-atoms is one of the most difficult materials to produce. Individual antimatter particles, however, are commonly produced by particle accelerators and in some types of radioactive decay. The nuclei of antihelium have been artificially produced with difficulty. These are the most complex anti-nuclei so far observed.^[3]

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There are some 500 terrestrial gamma-ray flashes daily. The red dots show those spotted by the Fermi Gamma-ray Space Telescope in 2010. The blue areas indicate where potential lighting can occur for terrestrial gamma-ray flashes.Play media

A video showing how scientists used the Fermi Gamma-ray Space Telescope's gamma-ray detector to uncover bursts of antimatter from thunderstorms

 

 

 

 

 

 

 

Formal definition

Formally, antimatter particles can be defined by their negative baryon number or lepton number, while "normal" (non-antimatter) matter particles have a positive baryon or lepton number.^[4][5] These two classes of particles are the antiparticle partners of one another.

History of the concept

The idea of negative matter appears in past theories of matter that have now been abandoned. Using the once popular vortex theory of gravity, the possibility of matter with negative gravity was discussed by William Hicks in the 1880s. Between the 1880s and the 1890s, Karl Pearson proposed the existence of "squirts"^[6] and sinks of the flow of aether. The squirts represented normal matter and the sinks represented negative matter. Pearson's theory required a fourth dimension for the aether to flow from and into.^[7]

The term antimatter was first used by Arthur Schuster in two rather whimsical letters to Nature in 1898,^[8] in which he coined the term. He hypothesized antiatoms, as well as whole antimatter solar systems, and discussed the possibility of matter and antimatter annihilating each other. Schuster's ideas were not a serious theoretical proposal, merely speculation, and like the previous ideas, differed from the modern concept of antimatter in that it possessed negative gravity.^[9]

The modern theory of antimatter began in 1928, with a paper^[10] by Paul Dirac. Dirac realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility of antielectrons. These were discovered by Carl D. Anderson in 1932 and named positrons (a portmanteau of "positive electron"). Although Dirac did not himself use the term antimatter, its use follows on naturally enough from antielectrons, antiprotons, etc.^[11] A complete periodic table of antimatter was envisaged by Charles Janet in 1929.^[12]

The Feynman–Stueckelberg interpretation states that antimatter and antiparticles are regular particles traveling backward in time.^[13]

Notation

One way to denote an antiparticle is by adding a bar over the particle's symbol. For example, the proton and antiproton are denoted as
p
and
p
, respectively. The same rule applies if one were to address a particle by its constituent components. A proton is made up of
u

u

d
quarks, so an antiproton must therefore be formed from
u

u

d
antiquarks. Another convention is to distinguish particles by their electric charge. Thus, the electron and positron are denoted simply as
e− and
e+ respectively. However, to prevent confusion, the two conventions are never mixed.

Properties

There are compelling theoretical reasons to believe that, aside from the fact that antiparticles have different signs on all charges (such as electric charge and spin), matter and antimatter have exactly the same properties.^[14][15] This means a particle and its corresponding antiparticle must have identical masses and decay lifetimes (if unstable). It also implies that, for example, a star made up of antimatter (an "antistar") will shine just like an ordinary star.^[16] This idea was tested experimentally in 2016 by the ALPHA experiment, which measured the transition between the two lowest energy states of antihydrogen. The results, which are identical to that of hydrogen, confirmed the validity of quantum mechanics for antimatter.^[17][18]

Origin and asymmetry

Almost all matter observable from the Earth seems to be made of matter rather than antimatter. If antimatter-dominated regions of space existed, the gamma rays produced in annihilation reactions along the boundary between matter and antimatter regions would be detectable.^[19]
Antiparticles are created everywhere in the universe where high-energy particle collisions take place. High-energy cosmic rays impacting Earth's atmosphere (or any other matter in the Solar System) produce minute quantities of antiparticles in the resulting particle jets, which are immediately annihilated by contact with nearby matter. They may similarly be produced in regions like the center of the Milky Way and other galaxies, where very energetic celestial events occur (principally the interaction of relativistic jets with the interstellar medium). The presence of the resulting antimatter is detectable by the two gamma rays produced every time positrons annihilate with nearby matter. The frequency and wavelength of the gamma rays indicate that each carries 511 keV of energy (i.e., the rest mass of an electron multiplied by c²).

Observations by the European Space Agency's INTEGRAL satellite may explain the origin of a giant antimatter cloud surrounding the galactic center. The observations show that the cloud is asymmetrical and matches the pattern of X-ray binaries (binary star systems containing black holes or neutron stars), mostly on one side of the galactic center. While the mechanism is not fully understood, it is likely to involve the production of electron–positron pairs, as ordinary matter gains kinetic energy while falling into a stellar remnant.^[20][21]

Antimatter may exist in relatively large amounts in far-away galaxies due to cosmic inflation in the primordial time of the universe. Antimatter galaxies, if they exist, are expected to have the same chemistry and absorption and emission spectra as normal-matter galaxies, and their astronomical objects would be observationally identical, making them difficult to distinguish.^[22] NASA is trying to determine if such galaxies exist by looking for X-ray and gamma-ray signatures of annihilation events in colliding superclusters.^[23]

Natural production

Positrons are produced naturally in β⁺ decays of naturally occurring radioactive isotopes (for example, potassium-40) and in interactions of gamma quanta (emitted by radioactive nuclei) with matter. Antineutrinos are another kind of antiparticle created by natural radioactivity (β⁻ decay). Many different kinds of antiparticles are also produced by (and contained in) cosmic rays. In January 2011, research by the American Astronomical Society discovered antimatter (positrons) originating above thunderstorm clouds; positrons are produced in gamma-ray flashes created by electrons accelerated by strong electric fields in the clouds.^[24][25] Antiprotons have also been found to exist in the Van Allen Belts around the Earth by the PAMELA module.^[26][27]

Antiparticles are also produced in any environment with a sufficiently high temperature (mean particle energy greater than the pair production threshold). It is hypothesized that during the period of baryogenesis, when the universe was extremely hot and dense, matter and antimatter were continually produced and annihilated. The presence of remaining matter, and absence of detectable remaining antimatter,^[28] is called baryon asymmetry. The exact mechanism which produced this asymmetry during baryogenesis remains an unsolved problem. One of the necessary conditions for this asymmetry is the violation of CP symmetry, which has been experimentally observed in the weak interaction.

Recent observations indicate black holes and neutron stars produce vast amounts of positron-electron plasma via the jets.^[29][30][31]

Observation in cosmic rays

Satellite experiments have found evidence of positrons and a few antiprotons in primary cosmic rays, amounting to less than 1% of the particles in primary cosmic rays. This antimatter cannot all have been created in the Big Bang, but is instead attributed to have been produced by cyclic processes at high energies. For instance, electron-positron pairs may be formed in pulsars, as a magnetized neutron star rotation cycle shears electron-positron pairs from the star surface. Therein the antimatter forms a wind which crashes upon the ejecta of the progenitor supernovae. This weathering takes place as "the cold, magnetized relativistic wind launched by the star hits the non-relativistically expanding ejecta, a shock wave system forms in the impact: the outer one propagates in the ejecta, while a reverse shock propagates back towards the star."^[32] The former ejection of matter in the outer shock wave and the latter production of antimatter in the reverse shock wave are steps in a space weather cycle.
Preliminary results from the presently operating Alpha Magnetic Spectrometer (AMS-02) on board the International Space Station show that positrons in the cosmic rays arrive with no directionality, and with energies that range from 10 GeV to 250 GeV. In September, 2014, new results with almost twice as much data were presented in a talk at CERN and published in Physical Review Letters.^[33][34] A new measurement of positron fraction up to 500 GeV was reported, showing that positron fraction peaks at a maximum of about 16% of total electron+positron events, around an energy of 275 ± 32 GeV. At higher energies, up to 500 GeV, the ratio of positrons to electrons begins to fall again. The absolute flux of positrons also begins to fall before 500 GeV, but peaks at energies far higher than electron energies, which peak about 10 GeV.^[35] These results on interpretation have been suggested to be due to positron production in annihilation events of massive dark matter particles.^[36]

Cosmic ray antiprotons also have a much higher energy than their normal-matter counterparts (protons). They arrive at Earth with a characteristic energy maximum of 2 GeV, indicating their production in a fundamentally different process from cosmic ray protons, which on average have only one-sixth of the energy.^[37]

There is no evidence of complex antimatter atomic nuclei, such as antihelium nuclei (i.e., anti-alpha particles), in cosmic rays. These are actively being searched for, because the detection of natural antihelium implies the existence of large antimatter structures such as an antistar. A prototype of the AMS-02 designated AMS-01, was flown into space aboard the Space Shuttle Discovery on STS-91 in June 1998. By not detecting any antihelium at all, the AMS-01 established an upper limit of 1.1×10⁻⁶ for the antihelium to helium flux ratio.^[38]

Artificial production

Positrons

Positrons were reported^[39] in November 2008 to have been generated by Lawrence Livermore National Laboratory in larger numbers than by any previous synthetic process. A laser drove electrons through a gold target's nuclei, which caused the incoming electrons to emit energy quanta that decayed into both matter and antimatter. Positrons were detected at a higher rate and in greater density than ever previously detected in a laboratory. Previous experiments made smaller quantities of positrons using lasers and paper-thin targets; however, new simulations showed that short, ultra-intense lasers and millimeter-thick gold are a far more effective source.^[40]

Antiprotons, antineutrons, and antinuclei

The existence of the antiproton was experimentally confirmed in 1955 by University of California, Berkeley physicists Emilio Segrè and Owen Chamberlain, for which they were awarded the 1959 Nobel Prize in Physics.^[41] An antiproton consists of two up antiquarks and one down antiquark (
u

u

d
). The properties of the antiproton that have been measured all match the corresponding properties of the proton, with the exception of the antiproton having opposite electric charge and magnetic moment from the proton. Shortly afterwards, in 1956, the antineutron was discovered in proton–proton collisions at the Bevatron (Lawrence Berkeley National Laboratory) by Bruce Cork and colleagues.^[42]

In addition to antibaryons, anti-nuclei consisting of multiple bound antiprotons and antineutrons have been created. These are typically produced at energies far too high to form antimatter atoms (with bound positrons in place of electrons). In 1965, a group of researchers led by Antonino Zichichi reported production of nuclei of antideuterium at the Proton Synchrotron at CERN.^[43] At roughly the same time, observations of antideuterium nuclei were reported by a group of American physicists at the Alternating Gradient Synchrotron at Brookhaven National Laboratory.^[44]

Antihydrogen atoms

In 1995, CERN announced that it had successfully brought into existence nine hot antihydrogen atoms by implementing the SLAC/Fermilab concept during the PS210 experiment. The experiment was performed using the Low Energy Antiproton Ring (LEAR), and was led by Walter Oelert and Mario Macri.^[45] Fermilab soon confirmed the CERN findings by producing approximately 100 antihydrogen atoms at their facilities. The antihydrogen atoms created during PS210 and subsequent experiments (at both CERN and Fermilab) were extremely energetic and were not well suited to study. To resolve this hurdle, and to gain a better understanding of antihydrogen, two collaborations were formed in the late 1990s, namely, ATHENA and ATRAP.
In 1999, CERN activated the Antiproton Decelerator, a device capable of decelerating antiprotons from 3500 MeV to 5.3 MeV — still too "hot" to produce study-effective antihydrogen, but a huge leap forward. In late 2002 the ATHENA project announced that they had created the world's first "cold" antihydrogen.^[46] The ATRAP project released similar results very shortly thereafter.^[47] The antiprotons used in these experiments were cooled by decelerating them with the Antiproton Decelerator, passing them through a thin sheet of foil, and finally capturing them in a Penning–Malmberg trap.^[48] The overall cooling process is workable, but highly inefficient; approximately 25 million antiprotons leave the Antiproton Decelerator and roughly 25,000 make it to the Penning–Malmberg trap, which is about 1/1000 or 0.1% of the original amount.

The antiprotons are still hot when initially trapped. To cool them further, they are mixed into an electron plasma. The electrons in this plasma cool via cyclotron radiation, and then sympathetically cool the antiprotons via Coulomb collisions. Eventually, the electrons are removed by the application of short-duration electric fields, leaving the antiprotons with energies less than 100 meV.^[49] While the antiprotons are being cooled in the first trap, a small cloud of positrons is captured from radioactive sodium in a Surko-style positron accumulator.^[50] This cloud is then recaptured in a second trap near the antiprotons. Manipulations of the trap electrodes then tip the antiprotons into the positron plasma, where some combine with antiprotons to form antihydrogen. This neutral antihydrogen is unaffected by the electric and magnetic fields used to trap the charged positrons and antiprotons, and within a few microseconds the antihydrogen hits the trap walls, where it annihilates. Some hundreds of millions of antihydrogen atoms have been made in this fashion.

In 2005, ATHENA disbanded and some of the former members (along with others) formed the ALPHA Collaboration, which is also based at CERN. The primary goal of these collaborations is the creation of less energetic ("cold") antihydrogen, better suited to study.^{[citation needed]}

In 2016 a new antiproton decelerator and cooler called ELENA (E Low ENergy Antiproton decelerator) was built. It takes the antiprotons from the antiproton decelerator and cools them to 90 keV which is "cold" enough to study. More than a hundred antiprotons can be captured per second, a huge improvement, but it would still take several thousand years to make a nanogram of antimatter.

Most of the sought-after high-precision tests of the properties of antihydrogen could only be performed if the antihydrogen were trapped, that is, held in place for a relatively long time. While antihydrogen atoms are electrically neutral, the spins of their component particles produce a magnetic moment. These magnetic moments can interact with an inhomogeneous magnetic field; some of the antihydrogen atoms can be attracted to a magnetic minimum. Such a minimum can be created by a combination of mirror and multipole fields.^[51] Antihydrogen can be trapped in such a magnetic minimum (minimum-B) trap; in November 2010, the ALPHA collaboration announced that they had so trapped 38 antihydrogen atoms for about a sixth of a second.^[52][53] This was the first time that neutral antimatter had been trapped.

On 26 April 2011, ALPHA announced that they had trapped 309 antihydrogen atoms, some for as long as 1,000 seconds (about 17 minutes). This was longer than neutral antimatter had ever been trapped before.^[54] ALPHA has used these trapped atoms to initiate research into the spectral properties of the antihydrogen.^[55]

The biggest limiting factor in the large-scale production of antimatter is the availability of antiprotons. Recent data released by CERN states that, when fully operational, their facilities are capable of producing ten million antiprotons per minute.^[56] Assuming a 100% conversion of antiprotons to antihydrogen, it would take 100 billion years to produce 1 gram or 1 mole of antihydrogen (approximately 6.02×10²³ atoms of anti-hydrogen).

Antihelium

Antihelium-3 nuclei (3He
) were first observed in the 1970s in proton–nucleus collision experiments at the Institute for High Energy Physics by Y. Prockoshkin's group (Protvino near Moscow, USSR)^[57] and later created in nucleus–nucleus collision experiments.^[58] Nucleus–nucleus collisions produce antinuclei through the coalescense of antiprotons and antineutrons created in these reactions. In 2011, the STAR detector reported the observation of artificially created antihelium-4 nuclei (anti-alpha particles) (4He
) from such collisions.^[59]

Preservation

Antimatter cannot be stored in a container made of ordinary matter because antimatter reacts with any matter it touches, annihilating itself and an equal amount of the container. Antimatter in the form of charged particles can be contained by a combination of electric and magnetic fields, in a device called a Penning trap. This device cannot, however, contain antimatter that consists of uncharged particles, for which atomic traps are used. In particular, such a trap may use the dipole moment (electric or magnetic) of the trapped particles. At high vacuum, the matter or antimatter particles can be trapped and cooled with slightly off-resonant laser radiation using a magneto-optical trap or magnetic trap. Small particles can also be suspended with optical tweezers, using a highly focused laser beam.^[60]

In 2011, CERN scientists were able to preserve antihydrogen for approximately 17 minutes.^[61]

Cost

Scientists claim that antimatter is the costliest material to make.^[62] In 2006, Gerald Smith estimated $250 million could produce 10 milligrams of positrons^[63] (equivalent to $25 billion per gram); in 1999, NASA gave a figure of $62.5 trillion per gram of antihydrogen.^[62] This is because production is difficult (only very few antiprotons are produced in reactions in particle accelerators), and because there is higher demand for other uses of particle accelerators. According to CERN, it has cost a few hundred million Swiss francs to produce about 1 billionth of a gram (the amount used so far for particle/antiparticle collisions).^[64] In comparison, to produce the first atomic weapon, the cost of the Manhattan Project was estimated at $23 billion with inflation during 2007.^[65]
Several studies funded by the NASA Institute for Advanced Concepts are exploring whether it might be possible to use magnetic scoops to collect the antimatter that occurs naturally in the Van Allen belt of the Earth, and ultimately, the belts of gas giants, like Jupiter, hopefully at a lower cost per gram.^[66]

Uses

Medical

Matter–antimatter reactions have practical applications in medical imaging, such as positron emission tomography (PET). In positive beta decay, a nuclide loses surplus positive charge by emitting a positron (in the same event, a proton becomes a neutron, and a neutrino is also emitted). Nuclides with surplus positive charge are easily made in a cyclotron and are widely generated for medical use. Antiprotons have also been shown within laboratory experiments to have the potential to treat certain cancers, in a similar method currently used for ion (proton) therapy.^[67]

Fuel

Isolated and stored anti-matter could be used as a fuel for interplanetary or interstellar travel^[68] as part of an antimatter catalyzed nuclear pulse propulsion or other antimatter rocketry, such as the redshift rocket. Since the energy density of antimatter is higher than that of conventional fuels, an antimatter-fueled spacecraft would have a higher thrust-to-weight ratio than a conventional spacecraft.

If matter–antimatter collisions resulted only in photon emission, the entire rest mass of the particles would be converted to kinetic energy. The energy per unit mass (9×10¹⁶ J/kg) is about 10 orders of magnitude greater than chemical energies,^[69] and about 3 orders of magnitude greater than the nuclear potential energy that can be liberated, today, using nuclear fission (about 200 MeV per fission reaction^[70] or 8×10¹³ J/kg), and about 2 orders of magnitude greater than the best possible results expected from fusion (about 6.3×10¹⁴ J/kg for the proton–proton chain). The reaction of 1 kg of antimatter with 1 kg of matter would produce 1.8×10¹⁷ J (180 petajoules) of energy (by the mass–energy equivalence formula, E = mc²), or the rough equivalent of 43 megatons of TNT – slightly less than the yield of the 27,000 kg Tsar Bomba, the largest thermonuclear weapon ever detonated.

Not all of that energy can be utilized by any realistic propulsion technology because of the nature of the annihilation products. While electron–positron reactions result in gamma ray photons, these are difficult to direct and use for thrust. In reactions between protons and antiprotons, their energy is converted largely into relativistic neutral and charged pions. The neutral pions decay almost immediately (with a lifetime of 85 attoseconds) into high-energy photons, but the charged pions decay more slowly (with a lifetime of 26 nanoseconds) and can be deflected magnetically to produce thrust.

Charged pions ultimately decay into a combination of neutrinos (carrying about 22% of the energy of the charged pions) and unstable charged muons (carrying about 78% of the charged pion energy), with the muons then decaying into a combination of electrons, positrons and neutrinos (cf. muon decay; the neutrinos from this decay carry about 2/3 of the energy of the muons, meaning that from the original charged pions, the total fraction of their energy converted to neutrinos by one route or another would be about 0.22 + (2/3)⋅0.78 = 0.74).^[71]

Weapons

Antimatter has been considered as a trigger mechanism for nuclear weapons.^[72] A major obstacle is the difficulty of producing antimatter in large enough quantities, and there is no evidence that it will ever be feasible.^[73] However, the U.S. Air Force funded studies of the physics of antimatter in the Cold War, and began considering its possible use in weapons, not just as a trigger, but as the explosive itself.^[74]